For complete combustion of ethanol, C2H5OH(l)+3O2(g)⟶CO2(g)+3H2O(l), the heat produced as measured in bomb calorimeter, is  1364.47kJmol−1 at 25°C. Assuming ideality the enthlapy of combustion, ΔcH, for the reaction will be R=8.314JK−1mol−1

# For complete combustion of ethanol, ${\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{OH}\left(\mathrm{l}\right)+3{\mathrm{O}}_{2}\left(\mathrm{g}\right)⟶{\mathrm{CO}}_{2}\left(\mathrm{g}\right)+3{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{l}\right)$, the heat produced as measured in bomb calorimeter, is  $1364.47\mathrm{kJ}{\mathrm{mol}}^{-1}$ at 25°C. Assuming ideality the enthlapy of combustion, ${\mathrm{\Delta }}_{\mathrm{c}}H,$ for the reaction will be $\left(R=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right)$

1. A

$-1350.50\mathrm{kJ}{\mathrm{mol}}^{-1}$

2. B

$-1366.95\mathrm{kJ}{\mathrm{mol}}^{-1}$

3. C

$-1361.95\mathrm{kJ}{\mathrm{mol}}^{-1}$

4. D

$-1460.50\mathrm{kJ}{\mathrm{mol}}^{-1}$

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### Solution:

For the given reaction, $\mathrm{\Delta }{v}_{\mathrm{g}}=-1$. Hence

$\begin{array}{l}\mathrm{\Delta }{H}^{\circ }=\mathrm{\Delta }{U}^{\circ }+\left(\mathrm{\Delta }{v}_{\mathrm{g}}\right)RT=\left(-1364.47\mathrm{kJ}{\mathrm{mol}}^{-1}\right)+\left(-1\right)\left(8.314×{10}^{-3}{\mathrm{kJK}}^{-1}{\mathrm{mol}}^{-1}\right)\left(298\mathrm{K}\right)\\ =-1366.95\mathrm{kJ}{\mathrm{mol}}^{-1}\end{array}$