Question

$K_P$ for reaction $A+B\rightleftharpoons C+D$ is 1.34 at ${60}^{o}C$ and 6.64 at ${100}^{o}C$. Determine the free energy change of this reaction at each temperature and $\Delta H^o$ for the reaction over this range of temperature?

• A. 405J/mol ; 5872 J/mol and 41.3 kJ/mol
• B. 810 J/mol ; 5870 J/mol and 41.3 kJ/mol
• C. 405J/mol ; 5 J/mol and 20.56 kJ/mol
• D. 810 J/mol ; 29362 J/mol and 20.56 kJ/mol

Answer 1

Answer: (B)

810 J/mol ; 5870 J/mol and 41.3 kJ/mol

$\Delta G=-RTlnK$

At 333 K,

$\Delta G=-8.314\times 333\times ln1.34=-810J/mol$

At 373 K,

$\Delta G=-8.314\times 373\times ln6.64=-5870J/mol$

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

Assume $\Delta H$ and $\Delta S$ are constant over temperature range.

$-810=\Delta H-333\times \Delta S$......(1)

$-5870=\Delta H-373\times \Delta S$......(2)

From equation (1) $\Delta S=\frac{\Delta H+810}{333}$

Substitute this in (2)

$-5870=\Delta H-\frac{373}{333}(\Delta H+810)$

$\Delta H=41300J/mol=41.3kJ/mol$