## Barry Halliwell and John M. C. Gutteridge

Print publication date: 2015

Print ISBN-13: 9780198717478

Published to Oxford Scholarship Online: October 2015

DOI: 10.1093/acprof:oso/9780198717478.001.0001

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# (p.697) Appendix Some basic chemistry

Source:
Free Radicals in Biology and Medicine
Publisher:
Oxford University Press

# A1 Atomic structure

Atoms consist of a positively charged nucleus surrounded by one or more negatively charged electrons. The nucleus contains two types of particle of approximately equal mass, the positively charged proton and the uncharged neutron. By comparison with these particles, the mass of the electron is negligible, so that virtually all of the mass of the atom is contributed by its nucleus. The atomic number of an element is the number of protons in its nucleus, the mass number is the number of protons plus neutrons. In the neutral atom, the atomic number also equals the number of electrons. The simplest atom is that of hydrogen, containing one proton (atomic number one, mass number one) and one electron. All other elements contain neutrons in the nucleus.

Some elements exist as isotopes, in which the atoms contain the same number of protons and electrons, but different numbers of neutrons. These isotopes can be stable (e.g. 15N) or unstable, the unstable ones undergoing radioactive decay at various rates (e.g. 14C). In this process, the nucleus of the radioactive isotope changes, and a new element forms. Carbon, hydrogen, nitrogen, and oxygen exist almost exclusively as one isotopic form in nature (Table A1), whereas chlorine is a mixture.

Table A1 Isotopes of some common elements.

Element

Isotope

Number of protons in nucleus

Number of neutrons in nucleus

Chlorine

$1735Cl$

17

18

Both isotopes are stable and occur naturally, 35Cl being more abundant.

$1737Cl$

17

20

Carbon

$612C$

6

6

Over 90% of naturally occurring carbon is $612C.$. Small amounts of the radioactive isotope $614C$ are formed by the bombardment of atmospheric CO2 with cosmic rays (streams of neutrons arising from outer space). This isotope undergoes slow radioactive decay (50% decay after 5600 years).

$613C$

6

7

$614C$

6

8

Nitrogen

$714N$

7

7

15N is a stable isotope of nitrogen often used as a ‘tracer’, e.g. $15NO3−$ can be fed to humans to study its metabolism.

$715N$

7

8

Oxygen

$816O$

8

8

Over 90% of naturally occurring oxygen is the isotope $816O$.

$817O$

8

9

$818O$

8

10

Hydrogen

$11H$

1

0

Over 99% of hydrogen is $11H$. Deuterium $(12H)$ is a stable isotope, whereas tritium $(13H)$ is radioactive. Deuterium oxide is known as ‘heavy water’, and is used in detecting singlet O2 (Section 6.8.3).

$12H$

1

1

$13H$

1

2

The superscript number on the left of the symbol for the element is the mass number, and the subscript the atomic number.

Electrons are negatively charged. Since they do not spiral into the positively charged nucleus, they must possess energy to counteract its attractive force. Electrons exist in specific orbits, or ‘electron shells’, each associated with a particular energy level. The ‘K’-shell electrons, lying closest to the nucleus, have the lowest energy, and the energy successively increases as one proceeds outwards to the so-called M- and N-shells. The K-shell can hold a maximum of two electrons, the L-shell, 8, M-shell, 18 and N-shell, 32. Table A2 shows the location of electrons in each of these shells for the elements up to atomic number 36.

Table A2 Location of electrons in shells for the elements with atomic numbers 1 to 36.

Atomic number of element

Element

Symbol

Shell K

Shell L

Shell M

Shell N

1

Hydrogen

H

1

2

Helium

He

2

3

Lithium

Li

2

1

4

Beryllium

Be

2

2

5

Boron

B

2

3

6

Carbon

C

2

4

7

Nitrogen

N

2

5

8

Oxygen

O

2

6

9

Fluorine

F

2

7

10

Neon

Ne

2

8

11

Sodium

Na

2

8

1

12

Magnesium

Mg

2

8

2

13

Aluminium

Al

2

8

3

14

Silicon

Si

2

8

4

15

Phosphorus

P

2

8

5

16

Sulphur

S

2

8

6

17

Chlorine

Cl

2

8

7

18

Argon

Ar

2

8

8

19

Potassium

K

2

8

8

1

20

Calcium

Ca

2

8

8

2

21

Scandium

Sc

2

8

9

2

22

Titanium

Ti

2

8

10

2

23

V

2

8

11

2

24

Chromium

Cr

2

8

13

1

25

Manganese

Mn

2

8

13

2

26

Iron

Fe

2

8

14

2

27

Cobalt

Co

2

8

15

2

28

Nickel

Ni

2

8

16

2

29

Copper

Cu

2

8

18

1

30

Zinc

Zn

2

8

18

2

31

Gallium

Ga

2

8

18

3

32

Germanium

Ge

2

8

18

4

33

Arsenic

As

2

8

18

5

34

Selenium

Se

2

8

18

6

35

Bromine

Br

2

8

18

7

36

Krypton

Kr

2

8

18

8

Electrons have some of the properties of a particle, and some of the properties of a wave. The position of an electron at a given time cannot be specified precisely, but only the region of space where it is most likely to be. These regions are called orbitals. Each electron in an atom has its energy defined by four quantum numbers. The first, or principal quantum number (n), defines the main energy level that the electron occupies. For the K-shell, $n= 1$; for L, $n= 2$; for M, $n= 3$; and for N, $n= 4$. The second, or azimuthal quantum number (l), governs the shape of the orbital and has values from zero up to $(n−1)$. When $l=0$, the electrons are called ‘s’ electrons; when $l=1$, they are ‘p’ electrons; $l=2$, ‘d’ electrons; and $l=3$ gives ‘f’ electrons. The third quantum number is the magnetic quantum number (m) and, for each value of l, m has values of l, $l−l,…,0,−1,…,…,−l$. Finally, the fourth quantum number, or spin quantum number, can only have values of 1/2 or −1/2. Table A3 shows how electrons with these different quantum numbers fill the electron shells. Pauli’s principle states that ‘no two electrons can have the same four quantum numbers’. Since the spin quantum number has only two possible values $±1/2$, it follows that an orbital can hold a maximum of two electrons (Table A3).

Table A3 Orbitals available in the principal electron shells.

In filling the available orbitals electrons enter the orbitals with the lowest energy first (Aufbau principle). The order is

Table A4 gives the electronic energy configurations of the elements with atomic numbers 1 to 32. When the elements are arranged in the periodic table (Figure A1), elements with similar electronic arrangements fall into similar groups (vertical rows), e.g. the group II elements all have two electrons in their outermost electron shell, and the group IV elements have four. Since the 4s-orbital is of lower energy than the 3d-orbitals, these latter orbitals remain empty until the 4s-orbital is filled (e.g. see potassium and calcium in Table A4). In subsequent elements the five 3d-orbitals (p.698) (p.699) (p.700) (p.701) receive electrons, creating the first row of the d-block in the periodic table (Figure A1). Some of these d-block elements are transition elements, meaning elements in which an inner shell of electrons is incomplete (in this case there are electrons in the fourth shell, but all the d-orbitals of the third shell are not yet full). The term transition element, as defined above, applies to scandium and subsequent elements as far as nickel, although it is often extended to include the whole of the first row of the d-block.

Figure A1 The periodic table.

Table A4 Electronic configuration of the elements.

Element

Atomic number

Symbol

Configuration

Place in periodic table

Hydrogen

1

H

1s1

Uncertain

Helium

2

He

1s2

Group 0 (inert gases)

Lithium

3

Li

1s22s1

Group I (alkali metals)

Beryllium

4

Be

1s22s2

Group II (alkaline-earth metals)

Boron

5

B

1s22s22p1

Group III

Carbon

6

C

1s22s22p2

Group IV

Nitrogen

7

N

1s22s22p3

Group V

Oxygen

8

O

1s22s22p4

Group VI

Fluorine

9

F

1s22s22p5

Group VII (halogen elements)

Neon

10

Ne

1s22s22p6

Group 0

Sodium

11

Na

1s22s22p63s1

Group I

Magnesium

12

Mg

1s22s22p63s2

Group II

Aluminium

13

Al

1s22s22p63s23p1

Group III

Silicon

14

Si

1s22s22p63s23p2

Group IV

Phosphorus

15

P

1s22s22p63s23p3

Group V

Sulphur

16

S

1s22s22p63s23p4

Group VI

Chlorine

17

Cl

1s22s22p63s23p5

Group VII

Argon

18

Ar

1s22s22p63s23p6

Group 0

Potassium

19

K

1s22s22p63s23p64s1

Group I

Calcium

20

Ca

1s22s22p63s23p64s2

Group II

Scandium

21

Sc

1s22s22p63s23p64s23d1

d-block

Titanium

22

Ti

1s22s22p63s23p64s23d2

d-block

23

V

1s22s22p63s23p64s23d3

d-block

Chromium

24

Cr

1s22s22p63s23p64s13d5

d-block

Manganese

25

Mn

1s22s22p63s23p64s23d5

d-block

Iron

26

Fe

1s22s22p63s23p64s23d6

d-block

Cobalt

27

Co

1s22s22p63s23p64s23d7

d-block

Nickel

28

Ni

1s22s22p63s23p64s23d8

d-block

Copper

29

Cu

1s22s22p63s23p64s13d10

d-block

Zinc

30

Zn

1s22s22p63s23p64s23d10

d-block

Gallium

31

Ga

1s22s22p63s23p64s23d104p1

Group III

Germanium

32

Ge

1s12s22p63s23p64s23d104p2

Group IV

If orbitals of equal energy are available, for example the three 2p-orbitals in the L-shell, or the five 3d-orbitals in the M-shell (Table A3), each is filled with one electron before any receives two (Hund’s rule). (p.702) Hence one can further analyse the electronic configurations in Table A4. For example, boron has two 1s, two 2s, and one 2p electrons. Three 2p-orbitals of equal energy are available (Table A3), often written as 2px, 2py, and 2pz. If we represent each orbital as a box and an electron as an arrow, boron can be represented as

For the next element, carbon, the extra electron enters another 2p-orbital in compliance with Hund’s rule,

And for nitrogen,

Further electrons will now begin to ‘pair up’ to fill the 2p-orbitals, for example the oxygen atom,

Table A5 uses the same ‘electrons-in-boxes’ notation for the elements in the first row of the d-block. Each of the five 3d-orbitals receives one electron, before any receives two.

Table A5 Electronic configuration of the elements scandium to zinc in the first row of the d-block of the periodic table.

# A2 Bonding between atoms

The description of chemical bonding below is the simplest possible needed to understand this book.

## A2.1 Ionic bonding

Essentially two types of chemical bond exist. The first is ionic bonding, and occurs when electropositive elements combine with electronegative ones. Electropositive elements, such as those in groups I and II of the periodic table (Figure A1), tend to lose their outermost electrons easily, whereas electronegative elements (group VII, and oxygen and sulphur in group VI) tend to accept extra electrons. By doing so, both gain the electronic configuration of the inert gases, which seems to be a particularly stable configuration in view of the lack of reactivity of these elements. Consider, for example, the combination of an atom of sodium with one of chlorine. Sodium, an electropositive group I element, has the electronic configuration 1s22s22p63s1. If a sodium atom loses one electron, it now has the configuration 1s22s22p6, that of the inert gas neon. It is still sodium because its nucleus is unchanged, but the loss of an electron leaves the atom with a positive charge, forming an ion or, more specifically, a cation (positively charged ion). For chlorine, configuration 1s22s22p63s23p5, acceptance of one electron gives the argon electron configuration 1s22s22p63s23p6, and produces a negatively charged ion (anion) Cl.

In the case of a group II element such as magnesium, it must lose two electrons to gain an inert gas electron configuration. Thus one atom of magnesium can provide electrons for acceptance by two chlorine atoms, giving magnesium chloride a formula MgC12,

$Display mathematics$

An atom of oxygen, however, can accept two electrons and combine with magnesium to form an oxide MgO,

$Display mathematics$

Once formed, anions and cations are held together by the attraction of their opposite charges. Each ion will exert an effect on each other ion in its vicinity, and these forces cause the ions to pack together into an ionic crystal lattice. As an example, in crystals of NaCl, each Na+ ion is surrounded by six Cl ions, and vice versa. Once the lattice has formed, it cannot be said that any one Na+ ion ‘belongs’ to any one Cl ion, nor can ‘molecules’ of sodium chloride be said to exist. The formula of an ionic compound merely indicates the ratio of the ions present. A lot of energy is needed to disrupt all the electrostatic forces between the many millions of ions in a crystal of an ionic compound, so such compounds are usually solids with high melting-points. Ionic compounds are mostly soluble in water, and the solutions conduct electricity because of the presence of ions to carry the current. The properties of an ionic compound in solution are those of its constituent ions.

## A2.2 Covalent bonding

This involves sharing a pair of electrons between the two bonded atoms. Usually each atom contributes one electron to the shared pair, but in dative covalent bonding, one atom contributes both. For example, hydrogen usually occurs as covalently bonded diatomic molecules, H2. If we represent the electron of each hydrogen atom by a cross (×) we can write

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(p.703) where $××$ is the shared pair of electrons. Many other gaseous elements, including oxygen and chlorine, exist as covalently bonded diatomic molecules. For the covalent compound ammonia, NH3, let us represent the outermost electrons of the N as circles and those of hydrogen as X,

Each atom contributes one electron to the bond. Ammonia also undergoes dative covalent bonding using the spare pair (lone pair) of electrons on the nitrogen. For example, it forms a covalent bond with a proton (H+). H+ is formed by loss of one electron from a hydrogen atom, and so has no electrons,

Once formed, each of the four covalent bonds in $NH4+$ is indistinguishable from the others.

Covalent compounds are usually gases, liquids, or low-melting-point solids at room temperature, because the forces of interaction between the molecules are weak. By contrast, covalent bonds themselves are usually strong and hard to break. Covalent bonds, unlike ionic bonds, have definite directions in space, and so their length, and the angles between them, can be measured.

Orbital theory (Section A1) also applies to covalent compounds, the bonding electrons occupying molecular orbitals formed by interaction of the atomic orbitals in which they were originally located. Various possible interactions produce molecular orbitals of different energy levels, each of which can hold a maximum of two electrons with opposite values of the spin quantum number (Pauli’s principle). In the simplest case, H2, two possible molecular orbitals can form by interaction of the 1s atomic orbitals of each H atom. The lowest energy orbital is the bonding molecular orbital (often written as σ‎1s) in which the electron is most likely to be found between the two nuclei. There is also an antibonding molecular orbital (written as σ‎*1s) of higher energy in which there is little chance of finding an electron between the two nuclei. A bonding molecular orbital is more stable than the atomic orbitals, whereas an antibonding molecular orbital is less stable. The two electrons in H2 have opposite spin, and both occupy the bonding molecular orbital. Hence H2 is much more stable than two H atoms.

P-type atomic orbitals can produce two types of molecular orbital (σ‎ and π‎) by overlapping in different ways. Hence, for a 2p-orbital (say 2px) combining with another one, there will be two bonding molecular orbitals, σ‎2px and π‎2px, and two antibonding molecular orbitals, σ‎*2px and π‎*2px. Energy increases in the order

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With this in mind, we can consider bonding in two more complex cases: the gases nitrogen and oxygen. The nitrogen atom has the configuration 1s22s22p3. If two atoms join to form N2, the four 1s-electrons (two from each atom) fully occupy a σ‎1s bonding and a σ‎*1s antibonding orbital, and so there is no net bonding. The four 2s-electrons similarly occupy σ‎2s and σ‎*2s molecular orbitals, again no net bonding. Six electrons are left, located in two 2px, two 2py, and two 2pz atomic orbitals. If the axis of the bond between the atoms is taken to be that of the 2px orbitals, they can overlap along this axis to produce a bonding σ‎2px molecular orbital that can hold both electrons. The 2py and 2pz atomic orbitals cannot overlap along their axes, but they can overlap laterally to give bonding π‎2py and π‎2pz molecular orbitals, each of which holds two electrons. The 2p antibonding orbitals are not occupied; and the net result is a triple covalent bond ; one σ‎ covalent bond and two π‎ covalent bonds. The N2 molecule is thus far more stable than individual N atoms.

The oxygen atom (configuration, 1s22s22p4) has one more electron, and so when O2 forms there are two more electrons to consider. These must occupy the next highest molecular orbital in terms of energy. In fact, there are two such orbitals of equal energy, π‎*2py and π‎*2pz. By Hund’s rule, each receives one electron. Since the presence of two electrons in antibonding orbitals energetically cancels out one of the π‎2p bonding orbitals, the two oxygen atoms are effectively joined by a double bond, that is $O=O$ (also see Fig 1.14).

The fluorine molecule contains two more electrons than does O2, and so the π‎*2py and π‎*2pz orbitals are both full. Since three bonding and two antibonding molecular orbitals are occupied, the F2 molecule effectively contains a single bond, F–F.

## A2.3 Non-ideal character of bonds

The discussion so far has implied an equal sharing of the bonding electrons between two atoms joined by a covalent bond. However, this only occurs when both atoms have a similar attraction for the electrons, i.e. are equally electronegative. This is often not the case. (p.704) Consider, for example, the water molecule, which contains two oxygen–hydrogen covalent bonds. Oxygen is more electronegative than hydrogen, and so takes a slightly greater ‘share’ of the bonding electrons, giving it a slight negative charge (written as δ). The hydrogen thus has a slight positive charge,

These charges give water many of its properties. They attract water molecules to each other, making it harder to separate them and so raising the boiling point of water to $100∘C$ at normal atmospheric pressure,

These weak ionic bonds are called hydrogen bonds. The δ+ and δ charges also allow water to hydrate ions; water molecules cluster around ions and help to stabilize them.

The energy released when ions become hydrated helps to provide the energy needed to disrupt the crystal lattice when ionic compounds dissolve in water. In some cases the energy of hydration is too small to disrupt the lattice, resulting in an ionic compound insoluble in water.

## A2.4 Hydrocarbons and electron delocalization

Carbon has four electrons in its outermost shell (Table A4), and normally forms four covalent bonds. Carbon atoms can covalently bond to each other to form long chains. For example, butane has the structure

Butane is a hydrocarbon, that is it contains only carbon and hydrogen. Two other hydrocarbon gases, ethane and pentane, are released during lipid peroxidation (Section 5.12.5.1). They have the structures

Carbon atoms can also form double covalent bonds (written as () and triple covalent bonds with each other. A double bond consists of four shared electrons (two pairs), and a triple bond has six shared electrons (three pairs). The simplest hydrocarbon containing a double bond is the gas ethene, sometimes called ethylene,

Ethene is produced in several assays for the detection of hydroxyl radicals (Table 6.14).

Ethyne, sometimes called acetylene, contains a triple bond and has the structure . Organic compounds containing carbon–carbon double or triple bonds are said to be unsaturated, for example PUFAs (Section 5.11.2).

The organic liquid benzene has the formula C6H6. Given that carbon forms four covalent bonds, the structure of benzene might be drawn as containing three carbon–carbon single bonds, and three double bonds, that is

This structure cannot be correct, however, since benzene does not show the characteristic chemical reactions of compounds containing double bonds. A carbon–carbon single bond is normally 0.154 nm long (one nanometre, nm, is 10−9 metre), and a carbon–carbon double bond, 0.134 nm; yet all the bond lengths between the carbon atoms in benzene are equal at 0.139 nm, that is, intermediate between the double and single bond lengths. The six electrons, which should have formed three double bonds, appear to be ‘spread around’ all six bonds. This is often drawn as

Compounds containing the benzene ring or similar ring structures are called aromatic compounds. Delocalization of electrons over several bonds greatly increases the stability of a molecule. Other examples can be seen in haem rings (Section 1.10.3), which show extensive delocalization of electrons, and in several ions such as nitrate $(NO3−)$ and carbonate $(CO32−)$. In each case the negative charge is spread between each of the bonds,

(each O has, on average, one-third of the negative charge).

(each O has, on average, two-thirds of a negative charge).

# A3 Moles and molarity

One mole of a substance is its relative molecular mass (‘molecular weight’) expressed in grams. Thus one mole of hydrogen (H2) is 2 g, one mole of water 18 g, and one mole of sodium hydroxide (NaOH) 40 g. One mole of any covalently bonded substance contains the same number of molecules, 6.023 × 1023 to be precise (Avogadro’s number). Thus molecules are found in 2 g of hydrogen, and $6.023×1023$ water molecules in 18 g of water. One mole of the ionic solid NaOH will contain $6.023×1023$ Na+ ions and the same number of OH ions.

Whereas moles are amounts, molarity is a concentration. Solution concentrations are usually expressed in molar terms because this relates to the actual number of ions or molecules present in the solution. A molar solution has one mole of solute (the substance dissolved) present in 1 dm3 (or 1 litre) of solution.

One millimole (1 mmol) is 10−3 moles. Thus a millimolar (1 mM) solution has 1 mmol of solute per dm3. One micromole (1 μ‎mol) is 10−6 moles. Thus a micromolar (1 μ‎M) solution has 1 μ‎mole of solute per dm3. A 1 mM solution has 1 μ‎mol of solute per cm3 (ml). One nanomole (1 nmol) is 10−9 moles. Thus a nanomolar (1 nM) solution has 1 nmol of solute per dm3. A 1 μ‎M solution has 1 nmol of solute per cm3 (ml).

# A4 pH and pKa

The pH of a solution is a measure of its acidity; pH 7.0 is neutral, pH <7 acidic, and pH >7 alkaline. Most cells operate at pH values at or close to 7.4, but ‘physiological pH’ ranges from <2 in the stomach to >8 in the stroma of illuminated chloroplasts. The term pH is defined as

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where the square brackets denote concentration. Thus pure water at $25∘C$ contains $10−7moles/dm3$ of H+ ions and its pH is 7. As temperature rises, heterolytic fission of water (Fig. 1.13) is favoured, [H+] rises and pH falls, so pure water at $37∘C$ is not neutral but slightly acidic.

An acid may be (somewhat simplistically) defined as a donor of hydrogen ions. Strong acids (HCl, HNO3, H2SO4) are completely ionized when mixed with water to give dilute aqueous solutions (but not as the pure acids, which are covalently bonded). However, most acids in living systems (e.g. HNO2, HOCl, $HO2∙$, are only partially ionized (so-called weak acids) and exist in an equilibrium:

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A is the conjugate base of the weak acid HA; a base is a hydrogen ion acceptor.

The acid dissociation constant, Ka, is the ratio of the concentrations,

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at equilibrium. The bigger the value of Ka, the stronger the acid. Values of Ka are affected by temperature. Another term often used is pKa,

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Thus, the higher Ka, the smaller is pKa.

Mixtures of weak acids and their conjugate bases form buffer solutions; their pH changes only slightly when acid or alkali (in moderate amounts) are added.

The equation governing the behaviour of buffers is the Henderson–Hasselbalch equation:

$Display mathematics$

Thus if equal amounts of a weak acid and its conjugate base are mixed, the pH of the resulting solution equals the pKa of the acid. If extra H+ is added, it is buffered by movement of the equilibrium

$Display mathematics$

towards the left; if alkali is added, [H+] falls and it is replaced by movement of the reaction towards the right. This is the essence of buffer action. (p.706)