Gibbs Free Energy (ΔG) Calculator
Determine spontaneity using either the thermodynamic relation ΔG = ΔH − TΔS (Simple) or the equilibrium/quotient forms ΔG° = −RT ln K and ΔG = ΔG° + RT ln Q (Advanced).
Background
A reaction is spontaneous (at the specified T) when ΔG < 0, non-spontaneous when ΔG > 0, and at equilibrium when ΔG ≈ 0. Mind the units: ΔH and ΔS must be consistent (J vs kJ) and T must be in Kelvin for the math (we’ll convert from °C if needed).
How to use this calculator
Choose a mode, enter your values, and hit Calculate. Use Swap to toggle kJ↔J output instantly, and Reset to clear the form.
Simple mode (ΔG = ΔH − TΔS)
- Enter ΔH (choose kJ/mol or J/mol) and ΔS (choose J/(mol·K) or kJ/(mol·K)).
- Enter T and its unit (K or °C). The calculator converts °C → K automatically.
- Click Calculate to see ΔG and a spontaneity verdict.
Advanced mode
- From K: enter temperature and the equilibrium constant K to compute ΔG° = −RT ln K.
- From Q: enter temperature, ΔG° (kJ/mol), and the reaction quotient Q to compute ΔG = ΔG° + RT ln Q.
- Pick output units (kJ/mol or J/mol); result updates immediately.
Quick tips
- Sign convention: ΔG < 0 → spontaneous; ΔG > 0 → non-spontaneous; ΔG ≈ 0 → near equilibrium.
- Be consistent with units: if ΔS is in J/(mol·K), ΔH in J/mol (or use the built-in unit toggles).
- Temperatures are handled in Kelvin internally; entering °C is fine.
- Use the example chips to autofill realistic values and see the workflow.
Formulae Used
Simple: ΔG = ΔH − TΔS (ensure ΔH and ΔS units match; T in K).
Advanced: ΔG° = −RT ln K and ΔG = ΔG° + RT ln Q (R = 8.314462618 J·mol⁻¹·K⁻¹).
Example Problems & Step-by-Step Solutions
Example 1 (Simple)
Given ΔH = −92.3 kJ/mol, ΔS = −198.5 J/mol·K, T = 298 K. Convert ΔS to kJ/mol·K: −0.1985 kJ/mol·K. ΔG = (−92.3) − (298)(−0.1985) ≈ −33.2 kJ/mol ⇒ spontaneous at 298 K.
Example 2 (Advanced, K)
T = 298 K, K = 1.0×10⁵. ΔG° = −(8.314 J/mol·K)(298 K)ln(1.0×10⁵) ≈ −(2478 J/mol)(11.51) ≈ −28.5 kJ/mol.
Example 3 (Advanced, Q)
T = 298 K, ΔG° = −8.6 kJ/mol, Q = 0.25. RT ln Q (in kJ/mol) = (8.314×298 / 1000) ln(0.25) ≈ 2.48×(−1.386) ≈ −3.44 kJ/mol. ΔG = ΔG° + RT ln Q ≈ (−8.6) + (−3.44) = −12.0 kJ/mol ⇒ spontaneous.
Frequently Asked Questions
Q: Which ΔH/ΔS units should I use?
Either is fine—select the correct unit next to each field and we’ll convert.
Q: Do I enter T in K or °C?
Enter either; we convert °C → K internally.
Q: What does the sign of ΔG mean?
ΔG < 0: spontaneous; ΔG > 0: non-spontaneous; ΔG ≈ 0: at equilibrium.
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