2015 AP Chemistry free response 3a

WEBVTT
Kind: captions
Language: en

00:00:00.187 --> 00:00:01.778
- [Voiceover] Potassium sorbate, and they

00:00:01.778 --> 00:00:03.299
give us its formula right over here,

00:00:03.299 --> 00:00:07.117
has a molar mass of 150 grams per mole.

00:00:07.117 --> 00:00:08.477
They put this decimal here to show us

00:00:08.477 --> 00:00:10.567
that these are actually
three significant figures.

00:00:10.567 --> 00:00:12.621
Even the zero is a significant digit here.

00:00:12.621 --> 00:00:16.023
Is commonly added to diet
soft drinks as a preservative.

00:00:16.023 --> 00:00:18.705
A stock solution of potassium sorbate,

00:00:18.705 --> 00:00:20.597
dissolvent's an aqueous solution here,

00:00:20.597 --> 00:00:23.419
of known concentration must be prepared.

00:00:23.419 --> 00:00:27.922
A student titrates 45
millileters of the stock solution

00:00:27.922 --> 00:00:32.922
with one point two five
molar hydrochloric acid

00:00:32.927 --> 00:00:36.452
using both an indicator and a pH meter.

00:00:36.452 --> 00:00:39.264
The value of K A for sorbic acid is

00:00:39.264 --> 00:00:42.748
one point seven times ten
to the negative fifth.

00:00:42.748 --> 00:00:46.159
All right, so let's tackle
this piece by piece.

00:00:46.159 --> 00:00:50.699
Write the net ionic equation
for the reaction between

00:00:50.699 --> 00:00:54.674
potassium sorbate and hydrochloric acid.

00:00:54.674 --> 00:00:56.973
All right, so first off, let's
write the ionic equation,

00:00:56.973 --> 00:00:58.831
and then we'll, I'll write
the net ionic equation,

00:00:58.831 --> 00:01:00.653
and hopefully you'll see the difference.

00:01:00.653 --> 00:01:04.953
So ionic, ionic equation.

00:01:06.273 --> 00:01:07.736
And the way we think about ionic equations

00:01:07.736 --> 00:01:09.886
is we think about well,
if these are dissolved

00:01:09.886 --> 00:01:12.068
in water, it's an aqueous
solution, these are going

00:01:12.068 --> 00:01:15.970
to disassociate into their, into ions.

00:01:15.970 --> 00:01:18.292
And so we would write
that out on both of the,

00:01:18.292 --> 00:01:21.170
on both the reactant and the product side.

00:01:21.170 --> 00:01:24.991
So the potassium sorbate,
we can write that as,

00:01:24.991 --> 00:01:29.517
it's gonna be a potassium ion dissolved

00:01:29.517 --> 00:01:34.517
in an aqueous solution, plus the

00:01:34.551 --> 00:01:39.551
C six H seven O two, this is also

00:01:39.671 --> 00:01:44.484
going to be an ion dissolved
in the aqueous solution,

00:01:44.484 --> 00:01:47.282
plus the hydrochloric acid
will dissolve, so you have

00:01:47.282 --> 00:01:52.282
the hydrogen proton dissolved
in the aqueous solution

00:01:52.413 --> 00:01:57.351
plus the chloride ion, or
anion I guess we could say it.

00:01:58.281 --> 00:02:02.966
so that's going to be
in our aqueous solution,

00:02:02.966 --> 00:02:05.011
and then they react.

00:02:05.011 --> 00:02:06.427
What happens?

00:02:06.427 --> 00:02:08.215
Well, you're going to have the

00:02:08.215 --> 00:02:10.595
C six H seven O two react with

00:02:10.595 --> 00:02:15.053
the hydrogen proton to get to sorbic acid.

00:02:15.053 --> 00:02:16.981
So you're gonna have sorbic acid,

00:02:16.981 --> 00:02:21.245
H C six H seven O two,
that's the sorbic acid.

00:02:25.185 --> 00:02:28.348
It's going to be in an aqueous solution.

00:02:28.348 --> 00:02:33.027
So I took care so far of that and that,

00:02:33.027 --> 00:02:35.100
and then you're going to have,

00:02:35.100 --> 00:02:39.247
and then you're going to
have your potassium ions,

00:02:39.247 --> 00:02:43.868
your potassium ions
and your chloride ions.

00:02:43.868 --> 00:02:45.660
It's going to be just like that.

00:02:45.660 --> 00:02:49.121
So this right over here
is the ionic equation,

00:02:49.121 --> 00:02:51.140
not the net ionic equation.

00:02:51.140 --> 00:02:53.103
I have the ions on the reaction,

00:02:53.103 --> 00:02:54.321
on the reactant side, and then on

00:02:54.321 --> 00:02:56.063
the product side right over here.

00:02:56.063 --> 00:02:57.840
And did I, yep, I included everything.

00:02:57.840 --> 00:02:59.499
Now you do the net ionic reaction,

00:02:59.499 --> 00:03:01.346
you can imagine what's
going to happen here.

00:03:01.346 --> 00:03:02.738
I have potassium ions on the left.

00:03:02.738 --> 00:03:04.225
I have potassium ions on the right.

00:03:04.225 --> 00:03:06.663
I could net them out on both sides.

00:03:06.663 --> 00:03:08.242
So let's net them out on both sides.

00:03:08.242 --> 00:03:09.820
I have chloride ions on the left.

00:03:09.820 --> 00:03:11.470
I have chloride ions on the right.

00:03:11.470 --> 00:03:13.318
I could net them out on both sides.

00:03:13.318 --> 00:03:15.802
And then I can write
the net ionic equation.

00:03:15.802 --> 00:03:20.486
So the net ionic equation,
net ionic equation,

00:03:24.486 --> 00:03:29.311
is going to be well, I
have my C six H seven O two

00:03:31.351 --> 00:03:34.505
ion dissolved in an aqueous solution.

00:03:34.505 --> 00:03:37.130
You combine that with the hydrogen proton

00:03:37.130 --> 00:03:42.109
dissolved in the aqueous
solution, and it's going to,

00:03:42.109 --> 00:03:45.825
it's going to give us sorbic acid:

00:03:45.825 --> 00:03:50.761
H C six H seven O two
in our aqueous solution.

00:03:53.561 --> 00:03:54.397
So there you have it.

00:03:54.397 --> 00:03:58.574
That is the net ionic equation.


2015 AP Chemistry free response 3b

WEBVTT
Kind: captions
Language: en

00:00:00.460 --> 00:00:03.136
- [Voiceover] A total of 29.95 milliliters

00:00:03.136 --> 00:00:07.492
of 1.25 molar hydrochloric
acid is required to reach

00:00:07.492 --> 00:00:08.871
the equivalence point.

00:00:08.871 --> 00:00:12.612
Calculate the concentration
of potassium sorbate,

00:00:12.612 --> 00:00:15.016
we put the brackets, so we're
talking about concentration,

00:00:15.016 --> 00:00:17.552
in the stock solution.

00:00:17.552 --> 00:00:18.683
So let's juts remind ourselves

00:00:18.683 --> 00:00:21.662
what the equivalence point is.

00:00:21.662 --> 00:00:25.356
The equivalence point
is the point at which

00:00:25.356 --> 00:00:29.362
all of the potassium sorbate has reacted

00:00:29.362 --> 00:00:32.582
with the acid, with the titrate.

00:00:32.582 --> 00:00:36.484
So, we have just gotten
to the right-hand side

00:00:36.484 --> 00:00:38.538
of this net ionic equation.

00:00:38.538 --> 00:00:40.213
So, another way to think about it is,

00:00:40.213 --> 00:00:43.131
it's the point in which,
because we are reacting,

00:00:43.131 --> 00:00:46.933
for every mole of the potassium sorbate

00:00:46.933 --> 00:00:50.037
that we want to turn into sorbic acid,

00:00:50.037 --> 00:00:53.849
we're adding a mole of
the hydrochloric acid.

00:00:53.849 --> 00:00:56.010
So, one way to think about
the equivalence point

00:00:56.010 --> 00:00:59.722
is if I've added a certain number of moles

00:00:59.722 --> 00:01:00.894
of hydrochloric acid,

00:01:00.894 --> 00:01:03.228
that must the exact number of moles

00:01:03.228 --> 00:01:06.084
of the potassium sorbate
that we started out with.

00:01:06.084 --> 00:01:08.603
We've added the exact number of molecules

00:01:08.603 --> 00:01:10.874
of hydrochloric acid as they originally

00:01:10.874 --> 00:01:12.737
were of potassium sorbate,

00:01:12.737 --> 00:01:16.149
so they can completely
cancel out with each other.

00:01:16.149 --> 00:01:18.595
So if we can figure out
the number of moles,

00:01:18.595 --> 00:01:20.341
if we can figure out the number of moles

00:01:20.341 --> 00:01:22.278
of hydrochloric acid here,

00:01:22.278 --> 00:01:24.608
then we could say, "Well,
the equivalence point",

00:01:24.608 --> 00:01:26.909
or if you needed that number of moles

00:01:26.909 --> 00:01:29.580
of hydrochloric acid to
reach the equivalent point,

00:01:29.580 --> 00:01:31.673
then that means your
original stock solution

00:01:31.673 --> 00:01:34.748
had that many moles of potassium sorbate,

00:01:34.748 --> 00:01:37.144
and then we can use that to calculate

00:01:37.144 --> 00:01:38.765
the actual concentration.

00:01:38.765 --> 00:01:39.743
So let's do the first part,

00:01:39.743 --> 00:01:42.869
let's think about how many
moles of hydrochloric acid,

00:01:42.869 --> 00:01:44.894
this is right over here,

00:01:44.894 --> 00:01:48.614
so I'll just write HCl,

00:01:48.614 --> 00:01:50.992
and so, if we have

00:01:50.992 --> 00:01:55.252
29.95

00:01:55.252 --> 00:01:57.022
milliliters,

00:01:57.022 --> 00:01:59.321
and let's just convert it into liters,

00:01:59.321 --> 00:02:00.157
because if we have,

00:02:00.157 --> 00:02:04.533
if our concentration is
given in terms of molarity,

00:02:04.533 --> 00:02:06.298
this is moles per liter,

00:02:06.298 --> 00:02:08.229
so let's make sure we get our units right,

00:02:08.229 --> 00:02:09.865
so let's multiply this times,

00:02:09.865 --> 00:02:11.711
so we wanna convert this to liters,

00:02:11.711 --> 00:02:13.914
so we want liters in the numerator,

00:02:13.914 --> 00:02:16.155
and milliliters in the
denominator, so these cancel out,

00:02:16.155 --> 00:02:19.545
so one liter's equal to 1000 milliliters,

00:02:19.545 --> 00:02:20.238
and that makes sense,

00:02:20.238 --> 00:02:21.794
if you wanna go from
milliliters to liters,

00:02:21.794 --> 00:02:25.601
you would multiply by
1000, or divide by 1000.

00:02:25.601 --> 00:02:28.574
So this would give us the total amount

00:02:28.574 --> 00:02:33.574
of hydrochloric acid solution
we've added in liters,

00:02:33.712 --> 00:02:35.900
and now let's figure out
how many moles that will be.

00:02:35.900 --> 00:02:38.737
Well, we multiply that times the molarity,

00:02:38.737 --> 00:02:41.822
times 1.25,

00:02:41.822 --> 00:02:44.746
instead of writing molar capital M,

00:02:44.746 --> 00:02:49.612
I'm gonna write 1.25 moles per liter,

00:02:49.612 --> 00:02:52.049
and what is this going to give us?

00:02:52.049 --> 00:02:54.325
Well, let me get my calculator out,

00:02:55.205 --> 00:02:59.396
and so, I'm gonna have 29.95

00:02:59.396 --> 00:03:03.807
divided by 1000, (mumbling) right there,

00:03:03.807 --> 00:03:05.540
times 1.25,

00:03:05.540 --> 00:03:09.551
times 1.25 is equal to,

00:03:09.551 --> 00:03:10.379
and let's see,

00:03:10.379 --> 00:03:13.586
I have three significant
figures here, four over here,

00:03:13.586 --> 00:03:15.708
so the product, I'm gonna have three,

00:03:15.708 --> 00:03:19.484
so 0.0374,

00:03:21.004 --> 00:03:25.000
0.0374,

00:03:25.000 --> 00:03:26.317
and the unit is all work out,

00:03:26.317 --> 00:03:27.680
milliliters cancels out with milliliters,

00:03:27.680 --> 00:03:29.631
liters cancel out with liters,

00:03:29.631 --> 00:03:34.046
and I have 0.0374 moles,

00:03:34.046 --> 00:03:37.026
and remember this is moles
of hydrochloric acid,

00:03:37.026 --> 00:03:40.625
so when they say that a
total of 29.95 milliliters

00:03:40.625 --> 00:03:44.965
of 1.25 molar solution of
hydrochloric acid is added,

00:03:44.965 --> 00:03:49.088
they really added this many
moles of hydrochloric acid.

00:03:49.088 --> 00:03:51.308
So, that means our original solution had

00:03:51.308 --> 00:03:55.367
that many moles of

00:03:55.367 --> 00:03:56.897
potassium sorbate.

00:03:56.897 --> 00:03:59.190
So it had that many moles
of potassium sorbate,

00:03:59.190 --> 00:04:01.427
we can now figure out the
original concentration

00:04:01.427 --> 00:04:02.971
of potassium sorbate.

00:04:04.131 --> 00:04:06.766
The concentration of our potassium sorbate

00:04:07.766 --> 00:04:12.312
C6H7O2

00:04:12.312 --> 00:04:15.450
is going to be equal
to the number of moles

00:04:15.450 --> 00:04:18.814
of potassium sorbate our stock
solution starts off with,

00:04:18.814 --> 00:04:21.767
so that's going to be the
same number right over here,

00:04:21.767 --> 00:04:26.363
0.0374

00:04:26.363 --> 00:04:30.547
moles divided by

00:04:30.547 --> 00:04:35.090
what was our original volume
of our original solution?

00:04:35.090 --> 00:04:36.267
Let's see.

00:04:36.267 --> 00:04:39.472
A student titrates 45.00,

00:04:39.472 --> 00:04:40.714
so we have four significant figures here,

00:04:40.714 --> 00:04:45.466
a student titrates 45 milliliters
of the stock solution.

00:04:45.466 --> 00:04:47.228
So the stock solution originally

00:04:47.228 --> 00:04:51.443
has a volume of 45 milliliters.

00:04:51.443 --> 00:04:52.672
So 45 milliliters,

00:04:52.672 --> 00:04:54.564
if we wanted to write
that in terms of liters,

00:04:54.564 --> 00:04:56.608
remember, the concentration,
the molarity here,

00:04:56.608 --> 00:05:01.143
we wanted it in terms of mole per liter,

00:05:01.143 --> 00:05:04.035
45 milliliters is the same thing as

00:05:04.035 --> 00:05:08.851
0.045,

00:05:08.851 --> 00:05:10.801
I can write zero there

00:05:10.801 --> 00:05:12.894
so that I have four
significant figures here,

00:05:12.894 --> 00:05:15.174
liters of solution,

00:05:15.174 --> 00:05:17.016
and what is this going to be equal to,

00:05:17.016 --> 00:05:19.463
and I just divided this by 1000,

00:05:19.463 --> 00:05:24.463
45 milliliters is the same thing
as 45 thousands of a liter.

00:05:24.757 --> 00:05:26.042
And so, what do we have?

00:05:27.792 --> 00:05:29.457
We'll take that number we just had,

00:05:29.457 --> 00:05:32.036
and then we divided it by

00:05:32.036 --> 00:05:34.896
.045,

00:05:34.896 --> 00:05:36.239
and I can add two more zeros there,

00:05:36.239 --> 00:05:37.695
but form the calculator point of view

00:05:37.695 --> 00:05:39.065
it doesn't make a difference,

00:05:39.065 --> 00:05:41.346
and that's going to be equal to,

00:05:41.346 --> 00:05:43.360
all right, how many
significant figures do we have?

00:05:43.360 --> 00:05:45.198
We have three significant figures,

00:05:45.198 --> 00:05:49.153
so 0.832,

00:05:49.153 --> 00:05:51.363
0.832,

00:05:52.383 --> 00:05:56.931
0.832

00:05:56.931 --> 00:05:58.161
moles per liter,

00:05:58.161 --> 00:06:02.644
or we could say 0.832 molar,
did I write that right?

00:06:03.624 --> 00:06:07.823
Yeah, 832, and there you have it,

00:06:07.823 --> 00:06:12.094
that's the initial concentration
of the potassium sorbate

00:06:12.094 --> 00:06:14.348
in our stock solution.


2015 AP Chemistry free response 3f

WEBVTT
Kind: captions
Language: en

00:00:00.749 --> 00:00:03.709
- The pH of the soft drink is 3.37

00:00:03.709 --> 00:00:07.053
after the addition of
the potassium sorbate.

00:00:07.053 --> 00:00:11.546
Which species, the sorbic
acid or the sorbate ion,

00:00:11.546 --> 00:00:14.112
has a higher concentration
in the soft drink.

00:00:14.112 --> 00:00:17.477
Justify your answer.

00:00:17.477 --> 00:00:19.870
So, this is related to the
question we've been doing

00:00:19.870 --> 00:00:23.075
because the sorbate ion,

00:00:23.075 --> 00:00:26.058
this is what happens when
you put potassium sorbate

00:00:26.058 --> 00:00:28.021
and it dis-associates in a solution.

00:00:28.021 --> 00:00:30.367
So the concentration of the sorbate ion

00:00:30.367 --> 00:00:31.817
is the same thing as the concentration.

00:00:31.817 --> 00:00:33.174
One way to think about it,

00:00:33.174 --> 00:00:34.910
is going to be the same as

00:00:34.910 --> 00:00:36.977
the concentration of
your potassium sorbate.

00:00:37.897 --> 00:00:42.038
So if we're thinking about
titrating potassium sorbate,

00:00:42.038 --> 00:00:43.480
which we've been doing

00:00:43.480 --> 00:00:45.331
in the last several parts of the problem.

00:00:45.331 --> 00:00:47.514
At what point do you have
an equal concentration

00:00:47.514 --> 00:00:51.542
of potassium sorbate and sorbic acid.

00:00:51.542 --> 00:00:53.888
Well you have equal concentrations

00:00:53.888 --> 00:00:55.977
at the half-equivalence point.

00:00:55.977 --> 00:00:57.302
We marked that out

00:00:57.302 --> 00:00:58.845
when we figured it out

00:00:58.845 --> 00:01:00.331
in the last few parts of this problem.

00:01:00.331 --> 00:01:03.500
And the half-equivalence
point happened at a pH of,

00:01:03.500 --> 00:01:06.647
we actually figured it out before, 4.77.

00:01:06.647 --> 00:01:08.296
So we could say...

00:01:10.206 --> 00:01:11.767
"half-equivalence point

00:01:20.737 --> 00:01:23.154
"of titration

00:01:25.804 --> 00:01:28.164
"of potassium sorbate

00:01:34.994 --> 00:01:37.903
"with hydrochloric acid

00:01:41.793 --> 00:01:45.948
"happens at a pH of,"

00:01:49.108 --> 00:01:52.890
let me write that pH of, "4.77."

00:01:53.796 --> 00:01:56.327
And that's the point at which
you have equal concentrations

00:01:56.327 --> 00:01:59.079
of, so we can put this in parentheses,

00:01:59.079 --> 00:02:03.166
"can be viewed as point

00:02:07.766 --> 00:02:11.966
"where we have equal

00:02:16.250 --> 00:02:18.921
"concentrations,

00:02:21.452 --> 00:02:25.596
"of C6H7O2 minus,"

00:02:28.581 --> 00:02:31.784
and ascorbic acid, "HC6H7O2."

00:02:38.961 --> 00:02:42.318
"pH of 3.37 is lower

00:02:47.051 --> 00:02:50.268
and will thus," or we could say,

00:02:51.311 --> 00:02:54.179
"will happen beyond

00:02:56.212 --> 00:02:58.511
"half-equivalence point."

00:02:58.511 --> 00:03:02.242
Beyond half-equivalence point.

00:03:08.652 --> 00:03:12.518
So, concentration of the
sorbic acid is higher.

00:03:12.518 --> 00:03:15.497
"So concentration

00:03:17.689 --> 00:03:20.952
"of sorbic acid,

00:03:23.569 --> 00:03:27.221
"HC6H7O2, is higher."

00:03:31.229 --> 00:03:33.101
When you're starting off,

00:03:33.101 --> 00:03:34.724
if you're doing a titration.

00:03:34.724 --> 00:03:36.710
Your concentration of potassium sorbate,

00:03:36.710 --> 00:03:38.520
it'll be higher then you keep titrating

00:03:38.520 --> 00:03:40.006
and it keeps reacting with
the hydrochloric acid.

00:03:40.006 --> 00:03:41.736
You get to the half-equivalence point

00:03:41.736 --> 00:03:43.466
where these two things

00:03:43.466 --> 00:03:45.230
are going to have equal concentrations.

00:03:45.230 --> 00:03:46.902
Then if you keep titrating it,

00:03:46.902 --> 00:03:48.087
well then you're going to become

00:03:48.087 --> 00:03:50.839
more acidic and your going to
have a higher concentration

00:03:50.839 --> 00:03:52.788
of the sorbic acid.

00:03:52.788 --> 00:03:54.309
So one way to think about,

00:03:54.309 --> 00:03:56.179
actually let me underline that whole part,

00:03:56.179 --> 00:03:58.606
"so concentration of
sorbic acid is higher."

00:03:58.606 --> 00:04:01.090
That's the main thing
that they're asking for.

00:04:01.090 --> 00:04:03.760
But the way to think about this soft drink

00:04:03.760 --> 00:04:06.488
is something it might not have,

00:04:06.488 --> 00:04:07.940
and obviously people are sitting there

00:04:07.940 --> 00:04:09.002
and titrating every soft drink.

00:04:09.002 --> 00:04:10.795
But you can kinda view this soft drink

00:04:10.795 --> 00:04:14.011
as well it got that point
after a theoretical titration

00:04:14.011 --> 00:04:15.498
that got us past the...

00:04:18.378 --> 00:04:19.741
half-equivalence point.

00:04:19.741 --> 00:04:20.956
And so therefore,

00:04:23.086 --> 00:04:25.153
most of our things that we care about

00:04:25.153 --> 00:04:26.999
is in the form, is in the acid form

00:04:26.999 --> 00:04:28.985
versus the conjugate base.

00:04:28.985 --> 00:04:31.944
Most of the sorbic acid

00:04:31.944 --> 00:04:34.313
is in its acid form.

00:04:34.313 --> 00:04:35.997
Or I guess you could say it the other way.

00:04:35.997 --> 00:04:38.841
Most of the sorbate has
become the conjugate acid.


2015 AP Chemistry free response 3d

WEBVTT
Kind: captions
Language: en

00:00:00.411 --> 00:00:02.245
- [Voiceover] Calculate the pH

00:00:02.245 --> 00:00:04.370
at the half-equivalence point.

00:00:04.370 --> 00:00:05.868
So, let's just remind ourselves

00:00:05.868 --> 00:00:09.246
what the half-equivalence point even is.

00:00:09.246 --> 00:00:12.845
The equivalence point is when the titrant,

00:00:12.845 --> 00:00:15.079
in this case the hydrochloric acid,

00:00:15.079 --> 00:00:18.302
completely reacts with
the potassium sorbate,

00:00:18.302 --> 00:00:20.213
the thing that we are titrating.

00:00:20.213 --> 00:00:22.315
Now the half-equivalence
point is the point

00:00:22.315 --> 00:00:24.463
at which half of the potassium sorbate

00:00:24.463 --> 00:00:27.284
has been converted to the sorbic acid.

00:00:27.284 --> 00:00:28.867
Or another way of thinking about it is,

00:00:28.867 --> 00:00:31.278
the concentrations of
the potassium sorbate

00:00:31.278 --> 00:00:33.797
and the sorbic acid are equivalent.

00:00:33.797 --> 00:00:36.119
Well, how do we relate that to pH,

00:00:36.119 --> 00:00:37.721
and what other information
have they given us

00:00:37.721 --> 00:00:39.498
to actually solve this?

00:00:39.498 --> 00:00:42.180
And a good thing to do whenever you are,

00:00:42.180 --> 00:00:43.648
if you feel a little bit stuck here, say,

00:00:43.648 --> 00:00:46.266
"Well, what other information
have they given us?"

00:00:46.266 --> 00:00:49.923
Well, they gave us the K-a of sorbic acid

00:00:49.923 --> 00:00:52.884
is being 1.7 times ten
to the negative fifth.

00:00:52.884 --> 00:00:56.771
So somehow, can we connect
the K-a of sorbic acid

00:00:56.771 --> 00:01:00.187
to the pH at the half-equivalence point?

00:01:00.187 --> 00:01:01.185
Well the other thing that they give you,

00:01:01.185 --> 00:01:03.008
is they give you a whole
series of formulas.

00:01:03.008 --> 00:01:04.912
In fact, they give you all the formulas

00:01:04.912 --> 00:01:07.559
that I'm using here in
the first couple of pages

00:01:07.559 --> 00:01:09.753
of the free-response section,

00:01:09.753 --> 00:01:11.518
and even a whole bunch of formulas

00:01:11.518 --> 00:01:15.814
on equilibria and all of these
different notations they use.

00:01:15.814 --> 00:01:19.239
And the one that might show
up that looks interesting

00:01:19.239 --> 00:01:21.572
is this one right over here
that you might recognize

00:01:21.572 --> 00:01:24.881
as the Henderson-Hasselbalch equation.

00:01:24.881 --> 00:01:26.530
And it's actually not hard to prove it.

00:01:26.530 --> 00:01:27.667
It comes straight out of the definition

00:01:27.667 --> 00:01:30.140
of K-a, and then rearranging things,

00:01:30.140 --> 00:01:32.265
and then taking the negative log

00:01:32.265 --> 00:01:33.786
of both sides and doing things like that.

00:01:33.786 --> 00:01:34.947
I encourage you to watch those videos

00:01:34.947 --> 00:01:37.071
on Khan Academy if you are curious,

00:01:37.071 --> 00:01:40.392
but what's neat here is it connects pH,

00:01:40.392 --> 00:01:45.318
it connects pH, it connects pH, to p-K-a,

00:01:45.318 --> 00:01:49.827
and the concentrations of an acid

00:01:49.827 --> 00:01:52.536
and its conjugate base.

00:01:52.536 --> 00:01:55.520
So how do we make a relationship here?

00:01:55.520 --> 00:01:58.353
Well, at the half-equivalence point,

00:01:58.353 --> 00:01:59.978
the acid in the conjugate base are gonna,

00:01:59.978 --> 00:02:02.671
their concentrations are
going to be equivalent.

00:02:02.671 --> 00:02:06.538
So this, and this are going to cancel out.

00:02:06.538 --> 00:02:07.942
You're just gonna get one.

00:02:07.942 --> 00:02:10.926
And log of one is just going to be zero.

00:02:10.926 --> 00:02:14.429
So, at the half-equivalence
point, the pH is going

00:02:14.429 --> 00:02:18.240
to be equal to the p-K-a.

00:02:18.240 --> 00:02:20.516
And so what is the p-K-a here?

00:02:20.516 --> 00:02:22.559
Well, they told us that the K-a,

00:02:22.559 --> 00:02:26.507
the K-a is equal to,

00:02:26.507 --> 00:02:29.885
and this is the K-a of sorbic acid,

00:02:29.885 --> 00:02:32.428
K-a of sorbic acid is 1.7 times ten

00:02:32.428 --> 00:02:34.854
to the negative fifth.

00:02:34.854 --> 00:02:38.430
1.7 times ten to the negative fifth.

00:02:38.430 --> 00:02:42.970
1.7 times ten to the negative fifth.

00:02:42.970 --> 00:02:44.386
And once again, when
we're thinking about K-a

00:02:44.386 --> 00:02:47.091
we're thinking about the
dissociation constant

00:02:47.091 --> 00:02:51.689
for the acid, and so that's
why we used sorbic acid there.

00:02:51.689 --> 00:02:53.570
And, either way, these two
concentrations are going

00:02:53.570 --> 00:02:54.626
to be the same.

00:02:54.626 --> 00:02:56.337
And if I want to find the p-K-a,

00:02:56.337 --> 00:02:59.351
I take the negative log of...

00:02:59.351 --> 00:03:00.988
I take the negative log of this.

00:03:00.988 --> 00:03:04.887
So, p-K-a, which is equal

00:03:04.887 --> 00:03:08.349
to the negative log, base ten, of the K-a.

00:03:08.349 --> 00:03:09.475
And they actually give
you all these formulas

00:03:09.475 --> 00:03:11.449
on the first page.

00:03:11.449 --> 00:03:14.746
This is going to be equal
to the negative log,

00:03:14.746 --> 00:03:18.864
base ten, of 1.7 times ten

00:03:18.864 --> 00:03:20.834
to the negative fifth power.

00:03:20.834 --> 00:03:23.628
And what is that going to be?

00:03:23.628 --> 00:03:25.319
Let me get a calculator out.

00:03:26.374 --> 00:03:27.669
So...

00:03:29.108 --> 00:03:33.473
So let's see, I'll write 1.7...

00:03:33.473 --> 00:03:37.235
These two capital Es,
that's times ten to the...

00:03:37.235 --> 00:03:40.787
So, times ten to the, not the fifth,

00:03:40.787 --> 00:03:42.471
the negative fifth power.

00:03:42.471 --> 00:03:44.294
Now I want to take log, base ten,

00:03:44.294 --> 00:03:45.153
that's this button here.

00:03:45.153 --> 00:03:47.526
If you're calculator just has a log button

00:03:47.526 --> 00:03:49.193
that defaults to base ten.

00:03:49.193 --> 00:03:51.027
So I take log, base ten, of that.

00:03:51.027 --> 00:03:53.489
And then I want to take
the negative of that.

00:03:53.489 --> 00:03:58.471
And so this is going to
be, approximately, 4.77.

00:03:58.471 --> 00:04:01.736
So, this is approximately,

00:04:01.736 --> 00:04:06.346
approximately, 4.77

00:04:06.346 --> 00:04:10.776
So, the pH is equal to the p-K-a

00:04:10.776 --> 00:04:14.083
which is equal to that, right over there.


2015 AP Chemistry free response 3c

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:02.207
- [Voiceover] The pH at
the equivalence point

00:00:02.207 --> 00:00:05.411
of the titration is measured to be 2.54.

00:00:05.411 --> 00:00:06.887
Which of the following indicators

00:00:06.887 --> 00:00:08.548
would be the best choice for determining

00:00:08.548 --> 00:00:10.614
the end point of the titration?

00:00:10.614 --> 00:00:12.402
Justify your answer.

00:00:12.402 --> 00:00:13.459
Well let's just remind ourselves,

00:00:13.459 --> 00:00:15.317
the endpoint of the titration

00:00:15.317 --> 00:00:17.616
is when the indicator changes color,

00:00:17.616 --> 00:00:20.890
and because that's our
signal, our visual signal,

00:00:20.890 --> 00:00:23.642
it's saying, "Hey, we must've
hit the equivalence point,"

00:00:23.642 --> 00:00:27.264
you want the pKa of your indicator

00:00:27.264 --> 00:00:29.377
to be as close as possible to the pH

00:00:29.377 --> 00:00:30.771
at the equivalence point.

00:00:30.771 --> 00:00:33.627
If the pH at the
equivalence point is 2.54,

00:00:33.627 --> 00:00:37.272
well which of these indicators
have the closes pKa to that?

00:00:37.272 --> 00:00:39.850
Well we see thymol blue has
it at two right over here,

00:00:39.850 --> 00:00:42.799
so we would choose to use thymol blue,

00:00:42.799 --> 00:00:43.799
thymol blue,

00:00:46.854 --> 00:00:48.399
because

00:00:48.399 --> 00:00:49.232
its pKa

00:00:52.255 --> 00:00:53.088
closest

00:00:54.128 --> 00:00:54.961
to pH

00:00:57.366 --> 00:00:59.622
at equivalence point.

00:00:59.622 --> 00:01:00.622
Equivalence,

00:01:01.828 --> 00:01:03.328
equivalence point.

00:01:05.705 --> 00:01:06.788
There you go.


2015 AP Chemistry free response 3e

WEBVTT
Kind: captions
Language: en

00:00:00.301 --> 00:00:02.484
- The initial pH and the equivalence point

00:00:02.484 --> 00:00:04.458
are plotted on the graph below.

00:00:04.458 --> 00:00:08.335
Accurately sketch the titration
curve on the graph below.

00:00:08.335 --> 00:00:10.623
Mark the position of the
half-equivalence point

00:00:10.623 --> 00:00:13.293
on the curve with an X.

00:00:13.293 --> 00:00:16.293
All right, so we have, they show us

00:00:18.319 --> 00:00:22.905
the initial pH right over
here, and they also show us

00:00:22.905 --> 00:00:25.891
the equivalence point right over here.

00:00:25.891 --> 00:00:28.021
And it's at a pH of, we actually saw that

00:00:28.021 --> 00:00:29.895
in the last problem with equivalence,

00:00:29.895 --> 00:00:32.217
the equivalence point, or
actually a couple of problems ago,

00:00:32.217 --> 00:00:33.882
the equivalence point was measured,

00:00:33.882 --> 00:00:37.098
the pH at the equivalence
point was measured to be 2.54,

00:00:37.098 --> 00:00:41.417
so that's why this right
over here is at 2.54

00:00:41.417 --> 00:00:44.122
when we've added about 29 point,

00:00:44.122 --> 00:00:45.445
I forgot what the number was.

00:00:45.445 --> 00:00:48.336
It was in, I think, the
second part of this problem.

00:00:48.336 --> 00:00:50.462
They said when you added
close to 30 milliliters

00:00:50.462 --> 00:00:53.342
of that hydrochloric acid, that 1.25

00:00:53.342 --> 00:00:55.548
molar hydrochloric acid solution,

00:00:55.548 --> 00:00:57.928
that is when we hit our equivalence point.

00:00:57.928 --> 00:01:00.041
And we see the pH right over there,

00:01:00.041 --> 00:01:02.142
and then the half-equivalence point.

00:01:02.142 --> 00:01:04.720
Well, that's going to be when
we've added half this amount.

00:01:04.720 --> 00:01:08.179
So it's going to be a
little bit less than 15,

00:01:08.179 --> 00:01:10.188
and we in the last problem, we figured out

00:01:10.188 --> 00:01:13.519
that that was going to be at a pH of 4.77.

00:01:13.519 --> 00:01:18.106
So a pH of 4.77 is going
to be something like,

00:01:18.106 --> 00:01:21.205
right over there, they
said mark that with an X.

00:01:21.205 --> 00:01:23.527
So half-equivalence
point, we've added half

00:01:23.527 --> 00:01:26.998
the titrate there, and we know the pH.

00:01:26.998 --> 00:01:29.367
We figured that out in the
last part of the problem.

00:01:29.367 --> 00:01:32.141
And now we just need to graph,

00:01:32.141 --> 00:01:34.626
we need to sketch the titration curve.

00:01:34.626 --> 00:01:36.077
So let's see.

00:01:36.077 --> 00:01:40.025
We keep adding more and
more hydrochloric acid.

00:01:40.025 --> 00:01:43.025
Hydrochloric acid, it lowers the pH.

00:01:44.227 --> 00:01:46.967
We get to the half-equivalence point.

00:01:46.967 --> 00:01:48.337
And then actually, we're going to

00:01:48.337 --> 00:01:50.801
start leveling off over here.

00:01:50.801 --> 00:01:54.178
The reason why you level off
is 'cause you're going to have,

00:01:54.178 --> 00:01:58.413
you're going to have more and
more of the conjugate acid

00:01:58.413 --> 00:02:02.580
there, and so as you react
with the conjugate base,

00:02:03.591 --> 00:02:05.251
with more and more of the conjugate base,

00:02:05.251 --> 00:02:06.993
the equilibrium between the conjugate base

00:02:06.993 --> 00:02:08.479
and the conjugate acid,
the more of that acid

00:02:08.479 --> 00:02:09.838
is going to go to conjugate base.

00:02:09.838 --> 00:02:11.173
So you're going to have a
little bit of a buffering

00:02:11.173 --> 00:02:14.609
going on, but at some
point you have reacted.

00:02:14.609 --> 00:02:17.976
You have completely
reacted with everything,

00:02:17.976 --> 00:02:20.797
and you've hit your equivalence point.

00:02:20.797 --> 00:02:22.377
You hit your equivalence point.

00:02:22.377 --> 00:02:25.952
And then, and you become much more acidic,

00:02:25.952 --> 00:02:28.194
and it might look something,

00:02:28.194 --> 00:02:31.676
it might look something like that.

00:02:31.676 --> 00:02:34.834
Let me see if I can do
a little bit better,

00:02:34.834 --> 00:02:36.540
a little bit better job.

00:02:36.540 --> 00:02:39.431
So it would look something,

00:02:39.431 --> 00:02:42.671
and we're obviously, it's not
going to be exactly right.

00:02:42.671 --> 00:02:44.818
It's important we go
through these three points.

00:02:44.818 --> 00:02:47.593
And it would look something like that.

00:02:47.593 --> 00:02:49.009
So that's the equivalence point,

00:02:49.009 --> 00:02:53.176
half-equivalence point, and
then this is our initial pH.


Parallel resistors (part 3)

WEBVTT
Kind: captions
Language: en

00:00:00.732 --> 00:00:02.277
- [Voiceover] In this video
we're gonna talk even some more

00:00:02.277 --> 00:00:04.192
about parallel resistors.

00:00:04.192 --> 00:00:06.515
Parallel resistors are resistors

00:00:06.515 --> 00:00:09.161
that are connected end to end,

00:00:09.161 --> 00:00:11.337
and share the same nodes.

00:00:11.337 --> 00:00:14.067
Here's R one and R two,
they share the same nodes.

00:00:14.067 --> 00:00:15.859
That one and that one.

00:00:15.859 --> 00:00:18.278
And that means they
share the same voltage.

00:00:18.278 --> 00:00:21.331
And we worked out an expression

00:00:21.331 --> 00:00:24.464
for how to replace that
with a single resistor.

00:00:24.464 --> 00:00:28.782
R parallel, and we found
that one over R parallel

00:00:29.912 --> 00:00:32.281
is one over R one

00:00:32.281 --> 00:00:37.076
plus one over R two.

00:00:37.076 --> 00:00:38.745
So in this video I'm gonna actually

00:00:38.745 --> 00:00:41.689
start working with this
expression a little bit more.

00:00:41.689 --> 00:00:43.850
And we'll just change it around
a little bit to an easier,

00:00:43.850 --> 00:00:45.802
an easy way to remember it,

00:00:45.802 --> 00:00:47.721
and then we're gonna do a special case,

00:00:47.721 --> 00:00:50.083
where R one and R two are the same value

00:00:50.083 --> 00:00:51.620
and we're gonna see what happens.

00:00:51.620 --> 00:00:54.317
So right now I wanna do
just a little bit of algebra

00:00:54.317 --> 00:00:57.546
on that expression, one over R p

00:00:57.546 --> 00:01:00.462
is the same as

00:01:00.462 --> 00:01:02.807
one over R one

00:01:02.807 --> 00:01:06.436
plus one over R two.

00:01:08.713 --> 00:01:10.590
What I wanna end up with
here is an expression

00:01:10.590 --> 00:01:13.965
that on this side says
R p equals something,

00:01:13.965 --> 00:01:16.738
and on this side I just
want one expression,

00:01:16.738 --> 00:01:18.567
not two fractions.

00:01:18.567 --> 00:01:19.584
So we're gonna go about that

00:01:19.584 --> 00:01:22.178
by combining these two fractions first.

00:01:22.178 --> 00:01:27.097
So the least common denominator here, LCD,

00:01:27.097 --> 00:01:31.228
equals R one times R two,

00:01:33.145 --> 00:01:34.275
and I'm gonna convert both these

00:01:34.275 --> 00:01:36.973
to convert this to that proper denominator

00:01:36.973 --> 00:01:40.750
I have to multiply it by R two over R two,

00:01:40.750 --> 00:01:42.673
so we'll do it.

00:01:42.673 --> 00:01:45.353
We'll do all the steps.

00:01:45.353 --> 00:01:49.468
We'll multiply it by R two over R two.

00:01:51.906 --> 00:01:56.138
This expression we have to
multiply it by R one over R one.

00:02:03.711 --> 00:02:07.076
And this equals, of course, one over R p.

00:02:10.491 --> 00:02:13.528
Continuing on, one over R p

00:02:15.808 --> 00:02:19.752
equals R two

00:02:19.752 --> 00:02:24.123
over R one R two

00:02:24.123 --> 00:02:25.629
plus

00:02:27.905 --> 00:02:30.993
R one over

00:02:30.993 --> 00:02:34.005
R one R two,

00:02:34.005 --> 00:02:37.338
and now I can combine them together.

00:02:37.338 --> 00:02:40.190
Let's move up here.

00:02:40.190 --> 00:02:43.569
One over R p

00:02:43.569 --> 00:02:48.331
equals, we'll keep everything
in numerical order,

00:02:48.331 --> 00:02:50.764
R one

00:02:50.764 --> 00:02:54.709
plus R two over

00:02:56.464 --> 00:02:59.728
R one R two.

00:03:00.943 --> 00:03:03.916
And now I'm gonna take the reciprocal

00:03:03.916 --> 00:03:05.614
of both sides of the expression

00:03:05.614 --> 00:03:08.423
so I get an expression in R p,

00:03:08.423 --> 00:03:12.901
R p equals, and just flip
over this expression,

00:03:12.901 --> 00:03:16.515
R one R two

00:03:16.515 --> 00:03:17.856
over

00:03:17.856 --> 00:03:21.973
R one plus R two.

00:03:26.022 --> 00:03:27.671
That

00:03:34.616 --> 00:03:37.880
is a way you can remember how
to combine parallel resistors.

00:03:37.880 --> 00:03:40.401
The parallel equivalent resistor, R p,

00:03:40.401 --> 00:03:44.231
is the product of the two
resistors over the sum.

00:03:44.231 --> 00:03:47.721
So it's the product

00:03:47.721 --> 00:03:49.473
over the sum.

00:03:49.473 --> 00:03:51.064
That's how I remember it.

00:03:51.064 --> 00:03:52.844
Now this arithmetic, this expression,

00:03:52.844 --> 00:03:55.657
is exactly the same as the
original one that we had,

00:03:55.657 --> 00:03:57.610
these are the same,

00:03:57.610 --> 00:03:58.543
and it's just a question of

00:03:58.543 --> 00:04:00.493
which one do you want to remember,

00:04:00.493 --> 00:04:02.205
which one's easier to remember

00:04:02.205 --> 00:04:04.403
and which one's easiest to calculate.

00:04:04.403 --> 00:04:06.845
I like to remember this one here.

00:04:06.845 --> 00:04:09.024
Let's do a quick example using it.

00:04:11.718 --> 00:04:14.337
I'll move the screen up a little bit.

00:04:15.607 --> 00:04:17.686
Let's leave that there so we can see it.

00:04:17.686 --> 00:04:20.704
Let's say we have two parallel resistors.

00:04:26.139 --> 00:04:30.052
And we'll say the first one is 1,000 ohms,

00:04:33.314 --> 00:04:36.988
and the second one is 4,000 ohms.

00:04:42.887 --> 00:04:45.038
And the question is, what
is the parallel combination

00:04:45.038 --> 00:04:45.984
of those things.

00:04:45.984 --> 00:04:49.047
How can I replace these with one resistor

00:04:49.047 --> 00:04:51.082
so the same current flows.

00:04:51.082 --> 00:04:52.918
And we'll use this expression here.

00:04:52.918 --> 00:04:56.360
So R p

00:04:56.360 --> 00:05:00.005
equals a product which is 1,000

00:05:00.005 --> 00:05:03.845
times 4,000

00:05:03.845 --> 00:05:06.505
divided by the sum

00:05:06.505 --> 00:05:09.004
1,000

00:05:09.004 --> 00:05:12.133
plus 4,000

00:05:13.956 --> 00:05:15.466
and that equals, oh my goodness

00:05:15.466 --> 00:05:16.516
there's a lot of zeroes here.

00:05:16.516 --> 00:05:18.791
Four and six zeroes,

00:05:18.791 --> 00:05:22.611
one, two, three, four, five, six

00:05:23.963 --> 00:05:27.948
over, that's easy, 5,000.

00:05:30.706 --> 00:05:31.654
All right?

00:05:31.654 --> 00:05:32.664
And let's say,

00:05:32.664 --> 00:05:35.682
let's take out three
zeroes out of this one.

00:05:37.064 --> 00:05:39.708
Let's knock off three zeroes here,

00:05:39.708 --> 00:05:41.821
and three zeroes here.

00:05:41.821 --> 00:05:45.034
And I have 4,000

00:05:45.034 --> 00:05:48.450
divided by five

00:05:48.450 --> 00:05:51.259
and that equals 800 ohms.

00:05:54.055 --> 00:05:55.941
So that is this

00:06:06.440 --> 00:06:08.478
and that's how we use this expression.

00:06:08.478 --> 00:06:09.574
Now just something to notice here,

00:06:09.574 --> 00:06:12.869
notice that R parallel, the
equivalent parallel resistor,

00:06:12.869 --> 00:06:15.721
is smaller than both of these.

00:06:15.721 --> 00:06:18.531
And that happens every time,
that happens every time.

00:06:18.531 --> 00:06:20.239
The parallel resistance

00:06:20.239 --> 00:06:22.240
is smaller than the smallest resistor.

00:06:22.240 --> 00:06:26.547
So here it was 1,000, it's
gonna be smaller than that.

00:06:26.547 --> 00:06:28.651
And that's a property
of parallel resistors.

00:06:28.651 --> 00:06:30.811
Because you have two current paths

00:06:30.811 --> 00:06:33.048
that allow current to
go two different ways,

00:06:33.048 --> 00:06:35.244
the effective resistance is always smaller

00:06:35.244 --> 00:06:38.010
than the smallest original path,

00:06:38.010 --> 00:06:41.669
because there's a way for
current to go around another way.

00:06:43.786 --> 00:06:47.452
So this is now the expression
for two parallel resistors,

00:06:47.452 --> 00:06:49.844
and that's a good one to remember.

00:06:53.450 --> 00:06:55.411
Now I'm gonna show you one special case,

00:06:55.411 --> 00:06:58.794
and we'll do this in this color.

00:07:00.497 --> 00:07:04.942
What if R one equals R two?

00:07:06.024 --> 00:07:08.932
What is R p?

00:07:13.275 --> 00:07:16.126
And for this special case,
we use the same expression,

00:07:16.126 --> 00:07:19.759
we say R p,

00:07:19.759 --> 00:07:24.152
we say R p is the product,

00:07:24.152 --> 00:07:26.175
we'll just use R because R is,

00:07:26.175 --> 00:07:27.477
it's the same value.

00:07:27.477 --> 00:07:29.220
R times R

00:07:29.220 --> 00:07:33.051
over R plus R,

00:07:34.548 --> 00:07:37.497
and that's multiplied.

00:07:37.497 --> 00:07:40.845
And so that is R squared

00:07:40.845 --> 00:07:43.699
over two R,

00:07:45.242 --> 00:07:47.534
and one of these Rs cancels,

00:07:47.534 --> 00:07:50.997
so let's cancel

00:07:50.997 --> 00:07:55.267
that R and that squared,

00:07:55.267 --> 00:07:56.921
and we end up with

00:07:58.747 --> 00:08:01.895
R over two.

00:08:01.895 --> 00:08:04.245
So for the special case,

00:08:04.245 --> 00:08:08.689
if R one equals R two,

00:08:10.822 --> 00:08:15.687
then R p

00:08:16.902 --> 00:08:20.687
equals R over two.

00:08:20.687 --> 00:08:23.051
It's just half, and
that should make sense.

00:08:23.051 --> 00:08:24.802
If we do something like this,

00:08:24.802 --> 00:08:28.089
if we draw two resistors in parallel,

00:08:28.089 --> 00:08:30.461
like this.

00:08:30.461 --> 00:08:33.749
and we say this is 300 ohms

00:08:33.749 --> 00:08:36.838
and this is 300 ohms,

00:08:36.838 --> 00:08:39.328
that means the effective,

00:08:39.328 --> 00:08:42.110
the effective parallel resistor,

00:08:47.266 --> 00:08:50.652
150 ohms.

00:08:52.961 --> 00:08:55.078
And that's got a very
pleasing symmetry to it

00:08:55.078 --> 00:08:56.750
because these resistors are the same,

00:08:56.750 --> 00:08:58.323
they have the same voltage,

00:08:58.323 --> 00:08:59.837
they're going to have the same current,

00:08:59.837 --> 00:09:01.986
basically twice as much current

00:09:01.986 --> 00:09:04.679
is gonna flow in this
circuit as would flow

00:09:04.679 --> 00:09:06.459
if there was just one of these guys,

00:09:06.459 --> 00:09:08.786
so that's where the
divide by two comes from.

00:09:08.786 --> 00:09:12.489
So for two resistors in parallel,

00:09:12.489 --> 00:09:15.216
if the resistors are the same value,

00:09:15.216 --> 00:09:19.284
the effective parallel
resistance is just half.


Series resistors

WEBVTT
Kind: captions
Language: en

00:00:01.026 --> 00:00:02.048
- [Voiceover] Now that
we have our collection

00:00:02.048 --> 00:00:04.846
of components, our favorite
batteries and resistors,

00:00:04.846 --> 00:00:07.563
we can start to assemble
these into some circuits.

00:00:07.563 --> 00:00:09.501
And here's a circuit shown here.

00:00:09.501 --> 00:00:12.844
It has a battery and
it has three resistors,

00:00:12.844 --> 00:00:14.117
and a configuration that's called

00:00:14.117 --> 00:00:17.240
a series resistor configuration.

00:00:17.240 --> 00:00:19.980
Series resistors is a familiar pattern,

00:00:19.980 --> 00:00:22.488
and what you're looking for is resistors

00:00:22.488 --> 00:00:25.483
that are connected head
to tail, to head to tail.

00:00:25.483 --> 00:00:27.782
So these three resistors are in series

00:00:27.782 --> 00:00:31.242
because their succession of nodes

00:00:31.242 --> 00:00:33.970
are all connected, one after the other.

00:00:33.970 --> 00:00:36.965
So that's the pattern that tells you

00:00:36.965 --> 00:00:41.667
this is a series resistor connection.

00:00:41.667 --> 00:00:43.583
So we're gonna label
these our resistors here.

00:00:43.583 --> 00:00:48.583
We'll call this R1, R2, and R3.

00:00:49.748 --> 00:00:51.989
And we'll label this as v.

00:00:51.989 --> 00:00:55.688
And the unknown in this
is what is the current

00:00:55.688 --> 00:00:58.579
that's flowing here, that's
what we want to know.

00:00:58.579 --> 00:01:01.261
We know v, we want to know i.

00:01:01.261 --> 00:01:02.917
Now one thing we know about i

00:01:02.917 --> 00:01:06.714
is i flows down into resistor R1,

00:01:06.714 --> 00:01:10.104
all of the current goes out of
the other end of resistor R1

00:01:10.104 --> 00:01:13.343
because it has to, it
can't pile up inside there.

00:01:13.343 --> 00:01:15.561
All that goes into here,

00:01:15.561 --> 00:01:18.277
and all that comes out of R3.

00:01:18.277 --> 00:01:23.277
And i returns to the place it came from,

00:01:23.583 --> 00:01:25.255
which is the battery.

00:01:25.255 --> 00:01:29.481
So that's a characteristic
of series resistors,

00:01:29.481 --> 00:01:34.481
is in a series configuration
is they are head to tail,

00:01:41.474 --> 00:01:44.017
and that means that all the components,

00:01:44.017 --> 00:01:49.017
all the resistors share the same current.

00:01:50.936 --> 00:01:55.534
Current.

00:01:55.534 --> 00:01:57.299
That's the key thing.

00:01:57.299 --> 00:01:58.425
The thing that we don't know

00:01:58.425 --> 00:02:00.735
that's different between each resistors,

00:02:00.735 --> 00:02:05.681
is the voltage here, and the voltage here,

00:02:05.681 --> 00:02:10.681
let's call that v1,
this is v2, plus, minus,

00:02:13.402 --> 00:02:18.402
and this is v3, plus, minus.

00:02:18.742 --> 00:02:22.457
So in general, if these
resistors are different values

00:02:22.457 --> 00:02:24.419
because they have the same
current going through them,

00:02:24.419 --> 00:02:28.483
Ohm's Law tells us these
voltages will all be different.

00:02:28.483 --> 00:02:30.898
So the question I want to
answer with series resistors

00:02:30.898 --> 00:02:34.137
is could I replace all three of these

00:02:34.137 --> 00:02:38.502
with a single resistor that
cause the same current to flow?

00:02:38.502 --> 00:02:41.498
That's the question we have
on the table right now.

00:02:41.498 --> 00:02:42.984
So we make some observations,

00:02:42.984 --> 00:02:47.984
we have Ohm's Law, our friend, Ohm's Law.

00:02:50.205 --> 00:02:55.205
And we know that means v equals i times R,

00:02:55.325 --> 00:02:56.718
for any resistor.

00:02:56.718 --> 00:03:00.643
That sets the ratio of voltage to current.

00:03:00.643 --> 00:03:02.686
And this is another
thing we know about this,

00:03:02.686 --> 00:03:07.686
which is that v3, plus v2, plus v1,

00:03:09.060 --> 00:03:11.777
those are the voltages
across each resistor,

00:03:11.777 --> 00:03:15.004
those three voltages have
to add up to this voltage

00:03:15.004 --> 00:03:17.721
because of the way the
wires are connected.

00:03:17.721 --> 00:03:21.204
So the main voltage from the battery

00:03:21.204 --> 00:03:26.204
equals v1, plus v2, plus v3.

00:03:30.585 --> 00:03:32.326
We know that's for sure,
and now what we're gonna do

00:03:32.326 --> 00:03:34.184
is we're gonna write Ohm's Law

00:03:34.184 --> 00:03:38.234
for each of these individual resistors.

00:03:38.234 --> 00:03:43.234
v1 equals i, and i is
the same for everybody,

00:03:43.712 --> 00:03:46.568
times R1.

00:03:46.568 --> 00:03:51.568
v2, this voltage here, equals i times R2.

00:03:54.265 --> 00:03:59.265
And v3 equals i times R3.

00:04:01.185 --> 00:04:04.169
Now you can see, if I had four,
or five, or six resistors,

00:04:04.169 --> 00:04:07.025
I would have four, or five, or
six equations just like this

00:04:07.025 --> 00:04:10.763
for each resistor that was in series.

00:04:10.763 --> 00:04:14.165
So now what I'm gonna do is
substitute these voltages

00:04:14.165 --> 00:04:17.230
into here, and then we'll
make an observation.

00:04:17.230 --> 00:04:20.109
So let's do that substitution.

00:04:20.109 --> 00:04:25.109
I can say v equals i, R1,

00:04:27.099 --> 00:04:32.099
plus i, R2, plus i, R3.

00:04:36.469 --> 00:04:39.476
And because it's the
same i on every resistor,

00:04:39.476 --> 00:04:44.476
I can write v equals i,
I'm gonna factor out the i.

00:04:45.397 --> 00:04:50.397
R1, plus R2, plus R3.

00:04:52.978 --> 00:04:54.955
Now what I want to do
is take a moment here

00:04:54.955 --> 00:04:59.955
and compare this expression
to this one here,

00:05:00.470 --> 00:05:02.888
the original Ohm's Law.

00:05:02.888 --> 00:05:04.761
Alright, there's Ohm's Law.

00:05:04.761 --> 00:05:08.895
So we have v equals i, some current,

00:05:08.895 --> 00:05:12.174
times some resistor.

00:05:12.174 --> 00:05:15.137
I can come up with a resistor value,

00:05:15.137 --> 00:05:20.036
a single resistor that would
give me the same Ohm's Law.

00:05:20.036 --> 00:05:25.036
And that is gonna be called,
let's draw it over here.

00:05:27.211 --> 00:05:30.976
Here's our battery.

00:05:30.976 --> 00:05:35.976
And I'm gonna say there's a
resistor that I can draw here,

00:05:37.588 --> 00:05:42.588
R series, that's equivalent
to the three resistors here.

00:05:44.345 --> 00:05:48.118
And it's equivalent in the sense that

00:05:48.118 --> 00:05:52.379
it makes i flow here, that's
what we mean by equivalent.

00:05:52.379 --> 00:05:56.756
So in our case, to get the
same current to flow there

00:05:56.756 --> 00:06:01.756
I would say v equals i times R series,

00:06:03.757 --> 00:06:07.762
in which case, what I've done
is I've said that R series

00:06:07.762 --> 00:06:10.804
is what, is the sum of these three things,

00:06:10.804 --> 00:06:15.804
R1 plus R2, plus R3.

00:06:21.776 --> 00:06:23.621
This is how we think
about series resistors.

00:06:23.621 --> 00:06:27.139
We can replace a set of series resistors

00:06:27.139 --> 00:06:30.297
with a single resistor
that's equivalent to it

00:06:30.297 --> 00:06:34.163
if we add the resistors up.

00:06:34.163 --> 00:06:36.799
Let's just do a really fast
example to see how this works.

00:06:36.799 --> 00:06:41.799
I'm gonna move this screen.

00:06:43.493 --> 00:06:45.653
Here's an example with three resistors.

00:06:45.653 --> 00:06:50.030
I have labeled them 100
ohms, 50 ohms, and 150 ohms.

00:06:50.030 --> 00:06:52.375
And what I want to know
is the current here.

00:06:52.375 --> 00:06:53.397
And we'll put in a voltage,

00:06:53.397 --> 00:06:56.961
let's say it's 1.5 volts,

00:06:56.961 --> 00:06:59.461
just a single small battery.

00:06:59.461 --> 00:07:04.163
So what is the equivalent resistance here?

00:07:04.163 --> 00:07:06.125
One way to figure this out
and to simplify the circuit

00:07:06.125 --> 00:07:09.829
is to replace all three of those resistors

00:07:09.829 --> 00:07:13.700
with a series resistor, RS,

00:07:13.700 --> 00:07:15.544
and that is, as we said here, is the sum,

00:07:15.544 --> 00:07:20.544
so it's 100, plus 50, plus 150.

00:07:26.886 --> 00:07:31.886
And that adds up to 300 ohms.

00:07:32.692 --> 00:07:34.700
So that's the value of the equivalent

00:07:34.700 --> 00:07:36.314
series resistor right here.

00:07:36.314 --> 00:07:41.314
And if I want to calculate the current, i,

00:07:43.954 --> 00:07:48.954
i equals v over R, and
this case, it's R series,

00:07:51.454 --> 00:07:56.454
and that equals 1.5 divided by 300.

00:08:00.231 --> 00:08:03.133
And if I do my calculations right,

00:08:03.133 --> 00:08:08.133
that comes out to .005 amperes.

00:08:10.656 --> 00:08:15.656
Or an easier way to say it is
five milliamps, milliamperes.

00:08:20.026 --> 00:08:22.719
So that's i.

00:08:22.719 --> 00:08:27.719
And now that I know i, I can
go ahead and I can calculate

00:08:29.256 --> 00:08:32.657
the voltage at each point
across each resistor

00:08:32.657 --> 00:08:35.061
because I know i, I know R,

00:08:35.061 --> 00:08:36.941
I can calculate v.

00:08:36.941 --> 00:08:41.941
So v1, v1, which is the
voltage across that resistor,

00:08:43.640 --> 00:08:48.640
v1 equals i, R1, as we said before.

00:08:51.616 --> 00:08:56.616
So it's five milliamps
times 100 ohms, 0.5 volts.

00:09:03.923 --> 00:09:08.923
Let's do it for the other one, v2,

00:09:12.201 --> 00:09:17.201
equals i, same i, this time times R2,

00:09:18.118 --> 00:09:23.118
five milliamps times 50 ohms,

00:09:23.853 --> 00:09:28.853
and that equals 0.25 volts.

00:09:31.295 --> 00:09:36.295
And finally, we do v3.

00:09:38.319 --> 00:09:42.722
This is plus, minus v3.

00:09:42.722 --> 00:09:47.722
And that equals the same
current again times 150 ohms,

00:09:54.248 --> 00:09:59.248
which is equal to 0.75 volts.

00:10:01.052 --> 00:10:03.873
So we've solved the
voltage and the current

00:10:03.873 --> 00:10:06.764
on every resistor, so this
circuit is completely solved.

00:10:06.764 --> 00:10:08.052
And let's do one final check.

00:10:08.052 --> 00:10:12.069
Let's add this up.

00:10:12.069 --> 00:10:15.703
Five, five (mumbles) is zero.

00:10:15.703 --> 00:10:20.452
Carry the one, six, seven eight.

00:10:20.452 --> 00:10:25.452
15, 1.5 volts, and that's very handy

00:10:26.744 --> 00:10:29.287
because that is the same as that.

00:10:29.287 --> 00:10:32.573
So indeed, the voltages across
the resistors did add up

00:10:32.573 --> 00:10:37.054
to the full battery that was applied.

00:10:37.054 --> 00:10:38.587
There's one more thing
I want to point out.

00:10:38.587 --> 00:10:43.587
Here's an example of
some series resistors.

00:10:46.005 --> 00:10:47.805
And that's a familiar pattern.

00:10:47.805 --> 00:10:49.605
And you'll say, "Oh, those
are series resistors."

00:10:49.605 --> 00:10:53.529
Now, be careful because if
there's a wire here going off

00:10:53.529 --> 00:10:56.884
and there's, doing this,
or there's a wire here,

00:10:56.884 --> 00:10:58.985
connected to this node here,

00:10:58.985 --> 00:11:00.390
this still looks like they're in series,

00:11:00.390 --> 00:11:02.654
but there might be current flowing

00:11:02.654 --> 00:11:04.686
in these branches here.

00:11:04.686 --> 00:11:06.729
If there's current flowing out

00:11:06.729 --> 00:11:09.249
anywhere along a series branch,

00:11:09.249 --> 00:11:12.174
anywhere along what looks
like a series branch,

00:11:12.174 --> 00:11:17.174
then this i may or may
not be the same as this i.

00:11:17.503 --> 00:11:20.731
And it might not be the same as this.

00:11:20.731 --> 00:11:21.764
So you gotta be careful here.

00:11:21.764 --> 00:11:25.050
If you see branches going
off your series resistors,

00:11:25.050 --> 00:11:30.050
these are not in series
unless these are zero current.

00:11:31.853 --> 00:11:35.348
If that's zero current, and
if that is zero current,

00:11:35.348 --> 00:11:37.925
then you can consider these in series.

00:11:37.925 --> 00:11:39.864
So that's just something to be careful of

00:11:39.864 --> 00:11:41.907
when you are looking at a circuit

00:11:41.907 --> 00:11:44.914
and you see things that
look like they're in series,

00:11:44.914 --> 00:11:46.691
but they have little branches coming off.

00:11:46.691 --> 00:11:49.953
So a little warning there.

00:11:49.953 --> 00:11:51.671
So that's our series resistors.

00:11:51.671 --> 00:11:53.448
If you have resistors and series,

00:11:53.448 --> 00:11:56.542
you add them up to get
an equivalent resistance.


Parallel resistors (part 1)

WEBVTT
Kind: captions
Language: en

00:00:01.220 --> 00:00:02.600
- [Voiceover] In this
video, we're gonna look at

00:00:02.600 --> 00:00:04.530
another familiar pattern of resistors

00:00:04.530 --> 00:00:06.632
called parallel resistors.

00:00:06.632 --> 00:00:10.567
And I've shown here two
resistors that are in parallel.

00:00:10.567 --> 00:00:13.764
This resistor is in
parallel with this resistor.

00:00:13.764 --> 00:00:17.685
And the reason is it shares nodes.

00:00:17.685 --> 00:00:19.825
These two resistors share the same nodes.

00:00:19.825 --> 00:00:22.340
And that means they have the same voltage.

00:00:22.340 --> 00:00:24.827
And they are called parallel resistors.

00:00:24.827 --> 00:00:26.463
So if you share a node.

00:00:29.520 --> 00:00:30.781
Share the same node.

00:00:34.205 --> 00:00:36.424
Then you share the same voltage.

00:00:46.914 --> 00:00:48.705
And you are in parallel.

00:00:51.795 --> 00:00:53.230
That's what that word means.

00:00:53.230 --> 00:00:55.323
Now, if we go look closer here,

00:00:55.323 --> 00:00:56.951
we'll see some interesting things.

00:00:58.101 --> 00:00:59.973
It's hooked up, we have a battery here,

00:00:59.973 --> 00:01:01.421
some voltage v.

00:01:02.461 --> 00:01:05.247
And because there's a path,
a complete path around here,

00:01:05.247 --> 00:01:06.637
we're gonna have a current.

00:01:06.637 --> 00:01:08.480
We're gonna have a current i

00:01:08.480 --> 00:01:10.168
flowing in this circuit.

00:01:11.158 --> 00:01:12.486
Let's label these resistors.

00:01:12.486 --> 00:01:15.632
Let's call this one R
one and this one R two.

00:01:17.522 --> 00:01:19.406
Those are our parallel resistors.

00:01:19.406 --> 00:01:21.458
When the current reaches this point here,

00:01:21.458 --> 00:01:23.380
when a current reaches this node,

00:01:23.380 --> 00:01:24.423
it's gonna split.

00:01:24.423 --> 00:01:26.245
It's gonna split into
two different currents.

00:01:26.245 --> 00:01:28.291
That current and that current.

00:01:28.291 --> 00:01:32.573
We'll call that one i one,
because it goes through R one.

00:01:32.573 --> 00:01:34.587
And we'll call this one i two.

00:01:34.587 --> 00:01:37.464
And that goes through R two.

00:01:37.464 --> 00:01:40.215
Now, we know any current
that goes into a resistor

00:01:40.215 --> 00:01:42.240
comes out the other side.

00:01:42.240 --> 00:01:44.605
Otherwise it would collect
inside the resistor,

00:01:44.605 --> 00:01:46.479
and we know that doesn't happen.

00:01:46.479 --> 00:01:47.839
This one comes here.

00:01:47.839 --> 00:01:50.231
And they rejoin when
they get to this node,

00:01:50.231 --> 00:01:52.065
and flow back to the battery.

00:01:52.065 --> 00:01:55.099
So the current down here is again i,

00:01:55.099 --> 00:01:56.646
the same one as up here.

00:01:58.246 --> 00:02:00.034
Now, what I want to do

00:02:00.034 --> 00:02:02.736
is I want to replace these two resistors

00:02:02.736 --> 00:02:05.931
with an equivalent resistor,
one that does the same thing.

00:02:05.931 --> 00:02:08.812
And by "the same thing," we mean

00:02:08.812 --> 00:02:13.812
causes the same current to
flow in the main branch.

00:02:14.415 --> 00:02:16.015
And so that's what's drawn over here.

00:02:16.015 --> 00:02:17.745
Here's a resistor here.

00:02:17.745 --> 00:02:20.068
We'll call this v again.

00:02:20.068 --> 00:02:23.207
And we'll call this R parallel.

00:02:23.207 --> 00:02:24.808
R P.

00:02:24.808 --> 00:02:29.808
And this resistor causes the
same current i to flow here.

00:02:32.148 --> 00:02:34.360
And now we're gonna work
out an expression for that.

00:02:35.950 --> 00:02:39.592
We want to figure out
how do we calculate R P

00:02:39.592 --> 00:02:42.809
in terms of the two
parallel resistors here.

00:02:42.809 --> 00:02:44.855
Okay, so let's go at it.

00:02:44.855 --> 00:02:45.820
What we know,

00:02:45.820 --> 00:02:48.135
let's see what we know
about this over here.

00:02:48.135 --> 00:02:49.637
What we know is the voltages

00:02:49.637 --> 00:02:51.594
on the two resistors are the same.

00:02:51.594 --> 00:02:53.948
We know there's two different currents,

00:02:53.948 --> 00:02:57.367
assuming that these are two
different-valued resistors.

00:02:57.367 --> 00:02:59.763
And now, with just that information,

00:02:59.763 --> 00:03:01.178
we can apply Ohm's law.

00:03:01.178 --> 00:03:03.410
And we use our favorite thing, Ohm's law.

00:03:08.870 --> 00:03:12.477
Which says that voltage
on a resistor equals

00:03:12.477 --> 00:03:15.318
the current in the resistor
times its resistance.

00:03:16.968 --> 00:03:18.515
So let's write down Ohm's law

00:03:18.515 --> 00:03:20.571
for R one and R two.

00:03:20.571 --> 00:03:24.872
Okay, we know the voltage,
we'll just call the voltage v.

00:03:24.872 --> 00:03:26.284
This is for R one.

00:03:29.706 --> 00:03:31.467
v equals

00:03:33.272 --> 00:03:37.048
i one times R one.

00:03:38.206 --> 00:03:43.154
And for R two, we can
write a similar equation,

00:03:43.154 --> 00:03:45.226
which is v, same v,

00:03:45.226 --> 00:03:48.686
equals i two R two.

00:03:51.076 --> 00:03:53.060
Now there's one more fact that we know,

00:03:53.060 --> 00:03:58.060
and that is that i one
and i two add up to i.

00:04:09.408 --> 00:04:10.500
And these are the three facts

00:04:10.500 --> 00:04:12.562
that we know about this circuit.

00:04:12.562 --> 00:04:14.251
What I'm gonna do now

00:04:14.251 --> 00:04:16.987
is come up with an expression
for i one and i two

00:04:16.987 --> 00:04:19.103
based on these expressions,

00:04:19.103 --> 00:04:20.849
plug them into this equation.

00:04:21.869 --> 00:04:24.485
Okay, I can rewrite this equation

00:04:24.485 --> 00:04:29.485
as i one equals v over R one.

00:04:30.051 --> 00:04:33.169
I can write this one as i two

00:04:34.488 --> 00:04:36.456
equals v over R two.

00:04:38.076 --> 00:04:40.432
And now I'm gonna plug
these two guys into here.

00:04:40.432 --> 00:04:41.974
Let's do that.

00:04:41.974 --> 00:04:46.644
i equals i one,

00:04:46.644 --> 00:04:50.339
which is v over R one

00:04:51.609 --> 00:04:55.953
plus v over R two.

00:04:56.982 --> 00:04:59.165
Let me move the screen up a little bit.

00:05:13.174 --> 00:05:14.440
Okay, now we're gonna continue here.

00:05:14.440 --> 00:05:16.387
I just want to rewrite this a little bit.

00:05:16.387 --> 00:05:20.708
i equals v

00:05:20.708 --> 00:05:24.326
times one over R one

00:05:25.596 --> 00:05:29.074
plus one over R two.

00:05:32.904 --> 00:05:35.218
Okay, so here we have an expression.

00:05:35.218 --> 00:05:37.755
It actually sort of looks like Ohm's law.

00:05:38.755 --> 00:05:41.044
It has an i term, a v term,

00:05:41.044 --> 00:05:44.917
and this R term here.

00:05:44.917 --> 00:05:46.302
Let me go back up here.

00:05:46.302 --> 00:05:47.704
Here's our original Ohm's law.

00:05:47.704 --> 00:05:48.745
I'm gonna write this,

00:05:48.745 --> 00:05:50.858
I'm gonna solve for i in terms of v,

00:05:50.858 --> 00:05:53.214
just to make it look
a little more obvious.

00:05:53.214 --> 00:05:57.907
I can say i equals v over R.

00:05:57.907 --> 00:05:59.414
And what I hope you see here

00:05:59.414 --> 00:06:01.115
is the similarity between this equation

00:06:01.115 --> 00:06:02.752
and this one down here.

00:06:02.752 --> 00:06:04.828
So I have this R here.

00:06:06.588 --> 00:06:08.559
And what's happening is this term

00:06:08.559 --> 00:06:12.905
is playing the role of that, resistance.

00:06:14.055 --> 00:06:16.427
So I'm gonna bring this
equation down here,

00:06:16.427 --> 00:06:18.147
and write it right down here.

00:06:24.360 --> 00:06:25.677
Times one over R.

00:06:27.977 --> 00:06:29.674
I'm gonna call this R P.

00:06:30.734 --> 00:06:32.523
Because what I want is

00:06:32.523 --> 00:06:35.660
for this expression and this expression,

00:06:35.660 --> 00:06:37.349
I'm gonna set those equal.

00:06:37.349 --> 00:06:39.995
Same i, same v.

00:06:39.995 --> 00:06:41.288
These guys are equal.

00:06:41.288 --> 00:06:43.415
I can write it all, I'll
just write it over here.

00:06:43.415 --> 00:06:47.469
One over R P equals

00:06:48.319 --> 00:06:50.486
one over R one

00:06:50.486 --> 00:06:55.486
plus one over R two.

00:06:55.545 --> 00:06:57.928
This says we have a resistor,

00:06:57.928 --> 00:07:00.426
we're gonna call it R P or R parallel,

00:07:00.426 --> 00:07:04.339
that acts like the parallel
combination of R one and R two.

00:07:07.078 --> 00:07:08.024
So this

00:07:12.006 --> 00:07:14.717
is the expression for a parallel resistor.

00:07:16.407 --> 00:07:18.489
If you want to calculate a replacement

00:07:18.489 --> 00:07:20.700
for R one and R two in parallel,

00:07:20.700 --> 00:07:25.700
you do this computation and you get R P.

00:07:25.853 --> 00:07:27.755
So let's do one of these for real.

00:07:30.763 --> 00:07:32.196
Here's an example.

00:07:37.644 --> 00:07:38.832
Here's an example where I've

00:07:38.832 --> 00:07:40.713
actually filled in some numbers for us.

00:07:40.713 --> 00:07:43.232
So I have a 20-ohm
resistor in parallel with

00:07:43.232 --> 00:07:46.533
a 60-ohm resistor, driven
by a three-volt battery.

00:07:46.533 --> 00:07:48.634
And what I want to do is I want to combine

00:07:48.634 --> 00:07:52.375
these two parallel resistors and find out

00:07:52.375 --> 00:07:55.205
what is the current right here.

00:07:55.205 --> 00:07:59.647
Find out what is the current,
that's my unknown thing here.

00:07:59.647 --> 00:08:01.378
I know everything else about this.

00:08:02.718 --> 00:08:03.932
So let's use our equation.

00:08:03.932 --> 00:08:05.485
We said that one over R P

00:08:07.715 --> 00:08:11.090
was equal to one over R one

00:08:11.090 --> 00:08:12.698
plus one over R two.

00:08:15.222 --> 00:08:16.747
And let's just fill in the numbers.

00:08:16.747 --> 00:08:21.314
One over R P equals one over 20

00:08:22.714 --> 00:08:25.003
plus one over 60.

00:08:25.983 --> 00:08:30.983
That equals, let's just make
60 the common denominator.

00:08:31.082 --> 00:08:33.766
So I have to multiply this one by three.

00:08:35.716 --> 00:08:40.422
Three over 60 plus one over 60.

00:08:41.622 --> 00:08:44.367
And that equals four over 60.

00:08:45.637 --> 00:08:48.439
And so now I'm gonna
take the reciprocal here.

00:08:48.439 --> 00:08:51.817
R P equals

00:08:53.129 --> 00:08:54.999
60 over four

00:08:56.429 --> 00:08:58.911
or R P equals

00:09:00.354 --> 00:09:02.734
15 ohms.

00:09:04.210 --> 00:09:06.263
So what this is telling us

00:09:06.263 --> 00:09:09.607
is if we have two resistors in parallel,

00:09:09.607 --> 00:09:11.217
20 ohms and 60 ohms,

00:09:11.217 --> 00:09:16.217
that is, for the purposes of
calculating the current here,

00:09:16.599 --> 00:09:18.417
that's the same as 15 ohms.

00:09:31.162 --> 00:09:32.583
It took the three volts.

00:09:32.583 --> 00:09:33.837
Just like that.

00:09:39.521 --> 00:09:41.023
Let's check what the current is.

00:09:41.023 --> 00:09:43.120
The current is i

00:09:44.010 --> 00:09:48.080
equals v over R

00:09:49.911 --> 00:09:54.911
equals three volts over 15 ohms.

00:09:56.772 --> 00:09:58.873
That's equal to 0.2 amps.

00:10:00.553 --> 00:10:05.553
Or you can say it's the
same as 200 milliamps.

00:10:10.237 --> 00:10:12.876
So we actually have now
simplified our circuit

00:10:12.876 --> 00:10:14.861
from two resistors to one resistor.

00:10:14.861 --> 00:10:19.538
And we were able to
compute the current here,

00:10:19.538 --> 00:10:24.427
which is 0.2 amps.

00:10:25.506 --> 00:10:26.954
And I would invite you to check this

00:10:26.954 --> 00:10:29.869
by going back and computing
this current up here

00:10:29.869 --> 00:10:31.053
to make sure it's the same.

00:10:31.053 --> 00:10:32.351
And the way you would do that

00:10:32.351 --> 00:10:34.382
is you would calculate the voltage.

00:10:34.382 --> 00:10:36.767
The voltage here is three volts.

00:10:36.767 --> 00:10:39.477
Three volts across 20,
three volts across 60.

00:10:39.477 --> 00:10:41.538
You'll get i one and i two.

00:10:41.538 --> 00:10:43.426
And if you add those together,

00:10:43.426 --> 00:10:45.518
you'll get the total i,

00:10:45.518 --> 00:10:47.621
and it should come out the same as this.

00:10:47.621 --> 00:10:51.068
And I think that's a good
exercise for you to do,

00:10:51.068 --> 00:10:55.158
to prove that the expression
for a parallel resistor,

00:10:55.158 --> 00:10:59.353
one over R parallel can be computed

00:10:59.353 --> 00:11:02.264
from one over R one

00:11:03.125 --> 00:11:06.284
plus one over R two.


Parallel resistors (part 2)

WEBVTT
Kind: captions
Language: en

00:00:00.369 --> 00:00:01.209
- [Voiceover] In the last video,

00:00:01.209 --> 00:00:03.089
we introduced the idea
of parallel resistors.

00:00:03.089 --> 00:00:05.609
These two resistors are in
parallel with each other

00:00:05.609 --> 00:00:07.889
because they share nodes and they have

00:00:07.889 --> 00:00:09.389
the same voltage across them.

00:00:09.389 --> 00:00:12.249
So that configuration is
called the parallel resistor.

00:00:12.249 --> 00:00:14.949
And we also showed that
these two resistors

00:00:14.949 --> 00:00:18.449
could be replaced by a single resistor

00:00:18.449 --> 00:00:22.229
we labeled this one R1, this is R2.

00:00:22.229 --> 00:00:25.229
We showed that we can replace R1 and R2

00:00:25.229 --> 00:00:28.729
by an equivalent parallel resistor

00:00:28.729 --> 00:00:31.789
with this expression
here for two resistors.

00:00:31.789 --> 00:00:36.789
RP ..one over RP equals one over R1 plus

00:00:38.289 --> 00:00:41.589
one over R2.

00:00:41.589 --> 00:00:44.189
So that's how you calculate
the equivalent resistance

00:00:44.189 --> 00:00:47.269
for two parallel resistors.

00:00:47.269 --> 00:00:50.209
Now you can ask and
it's a good thing to ask

00:00:50.209 --> 00:00:51.769
what if there's more resistors?

00:00:51.769 --> 00:00:54.489
What if there's more
resistors in parallel here?

00:00:54.489 --> 00:00:59.489
What if I have R3 and R4 and RN

00:01:02.049 --> 00:01:05.369
all connected up here.

00:01:07.629 --> 00:01:09.149
What happens in this expression?

00:01:14.559 --> 00:01:17.905
So like we did before
we had a current here

00:01:17.905 --> 00:01:19.935
and we know that current comes back here.

00:01:19.935 --> 00:01:23.115
The first current split, some current goes

00:01:23.115 --> 00:01:25.995
down through R1, some
current goes through R2

00:01:25.995 --> 00:01:28.515
and if we had more resistors
some goes down through

00:01:28.515 --> 00:01:32.325
R3, and some goes through RN.

00:01:33.955 --> 00:01:35.615
So the current basically
is coming down here

00:01:35.615 --> 00:01:38.475
and splitting amongst all the resistors.

00:01:38.475 --> 00:01:40.975
Now all the resistors share the same

00:01:40.975 --> 00:01:44.335
all the resistors share the same voltage.

00:01:44.335 --> 00:01:47.715
So that's just V, let's label V.

00:01:47.715 --> 00:01:50.195
That's just V, they all share the same V

00:01:50.195 --> 00:01:51.735
and they all have a different current.

00:01:51.735 --> 00:01:54.475
Assuming they all have a
different resistance value.

00:01:54.475 --> 00:01:56.295
So we do exactly the same analysis

00:01:56.295 --> 00:01:57.335
that we did before.

00:01:57.335 --> 00:02:01.295
Which was, we know that I here

00:02:01.295 --> 00:02:03.175
here

00:02:03.175 --> 00:02:04.625
has to be the sum,

00:02:06.815 --> 00:02:08.045
there's the summation symbol

00:02:10.255 --> 00:02:12.898
of all the I's.

00:02:12.898 --> 00:02:14.618
I1, plus I2, plus I3

00:02:14.618 --> 00:02:18.458
plus IN, that's as many as we have.

00:02:18.458 --> 00:02:19.458
So we know that's true.

00:02:19.458 --> 00:02:22.718
And we also know that

00:02:22.718 --> 00:02:24.679
the current, we also know that the current

00:02:24.679 --> 00:02:27.419
in each individual resistor

00:02:28.443 --> 00:02:30.571
IN

00:02:31.941 --> 00:02:33.981
is equal to one over that resistor

00:02:35.781 --> 00:02:39.121
times V, and V is the same
for every one of them.

00:02:39.121 --> 00:02:43.481
So now we substitute this
equation into here for I

00:02:45.521 --> 00:02:47.221
For I.

00:02:47.221 --> 00:02:52.221
We get the big I, the
overall I is equal to

00:02:53.900 --> 00:02:57.468
voltage times, it's gotta
be a big expression,

00:02:57.468 --> 00:03:01.918
one over R1 plus one over R2

00:03:03.948 --> 00:03:08.948
plus one over R3, plus as
many resistors as we have

00:03:13.508 --> 00:03:18.234
One over RN, like that.

00:03:19.834 --> 00:03:21.664
And we do the same thing as we did before

00:03:21.664 --> 00:03:23.774
which was we say that this expression here

00:03:23.774 --> 00:03:27.434
is equivalent to one parallel resistor

00:03:27.434 --> 00:03:29.574
we're going to make the equal
to one parallel resistor.

00:03:29.574 --> 00:03:32.634
So this whole guy here is gonna become

00:03:32.634 --> 00:03:35.694
one over RP

00:03:37.254 --> 00:03:39.814
That gives us a way to simplify
any number of resistors

00:03:39.814 --> 00:03:42.974
down to a single parallel resistor

00:03:42.974 --> 00:03:44.854
and I'll write that over here.

00:03:44.854 --> 00:03:47.614
So for N resistors, multiple resistors

00:03:47.614 --> 00:03:51.654
one over RP the equivalent
parallel resistor

00:03:51.654 --> 00:03:54.054
is equal to the same thing.

00:03:54.054 --> 00:03:58.054
One over R1 plus one over R2

00:03:59.898 --> 00:04:04.898
plus dot, dot, dot, one over RN.

00:04:05.247 --> 00:04:07.247
So this tells you how to simplify

00:04:08.947 --> 00:04:11.007
any number of parallel resistors

00:04:11.007 --> 00:04:14.375
down to one equivalent parallel resistor.


2015 AP Chemistry free response 2a (part 1 of 2)

WEBVTT
Kind: captions
Language: en

00:00:00.363 --> 00:00:03.794
- [Voiceover] Ethene, C2H4, molar mass

00:00:03.794 --> 00:00:08.440
of 28.1 grams per mole, may be prepared

00:00:08.440 --> 00:00:10.670
by the dehydration of ethanol,

00:00:10.670 --> 00:00:15.554
C2H5OH, molar mass 46.1 grams

00:00:15.554 --> 00:00:18.688
per mole, using a solid catalyst.

00:00:18.688 --> 00:00:20.947
A setup for the lab synthesis is shown

00:00:20.947 --> 00:00:22.595
in the diagram above.

00:00:22.595 --> 00:00:25.289
The equation for the dehydration reaction

00:00:25.289 --> 00:00:27.408
is given below.

00:00:27.408 --> 00:00:30.154
So, we have the ethanol,
and then in the presence

00:00:30.154 --> 00:00:33.609
of a catalyst, we're going
to yield, after our reaction,

00:00:33.609 --> 00:00:37.156
some ethene and some
water, and then we have

00:00:37.156 --> 00:00:39.971
some metrics on the actual reaction.

00:00:39.971 --> 00:00:44.649
A student added a 0.200 gram

00:00:44.649 --> 00:00:49.433
sample of ethanol, this is ethanol,

00:00:49.433 --> 00:00:54.433
C2H5OH, to a test tube,
using the setup shown above.

00:00:54.537 --> 00:00:57.809
So this is the glass wool with ethanol,

00:00:57.809 --> 00:00:59.971
so the ethanol is right over here.

00:00:59.971 --> 00:01:02.961
There's a solid catalyst right over there.

00:01:02.961 --> 00:01:05.277
The student heated the test tube gently

00:01:05.277 --> 00:01:09.208
with a Bunsen burner until
all of the ethanol evaporated,

00:01:09.208 --> 00:01:11.655
and gas generation stopped.

00:01:11.655 --> 00:01:14.397
So, here you see the heating,
all of the ethanol here

00:01:14.397 --> 00:01:17.216
evaporates, the gas generation stops.

00:01:17.216 --> 00:01:20.334
When the reaction stopped,
the volume of gas collected

00:01:20.334 --> 00:01:24.241
was 0.0854 liters

00:01:24.241 --> 00:01:27.711
at 0.822 atmospheres

00:01:27.711 --> 00:01:30.031
and 305 Kelvin.

00:01:30.031 --> 00:01:31.747
The vapor pressure of water

00:01:31.747 --> 00:01:36.018
at 305 Kelvin is 35.7 torr.

00:01:36.018 --> 00:01:39.437
So, what you have is, in the
presence of the catalyst,

00:01:39.437 --> 00:01:42.032
you have the ethanol, it's going to react,

00:01:42.032 --> 00:01:45.103
it's a dehydration, it's
a dehydration reaction

00:01:45.103 --> 00:01:46.770
right over here, so
you're going to produce

00:01:46.770 --> 00:01:50.062
ethene and water, and
so, you cool it down,

00:01:50.062 --> 00:01:51.920
and so the ethene gets
captured at the top,

00:01:51.920 --> 00:01:53.680
it's going to be in a gaseous state.

00:01:53.680 --> 00:01:56.449
The water, it's going to be water vapor,

00:01:56.449 --> 00:01:59.126
but then, of course, once
you've cooled it down,

00:01:59.126 --> 00:02:01.449
you're going to have
liquid, you're going to have

00:02:01.449 --> 00:02:05.111
liquid water here as well.

00:02:05.111 --> 00:02:08.639
So, let's try to answer their questions.

00:02:08.639 --> 00:02:12.868
Calculate the number of moles of ethene,

00:02:12.868 --> 00:02:15.104
one, that are actually
produced in the experiment

00:02:15.104 --> 00:02:18.001
and measured in the gas collection tube,

00:02:18.001 --> 00:02:19.366
and two, that would be produced

00:02:19.366 --> 00:02:22.042
if the dehydration reaction
went to completion.

00:02:22.042 --> 00:02:24.158
Part b, calculate the percent yield

00:02:24.158 --> 00:02:26.754
of ethene in the experiment.

00:02:26.754 --> 00:02:29.123
All right, so let's tackle part one.

00:02:29.123 --> 00:02:31.823
Let's tackle part one first, and so,

00:02:31.823 --> 00:02:33.667
somehow we have to figure out the,

00:02:33.667 --> 00:02:35.687
we have to figure out the actual moles

00:02:35.687 --> 00:02:38.052
produced in the experiment and measured

00:02:38.052 --> 00:02:39.844
in the gas collection tube.

00:02:39.844 --> 00:02:41.231
So, what do they tell us here?

00:02:41.231 --> 00:02:42.967
They said until all of
the ethanol evaporated

00:02:42.967 --> 00:02:44.412
and gas generation stopped.

00:02:44.412 --> 00:02:47.461
When the reaction stopped,
the volume of gas,

00:02:47.461 --> 00:02:52.425
so this volume of gas, so
this is our volume of gas

00:02:52.425 --> 00:02:54.880
right over here, that's
where our ethene is,

00:02:54.880 --> 00:02:58.113
our volume of gas was

00:02:58.113 --> 00:03:01.853
0.0854 liters,

00:03:01.853 --> 00:03:04.245
so we underline that,

00:03:05.165 --> 00:03:08.865
at 0.822 atmospheres,

00:03:08.865 --> 00:03:10.925
so that's the total pressure there.

00:03:10.925 --> 00:03:13.549
The temperature is 305 Kelvin,

00:03:13.549 --> 00:03:15.105
and then they give us the vapor pressure

00:03:15.105 --> 00:03:19.482
of water is 35.7, at 305 Kelvin,

00:03:19.482 --> 00:03:21.629
is 35.7 torr.

00:03:21.629 --> 00:03:22.687
The vapor pressure of water,

00:03:22.687 --> 00:03:24.319
you could view that as a partial pressure

00:03:24.319 --> 00:03:27.640
of water, and the reason
why that's useful is

00:03:27.640 --> 00:03:29.998
the partial pressure of water plus

00:03:29.998 --> 00:03:31.989
the partial pressure of the ethene

00:03:31.989 --> 00:03:35.606
is going to add up to
the total pressure here.

00:03:35.606 --> 00:03:37.378
And so, we can use that information

00:03:37.378 --> 00:03:40.368
to figure out the partial
pressure of the ethene.

00:03:40.368 --> 00:03:43.497
So, the partial pressure of the ethene.

00:03:43.497 --> 00:03:47.091
And if we know the partial
pressure of the ethene,

00:03:47.091 --> 00:03:48.826
well, then we can use the Ideal Gas Law

00:03:48.826 --> 00:03:51.003
to figure out how many moles of ethene,

00:03:51.003 --> 00:03:55.041
how many moles of ethene are
actually right over here.

00:03:55.041 --> 00:03:56.172
How can we do that?

00:03:56.172 --> 00:03:59.136
Well, just a little reminder
of the Ideal Gas Law.

00:03:59.136 --> 00:04:01.753
We have pressure, and
if we're talking about

00:04:01.753 --> 00:04:03.521
one particular thing, here we'd be talking

00:04:03.521 --> 00:04:05.592
about the partial pressure of ethene,

00:04:05.592 --> 00:04:08.869
times volume, they give us
the volume right over here,

00:04:08.869 --> 00:04:13.680
is equal to the number of
moles times the gas constant

00:04:13.680 --> 00:04:16.686
times the temperature.

00:04:16.686 --> 00:04:18.822
Well, we have the pressure,
we have-- or, we'll be able

00:04:18.822 --> 00:04:21.358
to figure it out, we have the volume,

00:04:21.358 --> 00:04:23.265
we have the gas constant.

00:04:23.265 --> 00:04:24.952
You don't have to memorize these things.

00:04:24.952 --> 00:04:26.488
Right over here, I copied and pasted

00:04:26.488 --> 00:04:29.398
what they give you at the
front of the actual AP exam,

00:04:29.398 --> 00:04:31.144
so that you don't have to
memorize these constants

00:04:31.144 --> 00:04:32.139
and things like that.

00:04:32.139 --> 00:04:34.544
So, we have the gas
constant, and then we have it

00:04:34.544 --> 00:04:35.956
in different units, depending on which one

00:04:35.956 --> 00:04:37.588
we want to use, and then, of course,

00:04:37.588 --> 00:04:38.965
the temperature, they give it to us.

00:04:38.965 --> 00:04:41.271
It is 305 Kelvin.

00:04:41.271 --> 00:04:44.267
So, if we want to figure
out the number of moles,

00:04:44.267 --> 00:04:46.187
right over here, you can divide both sides

00:04:46.187 --> 00:04:50.826
by RT, and so you could say n is equal to,

00:04:50.826 --> 00:04:54.646
is equal to R, sorry, n is equal to,

00:04:54.646 --> 00:04:58.121
we divide both sides,
if we divide both sides

00:04:58.121 --> 00:05:01.971
by RT, we're going to get PV, and I'll say

00:05:01.971 --> 00:05:04.784
the partial pressure of ethene,

00:05:04.784 --> 00:05:06.848
the partial pressure of ethene,

00:05:06.848 --> 00:05:10.069
times the volume, times the volume,

00:05:10.069 --> 00:05:15.069
over, over R times T

00:05:15.395 --> 00:05:17.845
over R times T.

00:05:17.845 --> 00:05:20.164
And so, let's figure out
everything over here.

00:05:20.164 --> 00:05:22.871
So, what is going to be the
partial pressure of the ethene?

00:05:22.871 --> 00:05:25.118
Well, the pressure of,
the partial pressure

00:05:25.118 --> 00:05:27.875
of the ethene is going to be equal

00:05:27.875 --> 00:05:31.179
to the total pressure, the total pressure

00:05:31.179 --> 00:05:33.426
minus the partial pressure,

00:05:33.426 --> 00:05:35.324
or you could say the vapor
pressure, of the water,

00:05:35.324 --> 00:05:39.637
the partial pressure of, the
partial pressure of the water.

00:05:39.637 --> 00:05:41.466
So, this is going to be equal to,

00:05:41.466 --> 00:05:46.466
our total pressure is 0.822 atmospheres,

00:05:46.767 --> 00:05:51.767
0.822 atmospheres.

00:05:51.951 --> 00:05:53.731
Now, what's the pressure of,

00:05:53.731 --> 00:05:55.118
what's the partial pressure of the water?

00:05:55.118 --> 00:05:56.226
They tell us the vapor pressure

00:05:56.226 --> 00:06:00.288
of water at 305 Kelvin is 35.7 torr.

00:06:00.288 --> 00:06:02.903
Well, they gave us the total
pressure in atmospheres,

00:06:02.903 --> 00:06:05.218
so we have to convert
from, we have to convert

00:06:05.218 --> 00:06:07.695
from torrs to atmospheres
if we want to stay

00:06:07.695 --> 00:06:08.872
in atmospheres.

00:06:08.872 --> 00:06:09.978
So I'll do it over here.

00:06:09.978 --> 00:06:13.808
So, the pressure, the pressure
of, the partial pressure

00:06:13.808 --> 00:06:18.808
of the water is equal to 35.7 torr,

00:06:18.940 --> 00:06:21.026
which is a unit of pressure.

00:06:21.026 --> 00:06:22.836
But if we want to convert
it to atmospheres,

00:06:22.836 --> 00:06:24.599
once again, you don't have
to memorize these things.

00:06:24.599 --> 00:06:26.119
They give it to you on the test.

00:06:26.119 --> 00:06:29.941
They tell us, one atmosphere is 760 torr.

00:06:29.941 --> 00:06:32.353
So, we wanna get rid of the torr.

00:06:32.353 --> 00:06:34.313
We wanna get rid of the
torr, and we want it

00:06:34.313 --> 00:06:38.851
in terms of atmospheres,
so one atmosphere is

00:06:38.851 --> 00:06:42.392
760 torr, so this is going to be equal

00:06:42.392 --> 00:06:46.425
to 35.7 divided by 760.

00:06:46.425 --> 00:06:48.521
So it's this is the total pressure,

00:06:48.521 --> 00:06:50.791
minus the partial pressure of the water.

00:06:50.791 --> 00:06:52.626
Let's see, the partial
pressure of the water,

00:06:52.626 --> 00:06:54.483
let me figure this out.

00:06:54.483 --> 00:06:58.480
It is going to be 35.7 torr

00:06:58.480 --> 00:07:00.500
times one atmosphere

00:07:00.500 --> 00:07:04.996
for every 760 torr, so
I'll just divide by 760,

00:07:04.996 --> 00:07:07.806
divided by 760, is equal to,

00:07:07.806 --> 00:07:10.232
and I have three significant digits here.

00:07:10.232 --> 00:07:15.232
So, 0.0470.

00:07:16.007 --> 00:07:19.737
0.0470.

00:07:19.737 --> 00:07:21.294
So this is going to be

00:07:22.644 --> 00:07:27.624
0.0470 atmospheres.

00:07:28.854 --> 00:07:30.005
So, let me write that down.

00:07:30.005 --> 00:07:32.739
So, the total pressure
minus the partial pressure

00:07:32.739 --> 00:07:33.677
of the water,

00:07:33.677 --> 00:07:38.677
0.0470 atmospheres,

00:07:39.287 --> 00:07:43.556
is going to be equal to,
is going to be equal to--

00:07:43.556 --> 00:07:45.716
So, let me just take my--

00:07:45.716 --> 00:07:48.042
Well, I could just make that a negative,

00:07:48.042 --> 00:07:49.871
and then add it to the total pressure,

00:07:49.871 --> 00:07:54.642
so, plus, plus .822

00:07:54.642 --> 00:07:58.376
or 0.822 is going to be equal to...

00:07:58.376 --> 00:08:01.153
So, the partial pressure of our ethene,

00:08:01.153 --> 00:08:02.889
three significant digits here,

00:08:02.889 --> 00:08:07.249
is going to be 775, 0.775.

00:08:07.249 --> 00:08:12.249
So, 0.775.

00:08:12.306 --> 00:08:14.132
And so now, we can substitute that in.

00:08:14.132 --> 00:08:16.355
We know everything to figure
out the number of moles.

00:08:16.355 --> 00:08:21.273
N is going to be equal to 0.775.

00:08:21.273 --> 00:08:23.148
The units here are atmospheres;

00:08:23.148 --> 00:08:24.340
we can always check to make sure

00:08:24.340 --> 00:08:27.458
that we get that right, atmospheres.

00:08:27.458 --> 00:08:29.016
Times our volume.

00:08:29.016 --> 00:08:30.299
Well, they tell us our volume.

00:08:30.299 --> 00:08:33.248
It's 0.0854 liters,

00:08:33.248 --> 00:08:38.248
0.0854 liters,

00:08:38.628 --> 00:08:41.835
and then we divide that by RT.

00:08:41.835 --> 00:08:44.304
Now, which version of R do we use?

00:08:44.304 --> 00:08:47.552
Well, we're dealing with atmospheres,

00:08:47.552 --> 00:08:50.308
moles, and Kelvin, so we could use,

00:08:50.308 --> 00:08:52.818
we could use this right over here.

00:08:52.818 --> 00:08:54.495
If we had converted everything to torr,

00:08:54.495 --> 00:08:57.351
we would use this constant.

00:08:57.351 --> 00:08:59.684
So, our R is going to be

00:08:59.684 --> 00:09:04.474
0.08206.

00:09:04.474 --> 00:09:06.369
They're giving us more significant digits.

00:09:06.369 --> 00:09:07.834
Doesn't hurt to use
them, but later we have

00:09:07.834 --> 00:09:10.051
to just realize that we're gonna convert

00:09:10.051 --> 00:09:11.410
to only three significant digits,

00:09:11.410 --> 00:09:13.709
because that's the minimum,
that's what we have.

00:09:13.709 --> 00:09:16.165
These are three, three, this
is more than three signifi--

00:09:16.165 --> 00:09:17.814
This is four significant digits.

00:09:17.814 --> 00:09:19.690
But let's just make
sure the units work out.

00:09:19.690 --> 00:09:21.342
So, this is going to be--

00:09:21.342 --> 00:09:26.342
So this is the units here
are liters times atmosphere,

00:09:26.699 --> 00:09:30.915
and so those will cancel
with these, divided by,

00:09:30.915 --> 00:09:33.463
we have to remember this is
in, this is in the denominator

00:09:33.463 --> 00:09:38.463
right over here, divided
by moles times Kelvin,

00:09:38.625 --> 00:09:40.939
and we multiply that
times the temperature,

00:09:40.939 --> 00:09:45.206
which is 305 Kelvin, 305 Kelvin.

00:09:45.206 --> 00:09:48.719
And we'll see, we could see that, well,

00:09:48.719 --> 00:09:50.002
this atmospheres is going to cancel

00:09:50.002 --> 00:09:51.709
with that atmospheres,
that liters is going

00:09:51.709 --> 00:09:53.810
to cancel with that liters,
this Kelvin is going

00:09:53.810 --> 00:09:56.974
to cancel with that Kelvin,
and so, in the denominator,

00:09:56.974 --> 00:09:58.294
you're dividing by moles, so that's gonna

00:09:58.294 --> 00:10:00.837
be the same thing as just
having moles as your units.

00:10:00.837 --> 00:10:02.943
And so, this is all going to be equal to,

00:10:02.943 --> 00:10:04.619
we deserve a little bit of a,

00:10:04.619 --> 00:10:06.776
we deserve a little
bit of a drumroll here.

00:10:06.776 --> 00:10:08.787
This is equal to--

00:10:08.787 --> 00:10:13.778
So, 0.775 atmospheres

00:10:15.508 --> 00:10:20.489
times .0854 liters

00:10:23.539 --> 00:10:28.539
divided by .08206,

00:10:30.981 --> 00:10:32.282
so that gets us that,

00:10:32.282 --> 00:10:34.525
and then we're going to divide by 305.

00:10:34.525 --> 00:10:36.166
We still have that in the denominator,

00:10:36.166 --> 00:10:38.586
divided by 305,

00:10:38.586 --> 00:10:42.203
is equal to, and if we do
three significant digits,

00:10:42.203 --> 00:10:47.134
it's 0.00264.

00:10:47.134 --> 00:10:49.681
So this is approximately, I could say,

00:10:49.681 --> 00:10:54.563
0.00264

00:10:54.563 --> 00:10:56.578
264 moles.

00:10:56.578 --> 00:10:58.593
Did I write that right?
I have a bad memory.

00:10:58.593 --> 00:11:01.176
0.00264, yeah,

00:11:01.176 --> 00:11:03.886
I rounded down to 264 moles.

00:11:03.886 --> 00:11:06.064
And there you have it, that's part one.

00:11:06.064 --> 00:11:09.034
The number of moles of ethene
that are actually produced

00:11:09.034 --> 00:11:12.489
in the experiment and measured
in the gas collection tube.


2015 AP Chemistry free response 2a (part 2/2) and b

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.678
- [Voiceover] Alright I'll tackle.

00:00:01.678 --> 00:00:04.924
In the last video we did
the first part of part A,

00:00:04.924 --> 00:00:07.606
now, so the second part of part A.

00:00:07.606 --> 00:00:11.466
So, the second part of part A,

00:00:11.466 --> 00:00:16.262
they say, "Calculate the
number of moles of ethene

00:00:16.262 --> 00:00:19.065
that would be produced if
the dehydration reaction

00:00:19.065 --> 00:00:21.002
went to completion".

00:00:21.842 --> 00:00:25.484
Well, this is the dehydration
reaction right over here,

00:00:25.484 --> 00:00:26.935
and they're telling us,

00:00:26.935 --> 00:00:28.944
they're telling us that we start

00:00:28.944 --> 00:00:32.769
with 0.200 grams

00:00:32.769 --> 00:00:34.459
of ethanol,

00:00:34.459 --> 00:00:36.811
so, if we start with

00:00:36.811 --> 00:00:41.541
0.200 grams of ethanol,

00:00:41.541 --> 00:00:44.672
and if we figure out how many
moles of ethanol that is,

00:00:44.672 --> 00:00:46.394
well, for every mole of ethanol,

00:00:46.394 --> 00:00:48.992
if we have the reaction go to,

00:00:48.992 --> 00:00:51.617
if the dehydration reaction
goes to completion,

00:00:51.617 --> 00:00:54.392
for every mole of ethanol
that we start with,

00:00:54.392 --> 00:00:57.017
we're going to have a mole of ethene,

00:00:57.017 --> 00:00:58.793
and a mole of water.

00:00:58.793 --> 00:00:59.732
So, if we can just figure out

00:00:59.732 --> 00:01:02.573
how many moles of ethanol this is,

00:01:02.573 --> 00:01:05.191
then we'll say, "Okay, if
this were completely react,

00:01:05.191 --> 00:01:08.264
we would have that many moles of ethene".

00:01:08.264 --> 00:01:09.939
So, let's figure this out.

00:01:09.939 --> 00:01:11.951
So if we say,

00:01:11.951 --> 00:01:14.698
so, we have ethanol,

00:01:15.868 --> 00:01:18.212
so for ethanol,

00:01:18.212 --> 00:01:21.275
we are starting with zero

00:01:21.275 --> 00:01:24.745
.200 grams,

00:01:24.745 --> 00:01:27.390
and we wanna convert this to moles,

00:01:27.390 --> 00:01:29.632
so we wanna multiply this times,

00:01:29.632 --> 00:01:31.490
we want grams in the denominator

00:01:31.490 --> 00:01:32.953
to cancel out with this grams,

00:01:32.953 --> 00:01:35.144
and moles in the numerator.

00:01:35.144 --> 00:01:38.564
So, one mole of ethanol is,

00:01:38.564 --> 00:01:41.104
as a mass of how many grams,

00:01:41.104 --> 00:01:44.147
well, they tell us that
earlier on the problem,

00:01:44.147 --> 00:01:46.005
they say, "Ethanol,

00:01:46.005 --> 00:01:50.295
molar mass 46.1 grams per mol",

00:01:50.295 --> 00:01:55.295
so, ethanol, molar mass
of 46.1 grams per mol,

00:01:55.583 --> 00:01:56.963
or another way to thinking about it,

00:01:56.963 --> 00:01:58.874
one mole would have mass of 46.1 grams

00:01:58.874 --> 00:02:02.664
of 46.1 grams,

00:02:02.664 --> 00:02:05.928
and so if we do this, we are going to get

00:02:05.928 --> 00:02:10.058
0.200 over

00:02:10.058 --> 00:02:12.268
46.1,

00:02:12.268 --> 00:02:14.456
and then grams cancel with the grams,

00:02:14.456 --> 00:02:16.526
and that going to be
how many moles we have,

00:02:16.526 --> 00:02:18.592
and this is going to be equal to,

00:02:18.592 --> 00:02:20.125
we have three significant digits

00:02:20.125 --> 00:02:21.807
that we're gonna be with
three significant digits

00:02:21.807 --> 00:02:24.452
divided by three significant digits,

00:02:24.452 --> 00:02:26.753
so this is going to be

00:02:26.753 --> 00:02:29.336
all right, so we clear this,

00:02:29.336 --> 00:02:32.359
so .2, I could write 00,

00:02:32.359 --> 00:02:33.485
but it's going to,

00:02:33.485 --> 00:02:35.367
for the calculator's purposes
this is the same thing,

00:02:35.367 --> 00:02:39.882
divided by 46.1 is equal to

00:02:41.102 --> 00:02:43.772
0.0043,

00:02:43.772 --> 00:02:45.908
I want three significant figures here,

00:02:45.908 --> 00:02:50.471
so 43 I'm gonna round up, 434,

00:02:50.471 --> 00:02:52.997
.00434

00:02:52.997 --> 00:02:57.997
so 0.00434

00:02:58.155 --> 00:02:59.165
moles.

00:02:59.165 --> 00:03:00.359
So, we've seen so far,

00:03:00.359 --> 00:03:03.450
if the ethanol were
(mumbling) the reaction,

00:03:03.450 --> 00:03:06.488
if we have this many moles of ethanol,

00:03:06.488 --> 00:03:08.581
well, and if they completely react,

00:03:08.581 --> 00:03:12.416
well, then we should end up
with that many moles of ethene,

00:03:12.416 --> 00:03:14.985
and so if we have,

00:03:14.985 --> 00:03:16.615
if it we get a dehydration,

00:03:16.615 --> 00:03:17.449
I'm gonna write it this way,

00:03:17.449 --> 00:03:19.751
if dehydration

00:03:21.571 --> 00:03:24.811
dehydration reaction

00:03:26.171 --> 00:03:27.251
goes to completion

00:03:28.551 --> 00:03:30.501
goes to completion

00:03:33.451 --> 00:03:34.908
every

00:03:35.898 --> 00:03:38.128
every mole of ethanol

00:03:41.458 --> 00:03:44.408
would be converted

00:03:47.378 --> 00:03:51.761
to a mole of ethene

00:03:53.991 --> 00:03:58.041
and a mole of water.

00:03:58.941 --> 00:04:01.064
I shouldn't write the shorthand there,

00:04:01.064 --> 00:04:02.446
a mole, if I'm writing it out,

00:04:02.446 --> 00:04:06.217
mole of and a mole water.

00:04:10.717 --> 00:04:15.395
So 0.00434

00:04:15.395 --> 00:04:19.385
mole of ethanol

00:04:20.745 --> 00:04:21.525
would

00:04:22.905 --> 00:04:23.905
yield,

00:04:24.905 --> 00:04:26.710
that same number of moles,

00:04:28.220 --> 00:04:32.260
0.00434

00:04:32.260 --> 00:04:36.520
moles of ethene.

00:04:36.520 --> 00:04:37.885
So, if the reaction went to completion

00:04:37.885 --> 00:04:39.342
that how many moles it would produce.

00:04:39.342 --> 00:04:42.176
What we actually measure is
a smaller number than that,

00:04:42.176 --> 00:04:45.145
so the reaction didn't
go fully to completion.

00:04:45.145 --> 00:04:47.267
So now let's tackle part B,

00:04:47.267 --> 00:04:50.939
let's tackle part B, and they ask us,

00:04:50.939 --> 00:04:54.641
"Calculate he percent yield
of ethene in the experiment".

00:04:54.641 --> 00:04:58.589
Well, the percent yield is
going to be how much we got,

00:04:58.589 --> 00:05:00.914
divide by how much we
would ideally have gotten

00:05:00.914 --> 00:05:03.674
if the reaction went fully to completion.

00:05:03.674 --> 00:05:04.560
So yield

00:05:05.710 --> 00:05:10.260
yield is going to be equal
to how much we actually got,

00:05:10.260 --> 00:05:12.109
which we figured out in part one,

00:05:12.109 --> 00:05:16.352
so 0.00264

00:05:16.352 --> 00:05:20.592
moles over what we
actually got, i'm sorry,

00:05:20.592 --> 00:05:23.713
what we actually got over
what we'd have ideally gotten

00:05:23.713 --> 00:05:25.735
if the reaction went to completion,

00:05:25.735 --> 00:05:27.638
so divided by

00:05:27.638 --> 00:05:32.538
0.00434

00:05:32.538 --> 00:05:33.548
moles,

00:05:33.548 --> 00:05:35.387
and this is going to be equal to

00:05:36.377 --> 00:05:38.579
this is going to be equal to

00:05:39.459 --> 00:05:43.761
so, 00264

00:05:43.761 --> 00:05:45.581
divided by

00:05:47.141 --> 00:05:52.141
00434, is equal to,

00:05:52.565 --> 00:05:54.724
and let's see, we have three
significant digits here,

00:05:54.724 --> 00:05:57.528
so 60, I can say .608,

00:05:57.528 --> 00:06:00.898
or I could say 60.8% yield.

00:06:00.898 --> 00:06:03.605
So, I'm gonna write this as

00:06:05.035 --> 00:06:06.335
actually this is gonna, I'm rounding,

00:06:06.335 --> 00:06:11.335
so I can say 60.8% yield,

00:06:11.571 --> 00:06:13.034
and there you go.