Question

The standard electrode potential for the reduction of the Cu(II) complex of EDTA is given by

${\mathrm{CuY}}^{2-}+2{\mathrm{e}}^{-}\rightleftharpoons {\mathrm{Cu}}^{2+}\left(s\right)+{\mathrm{Y}}^{4-}{E}^o=0.13\mathrm{V}$

Calculate the formation constant for the reaction

${\mathrm{Cu}}^{2+}+{\mathrm{Y}}^{4-}\rightleftharpoons {\mathrm{CuY}}^{2-}$

Short answer

The formation constant for the given reaction is $9.8\times {10}^6$.

Step-by-step solution

Given information 

The standard electrode potential for the reaction of the copper(II) complex of EDTA is given as $0.13\mathrm{V}$.

The chemical reaction is s follows:

${\mathrm{CuY}}^{2-}\rightleftharpoons {\mathrm{Cu}}^{2+}\left(s\right)+{\mathrm{Y}}^{4-}$

Formation constant  

Formation constant measures the strength of interaction between the reactant and the complex. It is equal to the ratio of complex or product to the reactants.

The formation constant for the ${\mathrm{Cu}}^{2+}+{\mathrm{Y}}^{4-}\rightleftharpoons {\mathrm{CuY}}^{2-}$reaction can be written as follows:

localid="1649235469557" $$\begin{gathered} K_f=\frac{\left[{\mathrm{CuY}}^{2-}\right]}{\left[{\mathrm{Cu}}^{2+}\right]\left[{\mathrm{Y}}^{4-}\right]} \\ \left[{\mathrm{Cu}}^{2+}\right]=\frac{\left[{\mathrm{CuY}}^{2-}\right]}{K_f\left[{\mathrm{Y}}^{4-}\right]}...........\left(1\right) \end{gathered}$$

Reduction reaction 

The reduction reaction for ${\mathrm{Cu}}^{2+}$to $\mathrm{Cu}$is as follows:

${\mathrm{Cu}}^{2+}+2{\mathrm{e}}^{-}\rightleftharpoons \mathrm{Cu}\left(s\right)$

The reduction potential is $0.337\mathrm{V}$.

Nernst equation  

The Nernst equation for the above reaction is represented as follows:

$E_{cell}=E_{cell}^o-\frac{0.0592}{2}\log \frac{\left[\mathrm{Cu}\right]}{\left[{\mathrm{Cu}}^{2+}\right]}........\left(2\right)$

It is assumed that the activity of the liquid and solid substance is taken as 1.

Nernst equation and reduction potential

Substitute the concentration of each substance and equation (1) in the above equation (2) as follows:

$$\begin{gathered} E_{cell}=E_{cell}^o-\frac{0.0592}{2}\log \frac{1}{\left[{\mathrm{Cu}}^{2+}\right]} \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}=E_{cell}^o-\frac{0.0592}{2}\log \frac{K_f{\left[{\mathrm{Y}}^{4-}\right]}^2}{\left[{\mathrm{CuY}}^{2-}\right]} \\ =E_{cell}^o-\frac{0.0592}{2}\log K_f...............\left(3\right) \end{gathered}$$

Formation constant for the given reaction

Subsitute $E_{cell}^o$and $E_{cell}$in the above equation (3) as follows:

data-custom-editor="chemistry" $$\begin{gathered} \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}{E}_{cell}=E_{cell}^o-\frac{0.0592}{2}\log K_f \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}0.13\mathrm{V}=0.337\mathrm{V}-\frac{0.0592}{2}\log K_f \\ 0.13\mathrm{V}-0.337\mathrm{V}=-\frac{\mathit{0}\mathit{.}\mathit{0592}}{\mathit{2}}\log K_{\mathit{f}} \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}-0.207\mathrm{V}=-0.0296\times \log K_f \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\log K_{\mathit{f}}=\frac{-0.207\mathrm{V}}{-0.0296} \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\log K_f=6.993 \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}{K}_f={10}^{6.993} \\ =9.8\times {10}^6 \end{gathered}$$