Free Energy of Mixing Calculator
A regular solution with x_B = 0.3 and Ω = 10 kJ/mol at 1000 K has a free energy of mixing of -2.97901 kJ/mol, still negative so the solution is stable.
-2.97900840410607 kJ/mol
Full answer, then cut to fewer decimals (not rounded):
- -2.97900840410607 kJ/mol
- -2.9790084041060 kJ/mol
- -2.979008404106 kJ/mol
- -2.97900840410 kJ/mol
- -2.9790084041 kJ/mol
- -2.979008404 kJ/mol
- -2.97900840 kJ/mol
- -2.9790084 kJ/mol
- -2.979008 kJ/mol
- -2.97900 kJ/mol
- -2.9790 kJ/mol
- -2.979 kJ/mol
- -2.97 kJ/mol
- -2.9 kJ/mol
- Enthalpy of mixing Ωx_Ax_B
- 2.1 kJ/mol
- Ideal entropy term RT Σ x ln x
- -5.079008404 kJ/mol
- Entropy of mixing −R Σ x ln x
- 5.079008404 J/(mol·K)
- Activity of B, x_B exp(Ω x_A²/RT)
- 0.5408364996
- Critical temperature of the miscibility gap Ω/2R
- 601.3617752 K
Step-by-step solution
- ΔG_mix = Ωx_Ax_B + RT(x_A ln x_A + x_B ln x_B)
- = 2.1 + -5.079008404 = -2.979008404 kJ/mol
Free Energy of Mixing Formula
ΔG_mix = Ωx_Ax_B + RT(x_A ln x_A + x_B ln x_B)
Ω interaction parameter (0 for ideal); critical temperature T_c = Ω/(2R)
Worked Example
A solution with x_B = 0.3 at 1000 K and Ω = 10 kJ/mol:
- ΔG_mix = Ωx_Ax_B + RT(x_A ln x_A + x_B ln x_B)
- = 2.1 + -5.079008404 = -2.979008404 kJ/mol
Ideal entropy term RT Σ x ln x: -5.079008404 kJ/mol · Entropy of mixing −R Σ x ln x: 5.079008404 J/(mol·K) · Activity of B, x_B exp(Ω x_A²/RT): 0.5408364996 · Critical temperature of the miscibility gap Ω/2R: 601.3617752 K
GATE tip
The ideal mixing entropy is largest at x = 0.5: −R(0.5 ln 0.5 × 2) = R ln 2 = 5.76 J/(mol·K).
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Frequently asked questions
When does a miscibility gap appear?
For Ω > 0 below T_c = Ω/(2R) the ΔG_mix curve develops two minima and the solution separates into two phases.
What is activity in a regular solution?
a_B = x_B exp(Ωx_A²/RT); Ω > 0 gives positive deviation from Raoult’s law (a_B > x_B).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Free Energy of Mixing Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/mixing-free-energy-calculator/
IEEE
Scientific Converters, "Free Energy of Mixing Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/mixing-free-energy-calculator/