JEE MAIN - Chemistry (2022 - 29th June Evening Shift - No. 17)
The cell potential for the given cell at 298 K
Pt| H2 (g, 1 bar) | H+ (aq) || Cu2+ (aq) | Cu(s)
is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu2+ is 10$$-$$x M. The value of x is ___________.
(Given : $$E_{C{u^{2 + }}/Cu}^\Theta $$ = 0.34 V and $${{2.303\,RT} \over F}$$ = 0.06 V)
Answer
7
Explanation
$\mathrm{Q}=\frac{\left[\mathrm{H}^{+}\right]^{2}}{\left[\mathrm{Cu}^{+2}\right] \mathrm{pH}_{2}}=\frac{10^{-6}}{\mathrm{C}} \quad \mathrm{pH}_{2}=1$
$$ \begin{aligned} &E=E_{\text {cell }}^{\circ}-\frac{0.06}{n} \log Q \\\\ &0.31=0.34-\frac{0.06}{2} \log \frac{10^{-6}}{C} \\\\ &\log \frac{10^{-6}}{C}=1 \\\\ &C=10^{-7} M \\\\ &x=7 \end{aligned} $$
$$ \begin{aligned} &E=E_{\text {cell }}^{\circ}-\frac{0.06}{n} \log Q \\\\ &0.31=0.34-\frac{0.06}{2} \log \frac{10^{-6}}{C} \\\\ &\log \frac{10^{-6}}{C}=1 \\\\ &C=10^{-7} M \\\\ &x=7 \end{aligned} $$
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