USING THE FREE-ENERGY EQUATION TO CALCULATE EQUILIBRIUM TEMPERATURE Lime (CaO) is produced by heating limestone [latex](CaCO_{3})[/latex] to drive off [latex]CO_{2}[/latex] 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. [latex]CaCO_{3}(s) → CaO(s) + CO_{2}(g)[/latex] 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)[latex]\left(0.1600\frac{kJ}{K}\right)[/latex] = +131.5 kJ Because ΔG is positive at this temperature, the reaction is nonspontaneous. The changeover point between spontaneous and nonspontaneous is approximately T = [latex]\frac{ΔH}{ΔS} = \frac{179.2 kJ}{0.1600 \frac{kJ}{K}}[/latex] = 1120K The reaction becomes spontaneous above approximately 1120 K (847 °C).

Question 8.12: USING THE FREE-ENERGY EQUATION TO CALCULATE EQUILIBRIUM TEMP...

Chemistry

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.

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