Equilibrium constants describe the balance between reactants and products in a chemical system, but their form depends on how the system is measured. Understanding when KP equals KC clarifies which reference state the calculation uses and how pressure and concentration connect.
This article explains the conditions where the pressure-based equilibrium constant KP matches the concentration-based KC, supported by definitions, examples, and a quick reference guide.
| Condition | KP Expression | KC Expression | When KP = KC |
|---|---|---|---|
| Ideal gases, partial pressures in bar, concentrations in mol/L | KP = Π (Pᵢ / P°)^νᵢ | KC = Π [Cᵢ]^νᵢ | When Δn_gas = 0 |
| Reactions with no change in moles of gas | KP = KC ∏ (RT)^(Δn_gas) KC = KP / (RT)^Δn_gas Δn_gas = 0|||
| Standard state choice: 1 bar vs 1 mol/L | P° = 1 bar | C° = 1 mol/L | Unit conversion factor becomes 1 |
| System composition expressed in concentrations only | Pᵢ = (nᵢ RT / V) | Cᵢ = (nᵢ / V) | KP and KC numerically match under fixed T, Δn = 0 |
Thermodynamic Definition of KP and KC
KP uses partial pressures relative to a standard pressure, while KC uses molar concentrations relative to a standard concentration. Both describe the same equilibrium but differ in units and practical measurement.
The relationship KP = KC (RT)^Δn_gas links the two constants through the gas constant R, temperature T, and the change in moles of gas Δn_gas. This formula shows that equality emerges only under specific conditions.
Impact of Δn_gas on KP and KC Equality
Δn_gas, the difference between gaseous product moles and gaseous reactant moles, dictates whether KP and KC can be identical. When this value is zero, the (RT) term disappears, making the constants numerically equal.
For reactions involving condensed phases only, Δn_gas is automatically zero, so KP and KC match by default regardless of pressure or concentration units.
Practical Measurement Conditions
In laboratory settings, KP is often derived from partial pressures, while KC comes from titrations or spectroscopy. The equality KP = KC is most useful when experiments use concentrations but the system involves gases with no net mole change.
Maintaining fixed temperature and using consistent standard states ensures that the relationship holds and that reported constants remain comparable across studies and industrial processes.
Connection to the Ideal Gas Law
Because partial pressure Pᵢ relates to concentration Cᵢ through Pᵢ = Cᵢ RT, substituting into the KP expression reveals the power of Δn_gas. If no net gas moles form or consume, pressure and concentration data yield the same equilibrium value.
Engineers exploit this link when designing reactors with gaseous feeds, ensuring that calculated KP aligns with measurable KC without unit conversions that could obscure interpretation.
Key Takeaways for Using KP and KC Correctly
- Check Δn_gas first; if it is zero, KP and KC are numerically equal.
- Standard state definitions affect numerical values, so document pressure and concentration references.
- Use KP for gas partial pressures and KC for solution or mixed-phase equilibria.
- Maintain consistent temperature, as RT links the two constants and can shift values significantly.
FAQ
Reader questions
Does KP always have units while KC is unitless?
KP and KC can both be unitless when standard states are applied consistently, but KP often carries pressure units if referenced to 1 bar, whereas KC uses concentration units referenced to 1 mol/L.
Can KP and KC be numerically equal if Δn_gas is not zero?
Only if the (RT)^Δn_gas correction factor equals 1, which occurs at specific temperatures and pressures where RT = 1 in the chosen units, a rare condition in practice.
Why do textbooks say KP equals KC for reactions with no gaseous moles change?
Because when Δn_gas = 0, the relationship KP = KC(RT)^Δn_gas simplifies to KP = KC, making them interchangeable in calculations and data reporting.
How do I choose between using KP and KC for industrial calculations?
Use KP when dealing with gas-phase reactions and pressure measurements, and choose KC when concentrations are monitored directly, switching between them via the Δn_gas formula when necessary.