The heat of combustion of ethanol into carbon dioxids and water is

Question:

The heat of combustion of ethanol into carbon dioxids and water is $-327 \mathrm{kcal}$ at constant pressure. The heat evolved (in cal) at constant volume and $27^{\circ} \mathrm{C}$ (if all gases behave ideally) is $\left(\mathrm{R}=2 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$ ______

Solution:

$(-326400)$

$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(l)$

$\Delta \mathrm{H}_{\mathrm{C}}=-327 \mathrm{Kcal}$

$\Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT}$

$\Rightarrow-327 \times 10^{3}=\Delta U+(-1) \times 2 \times 300$

$\Rightarrow \Delta U=-327 \times 10^{3}+600$

$\therefore \Delta \mathrm{U}=-326400 \mathrm{cal}$

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