Question

Consider the inter conversion of nitrosotriaceto amine into nitrogen, phorone and water.



The reaction is $1^{st}$ order in each direction, with an equilibrium constant of ${10}^4$. The activation energy for the backward reaction is 57.45 kJ/mol. Assume its Arrhenius pre exponential factor as ${10}^{12}{s}^{-1}$.

If the change in entropy of the reaction is $0.07kJ{K}^{-1}mo{l}^{-1}$ at 1 atm pressure. Calculate upto which temperature the forward reaction would not be spontaneous?

• A. T < 285.7 K
• B. T > 250 K
• C. T < 340.2 K
• D. T > 200 K

Answer 1

The correct option is A T < 285.7 K

$\Delta G=\Delta H-T\Delta S$
$\Delta G=20-T\times 0.07$
At equilibrium, $\Delta G=0$
$0=20-T\times 0.07$
$T=\frac{20}{0.07}=285.7K$
When T < 285.7, the reaction is non spontaneous