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 the electrochemical cell,

$$\left. {Mg\left( s \right)} \right|M{g^{2 + }}\left( {aq,1\,M} \right)\left\| {C{u^{2 + }}} \right.\left( {aq,1M} \right)\left| {Cu\left( s \right)} \right.$$

the standard $$emf$$ of the cell is $$2.70$$ $$V$$ at $$300$$ $$K.$$ When the concentration of $$M{g^{2 + }}$$ is changed to $$x$$ $$M,$$ the cell potential changes to $$2.67$$ $$V$$ at $$300$$ $$K.$$ The value of $$x$$ is ___________.

(given, $${F \over R} = 11500\,K{V^{ - 1}},$$ where $$F$$ is the Faraday constant and $$R$$ is the gas constant, In $$(10=2.30)$$

The conductance of a $$0.0015$$ $$M$$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $$Pt$$ electrodes. The distance between the electrodes is $$120$$ $$cm$$ with an area of cross section of $$1$$ $$c{m^2}.$$ The conductance of this solution was found to be $$5 \times {10^{ - 7}}S.$$ The $$pH$$ of the solution is $$4.$$ The value of limiting molar conductivity $$\left( {\Lambda _m^o} \right)$$ of this weak monobasic acid in aqueous solution is $$Z \times {10^2}S$$ $$c{m^2}$$ $$mo{l^{ - 1}}.$$ The value of $$Z$$ is

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If $$\lambda _{{x^ - }}^0 \approx \lambda _{{y^ - }}^0$$ the difference in their pK_a values, pK_a(HX) - pK_a(HY), is (consider degree of ionization of both acids to be << 1)