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Q. $C_2H_6\left(g\right) + 3.5 O_2\left(g\right) \to2CO_2\left(g\right) + 3H_2O\left(g\right)$
$\Delta S_{\text{vap}}\left(H_{2}O,l\right)=x_{1}cal K^{-1}\left(\text{boiling point}=T_{1}\right)$
$\Delta H_{f}\left(H_{2}O,l\right)=x_{2}$
$\Delta H_{f}\left(CO_{2}\right)=x_{3}$
$\Delta H_{f}\left(C_{2}H_{6}\right)=x_{4} $
Hence, $\Delta H$ for the reaction is

Thermodynamics

Solution:

$H_{2}O\left(l\right)\to H_{2}O\left(g\right)\Delta H_{\text{vap}}=\Delta S_{\text{vap}}T_{B.P}=x_{1}T_{1}$
$\Delta H_{f}\left(H_{2}O,g\right)=\Delta H_{f}\left(H_{2}O,l\right)+\Delta H_{\text{vap}}=x_{2}+x_{1}T_{1}$
$\Delta H_{\text{reaction}}=2\Delta H_{f}\left(CO_{2,g}\right)+3\Delta H_{f}\left(H_{2}Og\right)-\Delta H_{f}\left(C_{2}H_{6,}g\right)$
$=2x_{3}+3\left(x_{2}+x_{1}T_{1}\right)-x_{4} =2x_{3}+3x_{2}+3x_{1}T_{1}-x_{4}$