Library / Solution chemistry, equilibria and kinetics / SCH-06
Solution chemistry, equilibria and kinetics
Equilibrium constant for a combined reaction
Overall equilibrium constant of a reaction made by adding up to three component reactions, each scaled by a coefficient ν (negative to reverse it).
- Ref
- SCH-06
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- Knet
When reactions are added, their equilibrium constants multiply, and when a reaction is scaled by a factor ν its constant is raised to the power ν, so ln Knet = Σ νⱼ ln Kⱼ. A negative ν reverses the reaction, giving the inverse of its constant. All constants must be for the same temperature and the same standard states. A zero coefficient removes a reaction from the sum.
Overall equilibrium constant of a reaction made by adding up to three component reactions, each scaled by a coefficient ν (negative to reverse it). All constants are positive, dimensionless, and for the same temperature and standard states.
Calculator
- ln Knet1.504
- log₁₀ Knet0.6532
- ΔG° of the net reaction at 298.15 K, −RT ln K−3,729 J/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.
- Doubling reaction 1 and reversing reaction 2 gives Knet = 4.5, equivalent to −3.729 kJ/mol of standard Gibbs energy at 298 K.
- Because K values multiply while ΔG° values add, summing the logarithms is the same as adding the Gibbs energies of the steps.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| K1 Equilibrium constant of reaction 1 | 1e-6 to 1,000,000 | 5e-13 | 5e11 | 5e11 | +10% | +21 % |
| K2 Equilibrium constant of reaction 2 | 1e-6 to 1,000,000 | 9e-6 | 9,000,000 | 9,000,000 | +10% | −9.09 % |
| ν2 Coefficient of reaction 2 | −4 to 4 | 0.5625 | 144 | 143.4 | +0.16 | +11.7 % |
| ν1 Coefficient of reaction 1 | −4 to 4 | 0.006173 | 40.5 | 40.49 | +0.16 | +19.2 % |
| ν3 Coefficient of reaction 3 (zero if unused) | −4 to 4 | 4.5 | 4.5 | 0 | +0.16 | 0 % |
| K3 Equilibrium constant of reaction 3 | 1e-6 to 1,000,000 | 4.5 | 4.5 | 0 | +10% | 0 % |
Sweep of Coefficient of reaction 1
| Coefficient of reaction 1 | Overall equilibrium constant |
|---|---|
| −4 | 0.006173 |
| −3 | 0.01852 |
| −2 | 0.05556 |
| −1 | 0.1667 |
| 0 | 0.5 |
| 1 | 1.5 |
| 2 | 4.5 |
| 3 | 13.5 |
| 4 | 40.5 |
Sweep one variable
Variables and how each one contributes
Overall equilibrium constant
What the equation gives you. Everything else feeds it.
Coefficient of reaction 1
The coefficient of reaction 1 (negative to reverse it). Raises ln K by ν₁ times ln K₁, so the result changes by a power law. Raising it by 10 % (to 2.2) moves the result by +24.6 %, from 4.5 to 5.606.
Equilibrium constant of reaction 1
The equilibrium constant of reaction 1. Raises the result as K₁ to the power ν₁. Raising it by 10 % (to 3.3) moves the result by +21 %, from 4.5 to 5.445.
Coefficient of reaction 2
The coefficient of reaction 2 (negative to reverse it). Changes ln K by ν₂ times ln K₂, so the result changes by a power law. Raising it by 10 % (to −1.1) moves the result by −6.7 %, from 4.5 to 4.199.
Equilibrium constant of reaction 2
The equilibrium constant of reaction 2. Changes the result as K₂ to the power ν₂. Raising it by 10 % (to 2.2) moves the result by −9.09 %, from 4.5 to 4.091.
Coefficient of reaction 3 (zero if unused)
The coefficient of reaction 3, zero if unused. Changes ln K by ν₃ times ln K₃ (no change while K₃ = 1). Raising it by 10 % (to 0) moves the result by +0 %, from 4.5 to 4.5.
Equilibrium constant of reaction 3
The equilibrium constant of reaction 3. Changes the result as K₃ to the power ν₃ (no effect while ν₃ = 0). Raising it by 10 % (to 1.1) moves the result by +0 %, from 4.5 to 4.5.
Worked example with the values above
- Weighted logs: 2 ln 3 + −1 ln 2 + 0 ln 1 = 1.5041.
- Exponentiate.
- Knet = 4.5.
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