Question

For $A\to B,\Delta H=4kcalmo{l}^{-1},\Delta S=10calmo{l}^{-1}{k}^{-1}$ is spontaneous when temperature can be:

• A. $400K$
• B. $300K$
• C. $500K$
• D. $200K$

Answer 1

Answer: (C)

$500K$

Given $\Delta H=4kcalmo{l}^{-1}=4000calmo{l}^{-1}$

$\Delta S=10calmo{l}^{-1}{k}^{-1},\Delta G=0$

at equilibrium

$\Delta G=\Delta H-T\Delta S$

or

$0=4000-T$ $\times$ $10or10T=4000$

$\therefore T=\frac{4000}{10}=400K$

$\therefore$ At temperature above $400K$ the reaction is spontaneous.

$500K$ is the only choice above $400K$