JEE MAIN - Chemistry (2022 - 24th June Morning Shift - No. 15)
The cell potential for the following cell
Pt |H2(g)|H+ (aq)|| Cu2+ (0.01 M)|Cu(s)
is 0.576 V at 298 K. The pH of the solution is __________. (Nearest integer)
(Given : $$E_{C{u^{2 + }}/Cu}^o = 0.34$$ V and $${{2.303\,RT} \over F} = 0.06$$ V)
Answer
5
Explanation
$E_{\text {cell }}=E_{\text {cell }}^{0}-\frac{0.06}{2} \log \frac{\left[\mathrm{H}^{\oplus}\right]^{2}}{\left[\mathrm{Cu}^{+2}\right]}$
$0.576=0.34-0.03 \log \frac{\left[\mathrm{H}^{\oplus}\right]^{2}}{[0.01]}$
$0.576-0.34=-0.03 \log \left[\mathrm{H}^{\oplus}\right]^{2}+0.03 \log (0.01)$
$$ =0.06 \,\mathrm{pH}-0.06 $$
$\mathrm{pH} \simeq 4.93 \simeq 5$
$0.576=0.34-0.03 \log \frac{\left[\mathrm{H}^{\oplus}\right]^{2}}{[0.01]}$
$0.576-0.34=-0.03 \log \left[\mathrm{H}^{\oplus}\right]^{2}+0.03 \log (0.01)$
$$ =0.06 \,\mathrm{pH}-0.06 $$
$\mathrm{pH} \simeq 4.93 \simeq 5$
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