Electrochemistry 2 Question 39
38. (a) Will $\mathrm{pH}$ value of water be same at temperature $25^{\circ} \mathrm{C}$ and $4^{\circ} \mathrm{C}$ ? Justify in not more than 2 or 3 sentences.
(b) Two students use same stock solution of $\mathrm{ZnSO}{4}$ and a solution of $\mathrm{CuSO}{4}$. The emf of one cell is $0.03 \mathrm{~V}$ higher than the other. The concentration of $\mathrm{CuSO}{4}$ in the cell with higher emf value is $0.5 \mathrm{M}$. Find out the concentration of $\mathrm{CuSO}{4}$ in the other cell. Given : $2.303 R T / F=0.06 \mathrm{~V}$.
(2003, 2M)
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Solution:
- (a) $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$
In pure water, $\left[\mathrm{H}^{+}\right]$depends on value of $K_{w}$ which is
$$ K_{w}=\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right] $$
$\because \quad K_{w}$ is a function of temperature, $\left[\mathrm{H}^{+}\right]$will change with temperature.
(b) Let the emf of first cell be $X$ volt.
$\Rightarrow$ emf of 2nd cell $=(X+0.03)$ volt
$\left[\mathrm{Cu}^{2+}\right]$ in 2nd cell $=0.50 \mathrm{M}$
$\left[\mathrm{Cu}^{2+}\right]$ in 1 st cell $=$ ?
$$ \begin{aligned} E_{1} & =E_{1}^{\circ}-\frac{2.303 R T}{2 F} \log \frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]} \ E_{2} & =E_{1}^{\circ}-\frac{2.303 R T}{2 F} \log \frac{\left[\mathrm{Zn}^{2+}\right]}{\left[\mathrm{Cu}^{2+}\right]{2}} \ \Rightarrow \quad E{2}-E_{1} & =\frac{2.303 R T}{2 F}\left[\log \frac{\left[\mathrm{Cu}^{2+}\right]{2}}{\left[\mathrm{Cu}^{2+}\right]{1}}\right] \ \Rightarrow \quad 0.03 & =0.03 \log \frac{0.50}{\left[\mathrm{Cu}^{2+}\right]{1}} \ \Rightarrow \quad \frac{0.50}{\left[\mathrm{Cu}^{2+}\right]{1}} & =10 \Rightarrow\left[\mathrm{Cu}^{2+}\right]_{1}=0.05 \mathrm{M} \end{aligned} $$
