Gibbs Free Energy

Gibbs free energy (ΔG) determines whether a reaction is spontaneous. It combines enthalpy and entropy to predict if a reaction will occur without external energy input.

Gibbs Free Energy Equation

ΔG = ΔH - TΔS

Free energy change determines spontaneity

Variable Definitions

ΔG = Gibbs Free Energy Change

Units: J/mol or kJ/mol

Meaning: Energy available to do work

✓ ΔG < 0 → Spontaneous (exergonic)

• ΔG = 0 → Equilibrium

✗ ΔG > 0 → Non-spontaneous (endergonic)

ΔH = Enthalpy Change

Units: J/mol or kJ/mol

Meaning: Heat absorbed or released

ΔH < 0 = exothermic (releases heat)

T = Temperature

Units: Kelvin (K) — MUST use Kelvin!

Conversion: K = °C + 273.15

ΔS = Entropy Change

Units: J/(mol·K)

Meaning: Change in disorder

⚠️ Often in J/(mol·K) while ΔH is in kJ/mol — convert units!

Predicting Spontaneity

ΔHΔSΔGSpontaneity
Negative (-)Positive (+)Always negativeAlways spontaneous at all T
Negative (-)Negative (-)Negative at low TSpontaneous at low temperature
Positive (+)Positive (+)Negative at high TSpontaneous at high temperature
Positive (+)Negative (-)Always positiveNever spontaneous

Step-by-Step Example

Problem: Is a reaction spontaneous at 298 K if ΔH = -75 kJ/mol and ΔS = -120 J/(mol·K)?

Given:

  • ΔH = -75 kJ/mol
  • ΔS = -120 J/(mol·K)
  • T = 298 K

Step 1: Convert units

ΔH and TΔS must have same units. Convert ΔS to kJ/(mol·K):

ΔS = -120 J/(mol·K) × (1 kJ / 1000 J) = -0.120 kJ/(mol·K)

Step 2: Calculate TΔS

TΔS = 298 K × (-0.120 kJ/(mol·K)) = -35.8 kJ/mol

Step 3: Calculate ΔG

ΔG = ΔH - TΔS = -75 - (-35.8) = -39.2 kJ/mol

Answer: ΔG = -39.2 kJ/mol (negative)

✓ Spontaneous! Exothermic overcomes negative entropy.

Common Mistakes

❌ Mismatched units

ΔH is often in kJ/mol while ΔS is in J/(mol·K). Convert ΔS to kJ/(mol·K) or ΔH to J/mol!

❌ Forgetting the minus sign

It's ΔG = ΔH - TΔS, not ΔG = ΔH + TΔS. The minus is crucial!

❌ Using Celsius instead of Kelvin

Temperature MUST be in Kelvin. Convert °C to K by adding 273.15.

❌ Confusing spontaneous with fast

ΔG < 0 means thermodynamically favorable, NOT necessarily fast. Kinetics is separate!

Related Calculators

Frequently Asked Questions

What is Gibbs free energy?

ΔG = ΔH - TΔS. It predicts reaction spontaneity. ΔG < 0 means spontaneous, ΔG > 0 means non-spontaneous.

What does ΔG < 0 mean?

Negative ΔG means the reaction is thermodynamically favorable (spontaneous) and can occur without external energy input.

How do temperature changes affect ΔG?

Temperature affects the TΔS term. High T favors positive ΔS reactions, low T favors negative ΔH reactions.

What is the relationship between ΔG and equilibrium?

ΔG° = -RT ln K. When ΔG = 0, the system is at equilibrium. ΔG° relates to the equilibrium constant K.

Why are units important in this equation?

ΔH and TΔS must have matching units (both kJ/mol or both J/mol). ΔS is often given in J/(mol·K), requiring conversion.