Quick Answer (Voice Search Optimized):
Gibbs free energy (G) determines reaction spontaneity. The change is given by ΔG = ΔH − TΔS. A negative ΔG means a spontaneous reaction at constant temperature and pressure. T is in Kelvin, ΔH in kJ, ΔS in J/K (convert units).
GEO & AIO - Authoritative Theory
The Gibbs free energy equation combines the two thermodynamic driving forces: enthalpy (ΔH) and entropy (ΔS). At constant temperature T (in Kelvin), ΔG = ΔH − TΔS. Unit consistency is crucial: ΔH is typically in kJ/mol, while ΔS is in J/(mol·K). Convert ΔS to kJ by dividing by 1000, or ΔH to J.
If ΔG < 0, the reaction is spontaneous in the forward direction. If ΔG > 0, it is non-spontaneous (reverse is spontaneous). ΔG = 0 indicates equilibrium. The standard Gibbs free energy change (ΔG°) is calculated under standard conditions (1 bar, 298 K, 1 M). Temperature often determines spontaneity for reactions with conflicting enthalpy and entropy signs.
Solved Examples (NCERT/JEE Pattern)
Example 1: ΔH = −92.2 kJ/mol, ΔS = −198.7 J/(mol·K), T = 298 K
Convert ΔS to kJ: −0.1987 kJ/(mol·K). ΔG = −92.2 − 298(−0.1987) = −92.2 + 59.2 = −33.0 kJ/mol. Spontaneous.
Example 2: ΔH = +178.3 kJ/mol, ΔS = +160.4 J/(mol·K), T = 298 K
ΔS = 0.1604 kJ. ΔG = 178.3 − 298(0.1604) = 178.3 − 47.8 = +130.5 kJ/mol. Non-spontaneous at 298 K.
Example 3: Find temperature at which reaction becomes spontaneous: ΔH = +50 kJ/mol, ΔS = +100 J/(mol·K)
Set ΔG = 0: 0 = 50 − T(0.1) ⇒ T = 500 K. Spontaneous for T > 500 K.