The standard heat of formation \(\left(\Delta_{\mathrm{f}} \mathrm{H}_{298}^{0}\right)\) of ethane (in \(\mathrm{kJ} / \mathrm{mol}\) ), if the heat of combustion of ethane, hydrogen and graphite are \(-1560,-393.5\) and \(-286 \mathrm{~kJ} / \mathrm{mol}\) respectively is \_\_\_\_

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Chemical Thermodynamics

The standard heat of formation

(Δ_{f} H_{298}^{0})

of ethane (in

kJ / mol

), if the heat of combustion of ethane, hydrogen and graphite are

- 1560, - 393.5

and

- 286 kJ / mol

respectively is ____

Answer: -85

The formation of ethane from its elements is

2 C (graphite) + 3 H_{2} \to C_{2} H_{6}

. By Hess's law its enthalpy equals the heat released on burning the elements minus the heat released on burning ethane, so

Δ_{f} H = 2 Δ_{c} H (C) + 3 Δ_{c} H (H_{2}) - Δ_{c} H (C_{2} H_{6})

. The combustion of graphite contributes

- 393.5

for each of the two carbons and the combustion of hydrogen contributes

- 286

for each of the three hydrogen molecules, while ethane's own combustion is

- 1560

. Substituting,

Δ_{f} H = 2 (- 393.5) + 3 (- 286) - (- 1560) = - 787 - 858 + 1560 = - 85 kJ mo l^{- 1}

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Integer answer