Consider an electrochemical cell :

$$A\left( s \right)\left| {{A^{n + }}\left( {aq,2M} \right)} \right|{B^{2n + }}\left( {aq,1M} \right)\left| {B\left( s \right).} \right.$$

The value of $$\Delta {H^ \circ }$$ for the cell reaction is twice that of $$\Delta {G^ \circ }$$ at $$300$$ $$K.$$ If the $$emf$$ of the cell is zero, the $$\Delta {S^ \circ }$$ (in $$J\,{K^{ - 1}}mo{l^{ - 1}}$$) of the cell reaction per mole of $$B$$ formed at $$300$$ $$K$$ is ___________.

(Given: $$\ln \left( 2 \right) = 0.7,R$$ (universal gas constant) $$ = 8.3J\,{K^{ - 1}}\,mo{l^{ - 1}}.$$ $$H,S$$ and $$G$$ are enthalpy, entropy and Gibbs energy, respectively.)

For a first order reaction $$A\left( g \right) \to 2B\left( g \right) + C\left( g \right)$$ at constant volume and $$300K,$$ the total pressure at the beginning $$(t=0)$$ and at time $$t$$ are $${P_0}$$ and $${P_1},$$ respectively. Initially, only $$A$$ is present with concentration $${\left[ A \right]_0},$$ and $${t_{1/3}}$$ is the time required for the partial pressure of $$A$$ to reach $$1/{3^{rd}}$$ of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

The correct option(s) regarding the complex

$${\left[ {Co\left( {en} \right){{\left( {N{H_3}} \right)}_3}\left( {{H_2}O} \right)} \right]^{3 + }}\,\,$$ $$\left( {en = {H_2}NC{H_2}C{H_2}N{H_2}} \right)$$ is (are)

The surface of copper gets tarnished by the formation of copper oxide. $${N_2}$$ gas was passed to prevent the oxide formation during heating of copper at $$1250$$ $$K.$$ However, the $${N_2}$$ gas contains $$1$$ mole % of water vapor as impurity. The water vapor oxidises copper as per the reaction given below : $$2Cu\left( s \right) + {H_2}O\left( g \right) \to C{u_2}O\left( s \right) + {H_2}\left( g \right)$$

$${P_{H2}}$$ is the minimum partial pressure of $${H_2}$$ (in bar) needed to prevent the oxidation at $$1250$$ $$K.$$ The value of $$\ln \left( {{P_{H2}}} \right)$$ is ________.

Given: total pressure $$=1$$ bar, $$R$$ (universal gas constant ) $$=$$ $$8J{K^{ - 1}}\,\,mo{l^{ - 1}},$$ $$\ln \left( {10} \right) = 2.3.\,$$ $$Cu(s)$$ and $$C{u_2}O\left( s \right)$$ are naturally immiscible.

At $$1250$$ $$K:2Cu(s)$$ $$ + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}{O_2}\left( g \right) \to C{u_2}O\left( s \right);$$ $$\Delta {G^ \circ } = - 78,000J\,mo{l^{ - 1}}$$

$${H_2}\left( g \right) + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}{O_2}\left( g \right) \to {H_2}O\left( g \right);$$

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\Delta {G^ \circ } = - 1,78,000J\,mo{l^{ - 1}};$$ ($$G$$ is the Gibbs energy)