Overview
This lecture covers calculating Gibbs free energy (ΔG) to determine reaction spontaneity, including a worked example and finding the temperature where a reaction becomes spontaneous.
Calculating ΔG for a Reaction
- ΔG (Gibbs free energy) determines if a reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0).
- The equation is ΔG = ΔH – TΔS, where ΔH is enthalpy change and ΔS is entropy change.
- Ensure units match: convert ΔS from J/K to kJ/K if ΔH is in kJ (1,000 J = 1 kJ).
- Example: For decomposition of carbon tetrachloride,
- ΔH = +95.7 kJ
- ΔS = +142.2 J/K = +0.1422 kJ/K
- Temperature (T) in Kelvin: 25°C = 298 K
Example Calculation
- Substitute values: ΔG = 95.7 kJ – (298 K × 0.1422 kJ/K)
- ΔG = 95.7 kJ – 42.4 kJ = +53.3 kJ
- Since ΔG is positive, the reaction is non-spontaneous at 25°C.
Determining the Temperature for Spontaneity
- A reaction is at equilibrium when ΔG = 0.
- Set the equation to zero: 0 = ΔH – TΔS → T = ΔH / ΔS
- Using the values: T = 95.7 kJ / 0.1422 kJ/K ≈ 673 K
- The reaction becomes spontaneous above 673 K.
Key Terms & Definitions
- ΔG (Gibbs Free Energy) — Measures the spontaneity of a process; negative values mean spontaneous.
- ΔH (Enthalpy) — Heat content change during a reaction, typically in kJ.
- ΔS (Entropy) — Disorder change in a system, reported in J/K or kJ/K.
- Spontaneous Reaction — Proceeds without external energy (ΔG < 0).
- Equilibrium — State where ΔG = 0; no net reaction direction.
Action Items / Next Steps
- Practice calculating ΔG and temperature for spontaneity using different reaction data.
- Review entropy and enthalpy unit conversions.
- Read textbook section on Gibbs free energy and spontaneity.