When is Kp Equal to Kc? Chemical Equilibrium Guide

What Are Kp and Kc?

In chemical equilibrium, Kc and Kp are equilibrium constants that describe the ratio of product concentrations to reactant concentrations at equilibrium. The difference is what units they use.

Kc uses concentration (mol/L) for all species. It's the ratio you get when you write the equilibrium expression using molarity.

Kp uses partial pressure (atm, bar, or Pa) for gaseous species instead of concentration. You use it when the equilibrium involves gases and you want to work with pressure data.

Both constants describe the same equilibrium position. They're measuring the same thing—just in different units.

When Is Kp Equal to Kc?

Kp equals Kc when Δn = 0.

That's the short answer. The relationship between the two constants is:

Kp = Kc(RT)^Δn

Where:

• R = gas constant (0.0821 L·atm·mol^-1·K^-1 or 0.0831 L·bar·mol^-1·K^-1)
• T = temperature in Kelvin
• Δn = moles of gaseous products minus moles of gaseous reactants

When Δn = 0, (RT)⁰ = 1, which means Kp = Kc. Simple math.

What Does Δn = 0 Actually Mean?

Δn is the difference in the number of gas molecules between products and reactants. You count only gaseous species—liquids and solids don't appear in the expression.

Δn = 0 when the total number of gas molecules is the same on both sides of the equation.

Examples Where Kp = Kc

2NO(g) ⇌ N₂O₂(g)

• Left side: 2 gas molecules
• Right side: 1 gas molecule
• Δn = 1 - 2 = -1 → Kp ≠ Kc

H₂(g) + I₂(g) ⇌ 2HI(g)

• Left side: 2 gas molecules
• Right side: 2 gas molecules
• Δn = 2 - 2 = 0 → Kp = Kc

N₂(g) + O₂(g) ⇌ 2NO(g)

• Left side: 2 gas molecules
• Right side: 2 gas molecules
• Δn = 2 - 2 = 0 → Kp = Kc

I₂(g) ⇌ 2I(g)

• Left side: 1 gas molecule
• Right side: 2 gas molecules
• Δn = 2 - 1 = 1 → Kp ≠ Kc

Kp vs Kc: The Direct Relationship

Here's how the values relate based on Δn:

When more gas molecules form than react (Δn > 0), Kp is larger than Kc. When fewer gas molecules form (Δn < 0), Kc is larger.

How to Convert Between Kp and Kc

You don't always need Kp = Kc. Sometimes you just need to convert one to the other.

The formulas:

• Kp = Kc(RT)^Δn
• Kc = Kp(RT)^-Δn

Make sure R and T match your units. Use the same R value consistently—if you express pressure in atm, use R = 0.0821.

Getting Started: Solving Problems

Here's the process to follow:

1. Write the balanced equation and identify all gaseous species
2. Count gas moles on each side to find Δn
3. Check if Δn = 0 — if yes, Kp = Kc and you're done
4. If Δn ≠ 0, plug values into Kp = Kc(RT)^Δn
5. Solve for the unknown using algebra

Quick example:

For the reaction N₂O₄(g) ⇌ 2NO₂(g) at 298 K, Kc = 0.005. Find Kp.

• Δn = 2 - 1 = 1
• Kp = Kc(RT)¹
• Kp = 0.005 × (0.0821 × 298)
• Kp = 0.005 × 24.5
• Kp = 0.122

Kc and Kp are not equal here because Δn ≠ 0.

Temperature Matters

Notice the temperature term (RT) in the equation. Even if Δn = 0 makes Kp = Kc at one temperature, the actual numerical values of both constants will change with temperature. Equilibrium constants are temperature-dependent—that's separate from the Kp/Kc relationship.

What About Condensed Phases?

Solids and liquids don't appear in the equilibrium expression. You ignore them when counting Δn. Only count gaseous species.

For the reaction CaCO₃(s) ⇌ CaO(s) + CO₂(g):

• Only CO₂ is gaseous
• Δn = 1 - 0 = 1
• Kp ≠ Kc

The pure solids and liquids drop out completely.

The Bottom Line

Kp equals Kc only when the number of gas molecules doesn't change during the reaction (Δn = 0). For any other case, you need the conversion formula with RT raised to the appropriate power.

Most textbooks give you the formula. Now you know when to actually use it—and when you don't need to.