Question

The value of $\Delta U$ for the reaction $2A\left(g\right)+B\left(g\right)\rightleftharpoons A_{2}B\left(g\right)$ for which $K_p=1.0\times {10}^{-10}{atm}^{-2}$ and $\Delta S=5J{K}^{-1}$ and $T=300K$, is :

• A. 53.93 kJ
• B. 63.93 kJ
• C. 56.24 kJ
• D. 68.24 kJ

Answer 1

The correct option is B 63.93 kJ

As we know,
$\Delta G=-2.303RT\log K_p$
$=-2.303\times 8.314\times 300\times \log {10}^{-10}$
$=57.441kJ$

$\Delta H=\Delta G+T\Delta S=57.441+300\times 5\times {10}^{-3}$
$=58.941kJ$

$\Delta H=\Delta U+\Delta n_{g}RT$
or $58.941=\Delta U+(-2)\times 8.314\times 300\times {10}^{-3}$

$\therefore \Delta U=63.93kJ$

Hence, option B is correct.