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# what would be the expression in place of ? in the Van't Hoff equation: $log \frac{K_2}{K_1} = \frac {\Delta H^\circ}{2.303R} [?]$

(a) $\frac {1}{T_1} + \frac {1}{T_2}$

(b) $\frac {1}{T_1} - \frac {1}{T_2}$

(c) $\frac {1}{T_2} - \frac {1}{T_1}$

(d) $\frac {1}{T_1 T_2}$

Toolbox:
• The Vant Hoff equation is: $\frac{d ln K_p}{dT} = \frac {- \Delta H^\circ}{T^2}$

Answer: $log \frac{K_2}{K_1} = \frac {\Delta H}{2.303R} [ \frac {T_2 - T_1}{T_1 T_2}]$

The Vant Hoff equation is:
$\frac{d ln K_p}{dT} = \frac {- \Delta H^\circ}{T^2}$

Integrating the Vant Hoff equation we get,

$\Rightarrow \int \mathrm{d} ln K_p = \frac{\Delta H^\circ}{R} \int \frac {\mathrm{d} T}{T^2} T$
$\Rightarrow ln K_p = - \frac{\Delta H^\circ}{R} \frac {1}{T} + 1$

If equilibrium constants at $T_1$ and $T_2$ are $K_1$ and $K_2$ respectively,

$log \frac{K_2}{K_1} = \frac {\Delta H}{2.303R} [ \frac {T_2 - T_1}{T_1 T_2}]$

edited Nov 23, 2013