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
ΔG = ΔH – TΔS = 179.2 kJ – (298 K)\left(0.1600\frac{kJ}{K}\right) = +131.5 kJ
Because ΔG is positive at this temperature, the reaction is nonspontaneous.
The changeover point between spontaneous and nonspontaneous is approximately
T = \frac{ΔH}{ΔS} = \frac{179.2 kJ}{0.1600 \frac{kJ}{K}} = 1120K
The reaction becomes spontaneous above approximately 1120 K (847 °C).