Question

For the reaction, $2A\left(g\right)+B\left(g\right)\rightleftharpoons A_{2}B\left(g\right)$ for which $\Delta S=5.0J/K$, $K=1.0\times {10}^{-10}$, and $T=300K$, $\Delta E^o$ will be:

Answer 1

For the reaction,
$2A\left(g\right)+B\left(g\right)\rightleftharpoons A_{2}B\left(g\right)$
The change in the number of moles of gas, $\Delta n=-2$
$\Delta G=-2.303RT\log K$
$\Delta G=-2.303\times 8.314\times 300\times (-10)$
$\Delta G=57.3kJ$
$\Delta H^o=\Delta G^o+T\Delta S^o$
$\Delta H^o=57.3\times {10}^3+300\times 5$
$\Delta H^o=58.8kJ$
Assuming ideal gas behaviour,
$\Delta \left(pV\right)=\left(\Delta n\right)RT$
$\Delta E^o=\Delta H^o-\Delta \left(pV\right)$
$\Delta E^o=\Delta H^o-\left(\Delta n\right)RT$
$\Delta E^o=58.8-(-2)\times 8.314\times {10}^{-3}\times 300$
$\Delta E^o=63.8kJ$