The rate of effusion of an equilibrium mixture in one litre vessel of at 300 K ${\text{A}}_{\text{2}}\rightleftharpoons \text{\hspace{0.17em}2A}$ through a

pin hole is 0.707 times of rate of diffusion of ${\text{O}}_{\text{2}}$ under identical conditions of P and T. Which of

the following are correct if at. Wt. of A is 46:

$\frac{{\text{r}}_{\text{m}}}{{\text{r}}_{{\text{O}}_{\text{2}}}}\text{\hspace{0.17em}=\hspace{0.17em}}\sqrt{\frac{{\text{M}}_{{\text{O}}_{\text{2}}}}{{\text{M}}_{\text{mix}}}}\text{\hspace{0.17em}=\hspace{0.17em}}\sqrt{\frac{\text{32}}{\text{M}}}\text{\hspace{0.17em}=\hspace{0.17em}0.707\hspace{0.17em}or\hspace{0.17em}M\hspace{0.17em}=\hspace{0.17em}64}$

Let a mole of ${\text{A}}_2$ be present in mixture , then $\therefore \text{\hspace{0.17em}64\hspace{0.17em}=\hspace{0.17em}}\frac{\text{a\hspace{0.17em}×\hspace{0.17em}92\hspace{0.17em}+\hspace{0.17em}}(\text{100\hspace{0.17em}}-\text{\hspace{0.17em}a})\text{\hspace{0.17em}×\hspace{0.17em}46}}{\text{100}}$

A = a = 39.13 moles and ${\text{A}}_{\text{2}}\text{\hspace{0.17em}=\hspace{0.17em}60.87\hspace{0.17em}moles}$

$\therefore {\text{\hspace{0.17em}K}}_{\text{C}}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left[\text{A}\right]}^{\text{2}}}{\left[{\text{A}}_{\text{2}}\right]}\text{\hspace{0.17em}=\hspace{0.17em}}\frac{{\left(\text{39.13}\right)}^{\text{2}}}{\text{60.87}}\text{\hspace{0.17em}=\hspace{0.17em}25.16;}$

$\text{ΔG°\hspace{0.17em}=\hspace{0.17em}}-\text{\hspace{0.17em}2.303\hspace{0.17em}RT\hspace{0.17em}log\hspace{0.17em}K}$

$\text{ΔG°\hspace{0.17em}= -\hspace{0.17em}2.303\hspace{0.17em}×\hspace{0.17em}300\hspace{0.17em}×\hspace{0.17em}8.314\hspace{0.17em}log\hspace{0.17em}25.16\hspace{0.17em}=\hspace{0.17em}}-{\text{\hspace{0.17em}8.01\hspace{0.17em}×\hspace{0.17em}10}}^{\text{3}}\text{J}$