Question

40% of HI undergoes decomposition to $H_2$ and $I_2$ at $300K$. $\Delta G^{\circ }$ for this decomposition reaction at one atmosphere pressure is ______ $Jmo{l}^{–1}$. [nearest integer]
($\text{Use}R=8.31J{K}^{–1}mo{l}^{–1};log2=0.3010,ln10=2.3,log3=0.477)$

Answer 1

$HI\rightleftharpoons \frac{1}{2}{H}_2+\frac{1}{2}{I}_2$
$100$
$1-\alpha \frac{\alpha }{2}\frac{\alpha }{2}$
$\Delta G^{\circ }=-RT\ln K$
$=-RT\ln \frac{{\left(\frac{\alpha }{2}\right)}^{\frac{1}{2}}{\left(\frac{\alpha }{2}\right)}^{\frac{1}{2}}}{1-\alpha }$

$=-RT\ln \frac{\alpha }{2(1-\alpha )}(\alpha =0.4)$
$=-8.314\times 300\ln \frac{0.4}{2\times 0.6}$
$=+8.314\times 300\ln 3$
$=2735J/mol$