Question

Which of the following changes will cause the free energy of the cell reaction to decrease :

$Zn|ZnS{O}_{4\left(aq\right)}(x,M)||HC{l}_{\left(aq\right)}\left(x_{2}M\right)|H_{2\left(g\right)},Pt$

• A. increase in the volume of HCl solution from 100 ml to 200 ml
• B. Increase in pressure of hydrogen from 1 atm to 2 atm
• C. Increase in molarity $x_2$ from 0.1 to 1 M
• D. Decrease in molarity $x_1$ from 1 M to 0.1 M

Answer 1

Answer: (C), (D)

The correct options are
C Decrease in molarity $x_1$ from 1 M to 0.1 M
D Increase in molarity $x_2$ from 0.1 to 1 M

Anode: $Zn\left(s\right)\to Z{n}^{2+}\left(aq\right)+2e^{-}$

Cathode: $2H^{+}\left(aq\right)+2e^{-}\to H_2\left(g\right)$

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Net reaction: $Zn\left(s\right)+2H^{+}\left(aq\right)\to Z{n}^{2+}\left(aq\right)+H_2\left(g\right)$

The Nernst equation for the emf of the cell is $E_{cell}^0=E_{cell}^0-\frac{0.0592}{n}log\frac{{\lfloor {Zn}^{2+}\rfloor \times P}_{H2}}{{\lfloor H^{+}\rfloor }^2}$.

When the molarity $x_1$ decreases from 1 M to 0.1 M, the term $log\frac{{\lfloor {Zn}^{2+}\rfloor \times P}_{H2}}{{\lfloor H^{+}\rfloor }^2}$ becomes more negative and the e.m.f of cell increases.

The relationship between the standard Gibbs energy change and the e.m.f of cell is $\Delta G^0=-nF{E}_{cell}^0$. With increase in the e.m.f of cell, the $\Delta G^0$ value becomes more negative or it decreases. This is also true when the molarity $x_2$ increases from 0.1 M to 1 M.