a
\(C _{2} H _{5} OH ( l )+3 O _{2}( g ) \rightarrow 2 CO _{2}( g )+3 H _{2} O ( l )\)

\(\Delta E =-1364.47 kJ mol ^{-1}\)

\(\Delta H =?\)

\(T =298 K\)

\(\Delta n _{ g }=-1 \because\) complete combution

\(R =8.314 J mol ^{-1}=\frac{8.314}{1000} kJ mol ^{-1}\)

\(\because \Delta H =\Delta E + P \Delta V\)

but, \(P \Delta V =\Delta n _{ g } RT\)

\(\because \Delta H =\Delta E +\Delta n _{ g } RT\)

\(\Delta H =-1364.47+\left((-1) \times \frac{8.314}{1000} \times 298\right)\)

\(\Delta H =-1366.95 kJ mol ^{-1}\)