# Which is more amphoteric: zinc or copper hydroxide?

$\ce{K_{a} ~Cu(H2O)_6^2+}{=~5*10^{-7}}$

$\ce{K_{a} ~Zn(H2O)_6^2+}{=~2.5*10^{-10}}$

Given this information, which forms a more amphoteric hydroxide?

My reasoning is that copper hydroxide is more amphoteric than zinc hydroxide. My reasoning is that because $\ce{K_{a} ~Cu(H2O)_6^2+}$ > $\ce{K_{a} ~Zn(H2O)_6^2+}$, $\ce{Cu(OH)_2}$ should be more amphoteric because it will probably have the bigger $\ce{K_{a}}$. This fulfills half of the definition of amphoteric - behaving as both an acid and base.

But how do I compare the base strengths of $\ce{Zn(OH)_2}$ and $\ce{Cu(OH)_2}$? I need to, because being amphoteric means the substance acts as both an acid and a base!

Consider the following:

$1. ~{K_{a1}:} ~\ce{Cu(H2O)_6^2+ + H_2O -> Cu(H2O)_5(OH)^+ + H_3O^+}$

$2. ~{K_{a2}:} ~\ce{Cu(H2O)_5(OH)^+ + H_2O -> Cu(H2O)_4(OH)_2 + H_3O^+}$

$3. ~{K_{a3}:} ~\ce{Cu(H2O)_4(OH)_2 + H_2O -> Cu(H2O)_3(OH)_3^- + H_3O^+}$

Basic character of copper hydroxide is illustrated by the below equation:

$4. ~\ce{Cu(H2O)_4(OH)_2 + H_2O -> Cu(H2O)_5(OH)^+ + HO^-}$

The above equation, reversed, is:

$5. ~\ce{Cu(H2O)_5(OH)^+ + HO^- -> H_2O + Cu(H2O)_4(OH)_2 }$

This equation is very similar to $~{K_{a2}}$ except that the base is hydroxide ion instead of water.

We can write a similar equation for zinc hydroxide:

$6. ~\ce{Zn(H2O)_5(OH)^+ + HO^- -> H_2O + Zn(H2O)_4(OH)_2}$

Let's compare equations $5$ and $6$. We can expect $5$ to be a larger extent reaction than $6$ because hydrated copper ion is a stronger acid than hydrated zinc ion to start with. So:

${K_{rxn5} > K_{rxn6}}$

And therefore,

${K_{rxn4} < K_{rxn7}}$

$7. ~\ce{H_2O + Zn(H2O)_4(OH)_2 -> Zn(H2O)_5(OH)^+ + HO^-}$

• This info isn't enough to tell, it's even misleading I'm afraid. – Mithoron May 26 '16 at 18:10
• @Mithoron - could you expand your comment into an answer perhaps? :D. I'm very curious as to what your thoughts are. – Dissenter May 26 '16 at 22:15
• Can you define "more amphoteric"? More acidic and more basic are unambiguous, but this is not. – Zhe Oct 19 '16 at 20:22
• OK. Apply your definition to this scenario: Compounds A and B are amphoteric. A is a better acid, B is a better base. Which is more amphoteric? – Zhe Oct 19 '16 at 20:26
• I think you should come to chat to discuss questions. It may be cheaper then massive bounty. – Mithoron Oct 19 '16 at 20:31

Zinc hydroxide is more amphoteric as quantitatively investigated in Effect of pH, Concentration and Temperature on Copper and Zinc Hydroxide Formation/Precipitation in Solution

In summary, in the case of Cu(OH)2, only at extremely low concentrations and very high pH can a third OH- be coordinated.

At higher pH values, copper hydroxide, Cu(OH)2, is the dominant species up to pH 12.3 where the copper ion Cu(OH)3 - forms according to Equation 3. At higher copper concentrations, solid Cu(OH)2 is formed and precipitates out of solution at copper concentrations above the solubility product of copper hydroxide at 1×10-8 M. It is important to note that the domain of stability of solid Cu(OH)2 is expanding to lower and higher pH values with increasing copper concentration.

On the other hand:

Above pH 11.4, Zn(OH)3 - forms according to Equation 7. At higher zinc concentrations, solid Zn(OH)2 forms and precipitates out of solution at zinc concentrations above the solubility product of zinc hydroxide of 1×10-5 M.

So qualitatively both display similar amphoteric behavior in the limit of infinite dilution, but at a appreciably non-zero concentration zinc is more amphoteric.

The article says it is getting the equilibrium constant values from Mineral Equilibria, Low Temperature and Pressure.

An alternative source of this information is Hydrolysis of cations. Formation constants and standard free energies of formation of hydroxy complexes Inorg. Chem., 1983, 22 (16), pp 2297–2305, which gives quantitative values for OP equations 1, 2 and 3 as well as the corresponding equations for zinc, in terms of Gibbs energy of formation and in terms of cumulative equilibrium constants.

Simplifying the general equation in the paper to only mononuclear (one metal atom) complexes:

$$K_y$$ $$\ce{M^{n+} + yH2O <=> M(OH)_y^{n-y} + yH+}$$

$\ce{Cu^{2+}}$ :
$pK_1 = 7.96$
$pK_2 = 16.26$
$pK_3 = 26.7$
$pK_4 = 39.6$

$\ce{Zn^{2+}}$ :
$pK_1 = 8.96$
$pK_2 = 16.9$
$pK_3 = 28.4$
$pK_4 = 41.2$

(These are all experimental values, calculated values are also given)

So really, without considering the solid phase (solubility), Cu2+ and Zn2+ seem very similar, with Cu2+ showing slightly more acidity.

Another study, which does consider the solid phases, is Zinc Hydroxide: Solubility Product and Hydroxy-complex Stability Constants from 12.5-75 [degrees] C Can. J. Chem. 53, 3841.

This study approaches the problem with 5 equilibria involving the solid phase. (These authors use the symbol "c" for the solid phase.)

$\ce{Zn(OH)2(c) <=> Zn(OH)+ + OH-}$
$K_1 = [\ce{Zn(OH)+}][\ce{OH-}] = 2.54 \times 10^{-11}$

$\ce{Zn(OH)2(c) <=> Zn(OH)2(aq)}$
$K_2 = [\ce{Zn(OH)2}] = 2.62 \times 10^{-6}$

$\ce{Zn(OH)2(c) +OH- <=> Zn(OH)3-}$
$K_3 = [\ce{Zn(OH)3-}]/[\ce{OH-}] = 1.32 \times 10^{-3}$

$\ce{Zn(OH)2(c) +2OH- <=> Zn(OH)4^{2-}}$
$K_4 = [\ce{Zn(OH)4^{2-}}]/[\ce{OH-}]^2 = 6.47 \times 10^{-2}$

$\ce{Zn(OH)2(c) <=> Zn^{2+}} + \ce{2OH-}$
$K_{sp} = [\ce{Zn^{2+}}][\ce{OH-}]^2 = 1.74 \times 10^{-17}$

This study (see Fig. 1) shows that aqueous $\ce{Zn(OH)2}$ is only the major aqueous species in the pH range 9-11, having acted as an acid or base outside this range.

Instead, if I were just given the information in the OP, meaning the two supposed Ka values, as some kind of test or homework question, I would say copper is more amphoteric. My reasoning would be, for zinc, just to remove one proton, you need to get up to almost pH 10. For two more protons to be removed, as required to get to Zn(OH)2 and lose yet another proton to act as an acid, seems impossible because I would expect pKas to be spaced apart and if you would need to approach or go beyond pH 14 to observe the acidic behavior, that isn't reasonably considered amphoteric.

Note that EXAFS Investigations of Zn(II) in Concentrated Aqueous Hydroxide Solutions J. Phys. Chem. 1995, 99, 11967-11973 finds that rather than being 6-coordinate as indicated in the OP, 4 hydroxides coordinate Zn2+ tetrahedrally with no water ligands.