Question

For the hypothetical reaction, $A_2\left(g\right)+B_2\left(g\right)\rightleftharpoons 2AB\left(g\right)$, if ${\Delta }_r{G}^o$ and ${\Delta }_r{S}^o$ are $20kJ/mol$ and $-20{JK}^{-1}{mol}^{-1}$ respectively at 200 K. ${\Delta }_r{C}_p$ is $20J{K}^{-1}mo{l}^{-1}$.

Then value $\frac{{\Delta }_r{H}^o}{10}$ of ($kJ/mol$) at 400 K is:

Answer 1

The relationship between the standard Gibbs free energy change, the standard enthalpy change and the standard entropy change is as shown.

${\Delta G}_{200}^o={\Delta H}_{200}^0-T\Delta S_{200}^0$

$20\times {10}^3=\Delta H_{200}^0-200\times (-20)$

${\Delta H}_{200}^0=16000$ J mol${}^{-1}=16$ kJ mol${}^{-1}$.

The relationship between the enthalpy change at two different temperatures and the heat capacity at constant pressure is as shown.

${\Delta H}_{T_2}^0={\Delta H}_{T_2}+{\Delta C}_p[T_2-T_1]$

${\Delta H}_{400}^0={\Delta H}_{200}^0+\frac{20\times 200}{1000}$kJ mol${}^{-1}$.

$=16+4=20$kJ mol${}^{-1}$.

Hence, the standard enthalpy change for the reaction at 400 K is 20 kJ/mol.

$\frac{{\Delta H}_{400}^0}{10}=\frac{20}{10}=2$ kJ mol${}^{-1}$.