Question 8.12: Using the Free-Energy Equation to Calculate Equilibrium Temp......
Using the Free-Energy Equation to Calculate Equilibrium Temperature
Lime (CaO) is produced by heating limestone (CaCO_3) to drive off CO_2 gas, a reaction used to make Portland cement. Is the reaction spontaneous under standard conditions at 25 °C?
Calculate the temperature at which the reaction becomes spontaneous.
CaCO_3(s) → CaO(s) + CO_2(g) ΔH° = +179.2 kJ; ΔS° = +160.0 J/K
STRATEGY
The spontaneity of the reaction at a given temperature can be found by determining whether ΔG is positive or negative at that temperature. The changeover point between spontaneous and nonspontaneous can be found by setting ΔG = 0 and solving for T.
At 25 °C (298 K), we have
\Delta G=\Delta H-T \Delta S=179.2 \mathrm{~kJ}-(298 \mathrm{~K})\left(0.1600 \frac{\mathrm{kJ}}{\mathrm{K}}\right)=+131.5 \mathrm{~kJ}Because ΔG is positive at this temperature, the reaction is nonspontaneous. The changeover point between spontaneous and nonspontaneous is approximately
T=\frac{\Delta H}{\Delta S}=\frac{179.2 \mathrm{~kJ}}{0.1600 \frac{\mathrm{kJ}}{\mathrm{K}}}=1120 \mathrm{~K}The reaction becomes spontaneous above approximately 1120 K (847 °C).