Library / Solution chemistry, equilibria and kinetics / SCH-09
Solution chemistry, equilibria and kinetics
Equilibrium conversion in a reversible isomerisation
Forward extent per litre when A ⇌ B reaches equilibrium in an ideal constant-volume solution with K = [B]/[A] and starting concentrations A₀ and B₀.
- Ref
- SCH-09
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- x [mol/L]
For A ⇌ B in an ideal constant-volume solution with K = [B]/[A], the forward extent x at equilibrium satisfies K = (B₀ + x)/(A₀ − x), so x = (K A₀ − B₀)/(1 + K). A negative x means the reaction runs backward from the starting mixture. The equilibrium concentrations are A₀ − x and B₀ + x, and they always add up to A₀ + B₀.
Forward extent per litre when A ⇌ B reaches equilibrium in an ideal constant-volume solution with K = [B]/[A] and starting concentrations A₀ and B₀. The equilibrium concentrations are A₀ − x and B₀ + x.
Calculator
- Equilibrium concentration of A, (A₀ + B₀)/(1 + K)0.06 mol/L
- Equilibrium concentration of B, K(A₀ + B₀)/(1 + K)0.18 mol/L
- Check ratio [B]/[A] (equals K)3
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.
- At equilibrium A falls to 0.06 mol/L and B reaches 0.18 mol/L, a ratio of 3, which is K.
- Only the total A₀ + B₀ and K matter for the final composition, whatever the starting split.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| A0 Starting concentration of A | 0.001 to 5 mol/L | −0.00925 | 3.74 | 3.749 | +10% | +10.7 % |
| B0 Starting concentration of B | 0 to 5 mol/L | −1.1 | 0.15 | 1.25 | +10% | −0.714 % |
| K Equilibrium constant [B]/[A] | 0.001 to 1,000 | −0.03976 | 0.1998 | 0.2395 | +10% | +2.99 % |
Sweep of Equilibrium constant [B]/[A]
| Equilibrium constant [B]/[A] | Forward extent (mol/L) |
|---|---|
| 0.001 | −0.03976 |
| 0.005623 | −0.03866 |
| 0.03162 | −0.03264 |
| 0.1778 | −0.003765 |
| 1 | 0.08 |
| 5.623 | 0.1638 |
| 31.62 | 0.1926 |
| 177.8 | 0.1987 |
| 1,000 | 0.1998 |
Sweep one variable
Variables and how each one contributes
Forward extent
What the equation gives you. Everything else feeds it.
Equilibrium constant [B]/[A]
The equilibrium constant [B]/[A]. A larger K converts more A to B, raising x towards A₀. Raising it by 10 % (to 3.3) moves the result by +2.99 %, from 0.14 to 0.1442 mol/L.
Starting concentration of A
The starting concentration of A, in mol/L. Raises the extent in proportion to K/(1 + K). Raising it by 10 % (to 0.22) moves the result by +10.7 %, from 0.14 to 0.155 mol/L.
Starting concentration of B
The starting concentration of B, in mol/L. Lowers the extent, since B must be consumed first. Raising it by 10 % (to 0.044) moves the result by −0.714 %, from 0.14 to 0.139 mol/L.
Worked example with the values above
- Numerator: K A₀ − B₀ = 3 × 0.2 − 0.04 = 0.56 mol/L.
- Denominator: 1 + K = 4.
- x = 0.56 / 4 = 0.14 mol/L.
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