Chemistry - Thermodynamics - II Question with Solution | TestHub

Given: $\Delta U^{\circ }=2.1kcal$, $\Delta S^{\circ }=20cal/K$, $T=300K$.

For the reaction X₂O₄(ℓ) ⟶ 2XO₂(g), the change in moles of gas, $\Delta n_g=2-0=2$.

We use the relationship $\Delta H^{\circ }=\Delta U^{\circ }+\Delta n_{g}RT$.

Using $R=2calmo{l}^{-1}{K}^{-1}$:

$\Delta H^{\circ }=2.1kcal+(2mol)(2calmo{l}^{-1}{K}^{-1})(300K)$

$\Delta H^{\circ }=2.1kcal+1200cal=2.1kcal+1.2kcal=3.3kcal$.

Now, calculate $\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$.

$\Delta G^{\circ }=3.3kcal-(300K)(20cal/K)$

$\Delta G^{\circ }=3.3kcal-6000cal=3.3kcal-6.0kcal=-2.7kcal$.