Calculating K from the Standard Free-Energy Change (Molecular Equation) Find the value of the equilibrium constant K at 25°C (298 K) for the reaction 2NH3(g) + CO2(g) ⇌ NH2CONH2(aq) + H2O(l) The standard free-energy change, ΔG°, at 25°C equals 13.6 kJ. (We calculated this value of ΔG°=ΔH°-TΔS° just

Question

Calculating K from the Standard Free-Energy Change (Molecular Equation)

Find the value of the equilibrium constant [latex]K[/latex] at [latex]25^{\circ} \mathrm{C}(298 \mathrm{~K})[/latex] for the reaction

[latex]2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)[/latex]

The standard free-energy change, [latex]\Delta G^{\circ}[/latex], at [latex]25^{\circ} \mathrm{C}[/latex] equals [latex]-13.6 \mathrm{~kJ}[/latex]. (We calculated this value of [latex]\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}[/latex] just before Section 19.4.)

PROBLEM STRATEGY

Rearrange the equation [latex]\Delta G^{\circ}=-R T \ln K[/latex] to give

[latex]\ln K=\frac{\Delta G^{\circ}}{-R T}[/latex]

[latex]\Delta G^{\circ}[/latex] and [latex]R[/latex] must be in compatible units. You normally express [latex]\Delta G^{\circ}[/latex] in joules and set [latex]R[/latex] equal to [latex]8.31 \mathrm{~J} /(\mathrm{K} \cdot \mathrm{mol})[/latex].

Accepted Answer

Substituting numerical values into this equation,

[latex]\ln K=\frac{-13.6 imes 10^{3}}{-8.31 imes 298}=5.49[/latex]

Hence,

[latex]K=e^{5.49}=2.42 imes 10^{2}[/latex]

Note that although the value of [latex]K[/latex] indicates that products predominate at equilibrium, [latex]K[/latex] is only moderately large. You would expect that the composition could be easily shifted toward reactants if you could remove either [latex]\mathrm{NH}_{3}[/latex] or [latex]\mathrm{CO}_{2}[/latex] (according to Le Chatelier's principle). This is what happens when urea is used as a fertilizer. As [latex]\mathrm{NH}_{3}[/latex] is used up, more [latex]\mathrm{NH}_{3}[/latex] is produced by the decomposition of urea.

Question 19.8: Calculating K from the Standard Free-Energy Change (Molecula...

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