Consider the cell

$$\mathrm{Pt(s)|{H_2}(g)\,(1\,atm)|{H^ + }\,(aq,[{H^ + }] = 1)||F{e^{3 + }}(aq),F{e^{2 + }}(aq)|Pt(s)}$$

Given $$\mathrm{E_{F{e^{3 + }}/F{e^{2 + }}}^o = 0.771\,V}$$ and $$\mathrm{E_{{H^ + }/1/2\,{H_2}}^o = 0\,V,\,T = 298\,K}$$

If the potential of the cell is 0.712 V, the ratio of concentration of Fe$$^{2+}$$ to Fe$$^{3+}$$ is _____________ (Nearest integer)

At 298 K, a 1 litre solution containing 10 mmol of $$\mathrm{C{r_2}O_7^{2 - }}$$ and 100 mmol of $$\mathrm{Cr^{3+}}$$ shows a pH of 3.0.

Given : $$\mathrm{C{r_2}O_7^{2 - } \to C{r^{3 + }}\,;\,E^\circ = 1.330}$$V

and $$\mathrm{{{2.303\,RT} \over F} = 0.059}$$ V

The potential for the half cell reaction is $$x\times10^{-3}$$ V. The value of $$x$$ is __________

For a cell, $$\mathrm{Cu}(\mathrm{s})\left|\mathrm{Cu}^{2+}(0.001 \,\mathrm{M}) \| \mathrm{Ag}^{+}(0.01 \,\mathrm{M})\right| \mathrm{Ag}(\mathrm{s})$$

the cell potential is found to be $$0.43 \mathrm{~V}$$ at $$298 \mathrm{~K}$$. The magnitude of standard electrode potential for $$\mathrm{Cu}^{2+} / \mathrm{Cu}$$ is _________ $$\times 10^{-2} \mathrm{~V}$$.

[Given : $$E_{A{g^ + }/Ag}^\Theta $$ = 0.80 V and $${{2.303RT} \over F}$$ = 0.06 V]

Resistance of a conductivity cell (cell constant $$129 \mathrm{~m}^{-1}$$) filled with $$74.5 \,\mathrm{ppm}$$ solution of $$\mathrm{KCl}$$ is $$100 \,\Omega$$ (labelled as solution 1). When the same cell is filled with $$\mathrm{KCl}$$ solution of $$149 \,\mathrm{ppm}$$, the resistance is $$50 \,\Omega$$ (labelled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is i.e. $$\frac{\wedge_{1}}{\wedge_{2}}=x \times 10^{-3}$$. The value of $$x$$ is __________. (Nearest integer)

Given, molar mass of $$\mathrm{KCl}$$ is $$74.5 \mathrm{~g} \mathrm{~mol}^{-1}$$.