# 6.17   For the reaction at 298 K,             2A + B $\rightarrow$ C           $\Delta H = 400 kJ mol^ {-1 }\: \: and \: \: \Delta S = 0.2 kJ K ^{-1} mol^{-1}$ At what temperature will the reaction become spontaneous considering $\Delta H$ and $\Delta S$ to be constant over the temperature range.

From the equation,

$\Delta G = \Delta H-T\Delta S$
Suppose the reaction is at equilibrium, So the change in temperature is given as;

$T=\frac{\Delta H -\Delta G}{\Delta S}$
$= \frac{400}{0.2} =2000K$  ($\Delta G$ at equilibrium is zero)
To reaction should be spontaneous, $\Delta G$ should be neagtive. So, that for the given reaction T should be greater than 2000 K

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