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 $)+3{\mathrm{H}}_2(\mathrm{g})\to 1{\mathrm{C}}_2{\mathrm{H}}_6+\Delta {\mathrm{H}}_{\mathrm{f}}\left({\mathrm{C}}_2{\mathrm{H}}_6\right)$
(A) $C_2{H}_6+\frac{7}{2}{O}_2\to \text{2C}{\text{O}}_2+\text{3}{\text{H}}_{2}O$

$\Delta H_C=-\text{1560}$

(B) $H_2+\frac{1}{2}{O}_2\to H_{2}O$

$\Delta H_C=-\text{393}.5$

(C) C(graphite) $+O_2\to \text{C}{\text{O}}_2$

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

$\Delta H_f(C_2{H}_6)=3(-\text{393}.5)+2(-\text{286})+\text{156}0$

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

$=\text{192}.5$

$2C\left(graphite\right)+3H_2\to C_2{H}_6$ (1) eqⁿ

$C_2{H}_6+\frac{7}{2}{O}_2\to 2C{O}_2+3H_{2}O$ (2) eqⁿ

$H_2+\frac{1}{2}{O}_2\to 2C{O}_2+3H_{2}O$ (3) eqⁿ

$C\left(graphite\right)+H_{2}O\to C{O}_2$ (4) eqⁿ

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

$\Delta H_f$ of ethane $=1560+2\times \left(-286\right)+3(-393.5)$

$=1560-572-1180.5=192.5$