Kp and Extent of Reaction- Chemical Equilibrium Guide

What Is Kp in Chemistry?

Kp is the equilibrium constant expressed in terms of partial pressures. When gases are involved in a reaction at equilibrium, you use Kp instead of Kc (which uses concentrations). The "p" literally stands for pressure.

Most students encounter Kp when studying reversible gas-phase reactions. If your reaction involves gases that reach equilibrium, Kp is your go-to expression.

How to Write the Kp Expression

For a general reaction:

aA(g) + bB(g) ⇌ cC(g) + dD(g)

The Kp expression is:

Kp = (Pc)^c(Pd)^d / (Pa)^a(Pb)^b

Each gas partial pressure gets raised to the coefficient in the balanced equation. Pure solids and liquids don't appear in the expression—only gases matter.

Understanding Extent of Reaction (ξ)

The extent of reaction (symbol ξ, xi) tells you how far a reaction proceeds. It relates directly to the mole changes in your balanced equation.

The formula is:

Δn = ξ × (stoichiometric coefficient change)

Or rearranged:

ξ = Δn / ν

Where Δn is the change in moles of a component, and ν is that component's stoichiometric coefficient.

The Direct Connection: Kp and Extent of Reaction

Here's what textbooks often skip over. Kp and extent of reaction aren't just related—they're mathematically linked through the reaction quotient and equilibrium position.

When a reaction reaches equilibrium:

• A small Kp value means the equilibrium lies toward reactants
• A large Kp value means the equilibrium lies toward products
• The extent of reaction is small for small Kp, large for large Kp

For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) with Kp = 4.3 × 10⁻³, the extent of reaction is minimal. Most nitrogen and hydrogen remain unreacted. The ammonia forms, but barely.

Compare this to a reaction like H₂(g) + Cl₂(g) ⇌ 2HCl(g) with Kp = 1.4 × 10⁷. The equilibrium heavily favors products. The extent of reaction is massive—nearly all reactants convert to HCl.

Kp vs Kc: When to Use Which

This trips up a lot of people. Here's the practical rule:

• Use Kc when given concentrations in mol/L
• Use Kp when given partial pressures in atm, bar, or Pa
• For gas-phase reactions, you can convert between them

The conversion formula:

Kp = Kc(RT)^Δn

Where Δn = moles of gaseous products minus moles of gaseous reactants.

Kp Values and What They Mean

These are rough guidelines. Real chemistry is messier than these neat categories, but they give you a quick mental map.

How to Calculate Extent of Reaction Using Kp

Here's the step-by-step process for a typical problem:

Step 1: Write the Balanced Equation

Example: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

Step 2: Set Up an ICE Table

ICE stands for Initial, Change, Equilibrium. Fill in your starting amounts, the change (using ξ as the variable), and the equilibrium values.

Step 3: Express Equilibrium Partial Pressures

If PCl₅ starts at 2.0 atm and PCl₃, Cl₂ start at 0:

• PCl₅: 2.0 - ξ
• PCl₃: ξ
• Cl₂: ξ

Step 4: Write the Kp Expression

Kp = (Ppcl₃ × Pcl₂) / Ppcl₅

Assume Kp = 1.05 for this decomposition at your temperature.

Step 5: Solve for ξ

1.05 = (ξ × ξ) / (2.0 - ξ)

1.05(2.0 - ξ) = ξ²

2.1 - 1.05ξ = ξ²

Rearrange: ξ² + 1.05ξ - 2.1 = 0

Using the quadratic formula: ξ ≈ 0.91 atm

Step 6: Interpret Your Answer

The extent of reaction is 0.91 atm. This tells you PCl₃ and Cl₂ each reach 0.91 atm at equilibrium, while PCl₅ drops to 1.09 atm. The reaction proceeds to a moderate extent—not complete, not negligible.

Common Mistakes to Avoid

Forgetting Δn in conversions. When switching between Kp and Kc, Δn is not optional. Skip it, and your answer will be wrong by orders of magnitude.

Using concentrations for Kp problems. Kp requires partial pressures. If your problem gives mol/L, convert first or use Kc instead.

Misidentifying gaseous states. Only gases go into the equilibrium expression. Aqueous species use Kc terms. Solids and liquids are ignored entirely.

Rounding too early. Keep extra significant figures during calculations. Round only at the final answer. Intermediate rounding compounds errors.

Quick Reference: Kp Formula Summary

• General form: products over reactants, each raised to its coefficient
• Dimensionless: Kp values are technically dimensionless—atm units cancel out in the ratio
• Temperature matters: Kp changes with temperature because equilibrium constants are temperature-dependent
• No units in the expression: write Kp = 4.5, not Kp = 4.5 atm²

When Kp = 1: The Middle Ground

If Kp equals 1 (or is close to it), the equilibrium sits roughly in the middle. Neither reactants nor products are strongly favored. The extent of reaction is moderate, and small changes in conditions can shift the position noticeably.

This matters in industrial settings. Reactions with Kp near 1 are more sensitive to pressure and temperature adjustments than reactions with extreme Kp values.

Real-World Application: Haber Process

The synthesis of ammonia illustrates Kp and extent of reaction in action:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Δn = 2 - 4 = -2

At 400°C, Kp ≈ 4.3 × 10⁻³. This small value tells you the extent of reaction is limited at this temperature. High pressure (200 atm) shifts the equilibrium right because there are fewer gas moles on the product side, but the extent is still constrained by the unfavorable Kp at elevated temperatures.

Industry deals with this by:

• Using high pressure (favors fewer gas moles)
• Using a catalyst (speeds up the limited reaction that does occur)
• Continuously removing ammonia (shifts equilibrium right by Le Chatelier's principle)

You can't change Kp by adding pressure or catalyst. You can only manipulate the conditions to work within what Kp allows.