Electrochemistry question bank (Chemistry)

Consider the following two half-cell reactions along with the standard reduction potential given:
$CO_2 + 6H^+ + 6e^- \rightarrow CH_3 OH + H_2 O \quad E°_{red} = 0.02$ V
$\dfrac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2 O \quad E°_{red} = 1.23$ V
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of $1$ bar pressure and $298$ K temperature. The fuel cell works with $80\%$ efficiency. If the work derived from the cell using $1$ mol of $CH_3 OH$ is used to compress an ideal gas isothermally against a constant pressure of $1$ kPa, then the change in the volume of the gas, $\Delta V =$ _____ m$^3$. (nearest integer)
Given: $F = 96500$ C mol$^{-1}$

A volume of $x\,\mathrm{mL}$ of $5\,\mathrm{M}\,\mathrm{NaHCO_3}$ solution was mixed with $10\,\mathrm{mL}$ of $2\,\mathrm{M}\,\mathrm{H_2CO_3}$ solution to make an electrolytic buffer. If the same buffer was used in the following electrochemical cell to record a cell potential of $235.3\,\mathrm{mV}$, then the value of $x = \_\_\_\_$ mL (nearest integer).

$\mathrm{Sn(s)} \; \big| \; \mathrm{Sn(OH)_6^{2-}}(0.5\,\mathrm{M}) \; \big| \; \mathrm{HSnO_2^-}(0.05\,\mathrm{M}) \; \big| \; \mathrm{OH^-} \; \big| \; \mathrm{Bi_2O_3(s)} \; \big| \; \mathrm{Bi(s)}$

Consider up to one place of decimal for intermediate calculations.

$\begin{array}{ll}\text{Given:} & E^\circ_{\mathrm{[Sn(OH)_6]^{2-}/HSnO_2^-}} = -0.90\,\mathrm{V} \\[4pt]& E^\circ_{\mathrm{Bi_2O_3/Bi}} = -0.44\,\mathrm{V} \\[4pt]& \mathrm{p}K_a(\mathrm{H_2CO_3}) = 6.11 \\[4pt]& \dfrac{2.303\,RT}{F} = 0.059\,\mathrm{V} \\[6pt]& \text{Antilog}(1.29) = 19.5\end{array}$