Library / Solution chemistry, equilibria and kinetics / SCH-08
Solution chemistry, equilibria and kinetics
Reaction Gibbs energy away from equilibrium
Gibbs energy change of a reaction at its current composition, from the reaction quotient Q and the equilibrium constant K at the same temperature.
- Ref
- SCH-08
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- ΔrG [J/mol]
The Gibbs energy of a reaction at its current composition is ΔrG = RT ln(Q/K). It is negative when Q < K, so the mixture still has too much reactant and the forward reaction is favoured, and positive when Q > K. It is zero at equilibrium. Q and K must be dimensionless and for the same reaction written the same way.
Gibbs energy change of a reaction at its current composition, from the reaction quotient Q and the equilibrium constant K at the same temperature. A negative value means the forward reaction is favoured, zero means equilibrium.
Calculator
- Standard Gibbs energy, −RT ln K0 J/mol
- Ratio Q/K0.25
- Reaction Gibbs energy in kJ/mol−3.458 kJ/mol
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With Q/K = 0.25 at 300 K, ΔrG = −3,458 J/mol, so the reaction runs forward.
- A factor of 10 between Q and K is worth about 5.7 kJ/mol at 298 K, a handy sense of scale.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (J/mol) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q Reaction quotient | 1e-6 to 1,000,000 | −34,460 | 34,460 | 68,920 | +10% | −6.88 % |
| K Equilibrium constant | 1e-6 to 1,000,000 | −37,920 | 31,000 | 68,920 | +10% | +6.88 % |
| T Temperature | 200 to 700 K | −8,068 | −2,305 | 5,763 | +10% | +10 % |
Sweep of Reaction quotient
| Reaction quotient | Reaction Gibbs energy (J/mol) |
|---|---|
| 1e-6 | −34,460 |
| 3.162e-5 | −25,850 |
| 0.001 | −17,230 |
| 0.03162 | −8,615 |
| 1 | 0 |
| 31.62 | 8,615 |
| 1,000 | 17,230 |
| 31,620 | 25,850 |
| 1,000,000 | 34,460 |
Sweep one variable
Variables and how each one contributes
Reaction Gibbs energy
What the equation gives you. Everything else feeds it.
Temperature
The temperature, in K. Raises the size of ΔrG in direct proportion, for the same Q/K. Raising it by 10 % (to 330) moves the result by +10 %, from −3,458 to −3,804 J/mol.
Reaction quotient
The reaction quotient at the current composition. A larger Q (more product) raises ΔrG, making the forward reaction less favourable. Raising it by 10 % (to 0.275) moves the result by −6.88 %, from −3,458 to −3,220 J/mol.
Equilibrium constant
The equilibrium constant at T. A larger K lowers ΔrG, making the forward reaction more favourable. Raising it by 10 % (to 1.1) moves the result by +6.88 %, from −3,458 to −3,696 J/mol.
Worked example with the values above
- Ratio: Q/K = 0.25 / 1 = 0.25; ln = −1.3863.
- RT = 8.3144626 × 300 = 2,494.3 J/mol.
- ΔrG = 2,494.3 × −1.3863 = −3,457.9 J/mol.
Assumptions and limits
- Constants are dimensionless thermodynamic values for the same temperature and standard states, or consistent concentration-based values.
- Ideal solutions or ideal gases, with activities replaced by concentrations or pressures.
Common mistakes
- Using constants at different temperatures in one combination.
- Using °C in place of K in the van’t Hoff or Gibbs-energy equation.
- Reversing a reaction without inverting K, or scaling it without raising K to the same power.
Statistics and uncertainty
Equilibrium constants are known only to within a factor that depends on the source, often 5 % to 30 %, and the constant-ΔH assumption in the van’t Hoff equation limits it to modest temperature ranges.
Where it is used
- Combining step equilibria, and extrapolating a constant to another temperature.
- Judging which way a mixture will react and how far it is from equilibrium.
Maths you need
- Equilibrium constant: K, the ratio of products to reactants at equilibrium
- Reaction quotient: Q, the same ratio at any composition
- Gibbs energy: ΔG° = −RT ln K