Question

For the following cell,

$Zn\left(s\right)|ZnS{O}_4\left(aq\right)||CuS{O}_4\left(aq\right)|Cu\left(s\right)$

When the concentration of $Z{n}^{2+}$ is 10 times the concentration of $C{u}^{2+}$, the expression for $\Delta G\left(inJmo{l}^{-1}\right)$ is [F is Faraday constant, R is gas constant; T is temperature; $E^{\circ }$(cell) = 1.1V]

• A. 1.1 F
• B. 2.303 RT - 2.2 F
• C. 2.303 RT + 1.1 F
• D. - 2.2 F

Answer 1

The correct option is B 2.303 RT - 2.2 F

$Zn-2e^{-}\to Z{n}^{2+}$
$\underset{–}{C{u}^{2+}+2e\to Cu}$
$Zn+C{u}^{2+}\to Z{n}^{2+}+Cu$

$E_{cell}=E_{cell}^{\circ }-\frac{2.303RT}{nF}log\frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}$

$E_{cell}=1.1-\frac{2.303RT}{2F}log10$

$=1.1-\frac{2.303RT}{2F}$

$\Delta G=-nF{E}_{cell}$

$=-2F(1.1-\frac{2.303RT}{2F})$

$=2.303RT-2.2F$