Question

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

• A. 192.5
• B. - 192.5
• C. 96.25
• D. +96.25

Answer 1

Answer: (A)

$2 \mathrm{C}($ graphite $)+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow 1 \mathrm{C}_2 \mathrm{H}_6+\Delta \mathrm{H}_{\mathrm{f}}\left(\mathrm{C}_2 \mathrm{H}_6\right)$
(A) $C_{2}H_{6}+\frac{7}{2}O_{2} \rightarrow \text{2C}\text{O}_{2}+\text{3}\text{H}_{2}O$

$\Delta H_{C}=-\text{1560}$

(B) $H_{2}+\frac{1}{2}O_{2} \rightarrow H_{2}O$

$\Delta H_{C}=-\text{393}.5$

(C) C(graphite) $+O_{2} \rightarrow \text{C}\text{O}_{2}$

$\Delta H_{C}=-\text{286kJ/mol}$

$\Delta H_{f}\left(\right.C_{2}H_{6}\left.\right)=3\left(\right.-\text{393}.5\left.\right)+2\left(\right.-\text{286}\left.\right)+\text{156}0$

$=-\text{118}0.5+\left(\right.-\text{572}\left.\right)+\text{156}0$

$=\text{192}.5$

$2C\left(g r a p h i t e\right)+3H_{2} \rightarrow C_{2}H_{6}$ (1) eqⁿ

$C_{2}H_{6}+\frac{7}{2}O_{2} \rightarrow 2CO_{2}+3H_{2}O$ (2) eqⁿ

$H_{2}+\frac{1}{2}O_{2} \rightarrow 2CO_{2}+3H_{2}O$ (3) eqⁿ

$C\left(g r a p h i t e\right)+H_{2}O \rightarrow CO_{2}$ (4) eqⁿ

To get equation (1) eqⁿ (2) + 2 × eqⁿ (3) 2 × eqⁿ

$\Delta H_{f}$ of ethane $=1560+2\times \left(- 286\right)+3\left(\right.-393.5\left.\right)$

$=1560-572-1180.5=192.5$