Electrochemistry Result Question 38
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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Answer:
Correct Answer: 38. $( 0.05$ $ M )$
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 2 nd cell $=(X+0.03)$ volt
$\left[\mathrm{Cu}^{2+}\right]$ in 2 nd cell $=0.50 \mathrm{M}$
$\left[\mathrm{Cu}^{2+}\right]$ in 1st 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+} \mathrm{k}\right.} \\ \Rightarrow \quad E_2-E_1 & =\frac{2.303 R T}{2 F}\left[\log \frac{\left[\mathrm{Cu}^{2+} \mathrm{b}\right.}{\left[\mathrm{Cu}^{2+}\right]_1}\right] \\ \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} $
BETA
