# If the values of $\Delta H_f^{\circ}\: for\: CH_4(g), C_2H_6(g), CO_2(g)\: and \: H_2O(l)$ are respectively $-74.85, -84.68, -393.5 \: and\: -286\: kJ/mol,$ predict which is more efficient fuel?

$\begin {array} {1 1} (A)\;ethane & \quad (B)\;methane \\ (C)\;Both \: are\: equally\: efficient & \quad (D)\;Can’t\: be\: determined \end {array}$

$CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l)$
$\Delta H_1 = [2(-286) + (-393.5)] – [-74.84]$
$= -890.66\: kJ/mol$
$C_2H_6(g) + \large\frac{7}{2}$$O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l) \Delta H_2 = [3 \Delta H_f(H_2O) + 2 \Delta H_f(CO_2)] – [ \Delta H_f(C_2H_6) + \large\frac{7}{2} \times 0] = [3(-286) + 2(-393.5) – [-84.68] = -1560.32\: kJ Now, heat evolved per gram of CH_4, H_1 = \large\frac{890.66}{16}$$ = 55.66\: kJ/g$