If, for a dimerization reaction, 2A_(g) → A_2(g)  at   298 K , ∆U^Θ = -20 kJ mol^-1   ∆S^Θ   = - 30 J K^-1mol^-1 , then ∆G^Θ  will be:

1. -10. 4 kJ

2. 18.9 kJ

3. -13.5 kJ

4. 17. 4 kJ

The incorrect expression among the following is -

1. In isothermal process, ${\mathrm{W}}_{\text{reversible\hspace{0.17em}}}=-\mathrm{nRT}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\frac{{\mathrm{V}}_{\mathrm{f}}}{{\mathrm{V}}_{\mathrm{i}}}$

2. $\ln K=\frac{{\mathrm{\Delta H}}^{\circ }-{\mathrm{T\Delta S}}^{\circ }}{\mathrm{RT}}$

3. $\mathrm{K}={\mathrm{e}}^{-{\mathrm{\Delta G}}^{\circ }/\mathrm{RT}}$

4. $\frac{{\mathrm{\Delta G}}_{\text{system\hspace{0.17em}}}}{{\mathrm{\Delta S}}_{\text{total\hspace{0.17em}}}}=-\mathrm{T}$

Assuming ideal behaviour, the magnitude of log K for the following reaction at 25°C is
x × 10^–1 . The value of x is:

$3\mathrm{HC}\equiv {\mathrm{CH}}_{\left(\mathrm{g}\right)}\rightleftharpoons {\mathrm{C}}_6{{\mathrm{H}}_6}_{\left(\mathrm{l}\right)}$

$[\text{\hspace{0.17em}Given:\hspace{0.17em}}$
${\mathrm{\Delta }}_f{\mathrm{G}}^{\circ }(\mathrm{HC}\equiv \mathrm{CH})=-2.04\times {10}^5\mathrm{J}{\mathrm{mol}}^{-1}$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\circ }\left({\mathrm{C}}_6{\mathrm{H}}_6\right)=-1.24\times {10}^5\mathrm{J}{\mathrm{mol}}^{-1}$

$\mathrm{R}=8.314\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}]$

1. 860

2. 875

3. 855

4. 895