MCQ
Calculate $E_{cell}$  .............. $\mathrm{V}$

$Pt(s)|\mathop {{H_2}(g)}\limits_{1\ atm} |HA\,\,\,\,\,\mathop {1\,M}\limits_{({K_a} = {{10}^{ - 7}})} \,\,||\,HB\,\,\,\,\,\mathop {1\,M}\limits_{({K_1} = {{10}^{ - 5}})}$

$\,|\mathop{{H_2}(g)}\limits_{1\ atm} |Pi(s)$

  • $0.06$
  • B
    $0.03$
  • C
    $0.04$
  • D
    $0.05$

Answer

Correct option: A.
$0.06$
a
${{\text{H}}_{2}}(\text{g})\to 2\text{H}_{\text{anode }}^{+}+2{{\text{e}}^{-}}$

$\underline{2\text{H}_{\text{cathode }}^{+}+2{{\text{e}}^{-}}\to {{\text{H}}_{2}}(\text{g})}$

$\underline{{{\text{H}}_{2}}(\text{g})+2\text{H}_{\text{cathode }}^{+}\to 2\text{H}_{\text{anode }}^{+}+{{\text{H}}_{2}}(\text{g})}$

$\text{Q}=\frac{\left[ {{\text{H}}^{+}} \right]_{\text{anode }}^{2}}{\left[ {{\text{H}}^{+}} \right]_{\text{cathode }}^{2}}$ $=\frac{{{10}^{-7}}}{{{10}^{-5}}}={{10}^{-2}}$

$\mathrm{n}=2$

$\mathrm{E}_{\text {cell }}^{\circ}=0$

$\mathrm{E}_{\text {cell }}=0-\frac{0.06}{2} \log \,10^{-2}=0.06\, \mathrm{V}$

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