Consider the cell

$$\mathrm{Pt}_{(\mathrm{s})}\left|\mathrm{H}_{2}(\mathrm{~g}, 1 \mathrm{~atm})\right| \mathrm{H}^{+}(\mathrm{aq}, 1 \mathrm{M})|| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \operatorname{Pt}(\mathrm{s})$$

When the potential of the cell is $$0.712 \mathrm{~V}$$ at $$298 \mathrm{~K}$$, the ratio $$\left[\mathrm{Fe}^{2+}\right] /\left[\mathrm{Fe}^{3+}\right]$$ is _____________. (Nearest integer)

Given : $$\mathrm{Fe}^{3+}+\mathrm{e}^{-}=\mathrm{Fe}^{2+}, \mathrm{E}^{\theta} \mathrm{Fe}^{3+}, \mathrm{Fe}^{2+} \mid \mathrm{Pt}=0.771$$

$$ \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{~V} $$

The equilibrium constant for the reaction

$$\mathrm{Zn(s)+Sn^{2+}(aq)}$$ $$\rightleftharpoons$$ $$\mathrm{Zn^{2+}(aq)+Sn(s)}$$ is $$1\times10^{20}$$ at 298 K. The magnitude of standard electrode potential of $$\mathrm{Sn/Sn^{2+}}$$ if $$\mathrm{E_{Z{n^{2 + }}/Zn}^\Theta = - 0.76~V}$$ is __________ $$\times 10^{-2}$$ V. (Nearest integer)

Given : $$\mathrm{\frac{2.303RT}{F}=0.059~V}$$

Following figure shows dependence of molar conductance of two electrolytes on concentration. $$\Lambda \mathop m\limits^o $$ is the limiting molar conductivity.

The number of $$\mathrm{\underline {incorrect} }$$ statement(s) from the following is ___________

(A) $$\Lambda \mathop m\limits^o $$ for electrolyte A is obtained by extrapolation

(B) For electrolyte B, $$\Lambda \mathop m\limits $$ vs $$\sqrt c$$ graph is a straight line with intercept equal to $$\Lambda \mathop m\limits^o $$

(C) At infinite dilution, the value of degree of dissociation approaches zero for electrolyte B.

(D) $$\Lambda \mathop m\limits^o $$ for any electrolyte A and B can be calculated using $$\lambda^\circ$$ for individual ions

$$Pt(s)|{H_2}(g)(1\,bar)|{H^ + }(aq)(1\,M)||{M^{3 + }}(aq),{M^ + }(aq)|Pt(s)$$

The $$\mathrm{E_{cell}}$$ for the given cell is 0.1115 V at 298 K when $${{\left[ {{M^ + }(aq)} \right]} \over {\left[ {{M^{3 + }}(aq)} \right]}} = {10^a}$$

The value of $$a$$ is ____________

Given : $$\mathrm{E_{{M^{3 + }}/{M^ + }}^\theta = 0.2}$$ V

$${{2.303RT} \over F} = 0.059V$$