MCQ
For the hypothetical reaction

${A_2}\left( g \right) + {B_2}\left( g \right) \rightleftharpoons 2AB\left( g \right)$

${\Delta _r}{G^o}$ and ${\Delta _r}{S^o}$ are $20\, kJ/mol$ and $-20\, JK^{-1}\, mol^{-1}$ respectively at $200\, K$.

If ${\Delta _r}{C_P}$ is $20\, JK^{-1}\, mol^{-1}$ then ${\Delta _r}{H^o}$ at $400\, K$ is.....$kJ/mol$

  • $20$
  • B
    $7.98$
  • C
    $28$
  • D
    None of these

Answer

Correct option: A.
$20$
a
$\Delta \mathrm{G}_{200}^{\circ}=\Delta \mathrm{H}_{200}^{\circ}-\mathrm{T} \Delta \mathrm{S}_{200}^{\circ}$

$\Delta \mathrm{H}_{2 \mathrm{0} 0}^{\circ}=20-4=16\, \mathrm{kJ} / \mathrm{mol}$

$\Delta \mathrm{H}_{\mathrm{T}_{2}}^{\circ}=\Delta \mathrm{H}_{\mathrm{T}_{1}}^{\circ}+\Delta \mathrm{C}_{\mathrm{P}}\left[\mathrm{T}_{2}-\mathrm{T}_{1}\right]$

$\Delta \mathrm{H}_{400}^{\circ}=\Delta \mathrm{H}_{200}^{\circ}+\frac{20 \times 200}{1000} \,\mathrm{kJ} / \mathrm{mol}$

$=16+4=20 \,\mathrm{kJ} / \mathrm{mole}$

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