The reduction potential $\left(E^{0}\right.$, in $\left.\mathrm{V}\right)$ of $\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})$ is __________.

[Given: $E_{\left(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{MnO}_{2}(\mathrm{~s})\right)}^{0}=1.68 \mathrm{~V} ; E_{\left(\mathrm{MnO}_{2}(\mathrm{~s}) / \mathrm{Mn}^{2+}(\mathrm{aq})\right)}^{0}=1.21 \mathrm{~V} ; E_{\left(\mathrm{Mn}^{2+}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})\right)}^{0}=-1.03 \mathrm{~V}$ ]

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $$\alpha$$ and the molar conductivity is y $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y $$\times$$ 10² S cm² mol^$$-$$1.

The value of $$\alpha$$ is __________.

At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $$\alpha$$ and the molar conductivity is y $$\times$$ 10² S cm² mol^$$-$$1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y $$\times$$ 10² S cm² mol^$$-$$1.

The value of y is __________.

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is

$${H_2}(g) + {1 \over 2}{O_2}(g)\buildrel {} \over \longrightarrow {H_2}O(l)$$

The work derived from the cell on the consumption of 1.0 $$ \times $$ 10^$$-$$3 mole of H₂(g) is used to compress 1.00 mole of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in K) of the ideal gas?

The standard reduction potentials for the two half-cells are given below :

$${O_2}(g) + 4{H^ + }(aq) + 4{e^ - }\buildrel {} \over \longrightarrow 2{H_2}O(l),$$

$${E^o} = 1.23V$$

$$2{H^ + }(aq) + 2{e^ - }\buildrel {} \over \longrightarrow {H_2}(g),$$

$${E^o} = 0.00\,V$$

Use, $$F = 96500\,C\,mo{l^{ - 1}}$$, $$R = 8.314\,J\,mo{l^{ - 1}}\,{K^{ - 1}}$$.