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The electrochemical cell shown below is concentration cell. $M|M^{2+}\ ($saturated solution of a sparingly soluble salt$, MX_2) || M^{2+} (0.001\ mol\ dm^{-3})\ |M$ The emfof the cell depends on the difference in concentrations of $M^{2+}$ ions at the two electrodes. The emf of the cell at $298 K$ is $0.059V$. The following questions are multiple choice questions. Choose the most appropriate answer:

1. The solubility product $(K_{sp'}\ mol^3\ dm^{-9})$ of $MX_2$ at $298 K$ based on the information available for the given concentration cell is $(\text{take }2.303 \times \text{R}\times \frac{298}{\text{F}} = 0.059)$

1. $2 \times 10^{-15}$
2. $4 \times 10^{-15}$
3. $3 \times 10^{-12}$
4. $1 \times 10^{-12}$

2. The value of $\triangle\text{G}\ ($in $kJ\ mol^{-1})$ for the given cell is $($take $1 F = 96500 C\ mol^{-1})$

1. $3.7$
2. $-3.7$
3. $10.5$
4. $-11.4$

3. The equilibrium constant for the following reaction is:

$\text{Fe}^{2+}+\text{Ce}^{4+}\rightleftharpoons\text{Ce}^{3+}+\text{Fe}^{3+}$
(Given, $\text{E}^\circ_\frac{\text{Ce}^{4+}}{\text{Ce}^{3+}}=1.44\text{V}$ and $\text{E}^\circ_\frac{\text{Fe}^{3+}}{\text{Fe}^{2+}}=0.68\text{V})$

1. $7.6 \times 10^{12}$
2. $6.5 \times 10^{10}$
3. $5.2 \times 10^9$
4. $3.4 \times 10^{12}$

4. The solubility product of a saturated solution of $\ce{Ag2CrO4}$ in water at $298 K$ if the emf of the cell

$Ag|Ag^+ ($satd. $\ce{Ag2CrO4}$ soln$) || Ag^+ (0.1 M) | Ag$
is $0.164V$ at $298 K,$ is :

1. $3.359 \times 10^{-12}\ mol^3\ L^{-3}$
2. $2.287 \times 10^{-12}\ mol^3\ L^{-3}$
3. $1.158 \times 10^{-12}\ mol^3\ L^{-3}$
4. $4.135 \times 10^{-12}\ mol^3\ L^{-3}$

5. To calculate the emf of the cell, which of the following options is correct?

1. $emf = E_{cathode }- E_{anode}$
2. $emf = E_{anode }- E_{cathode}$
3. $emf = E_{anode} + E_{cathode}$
4. None of these.