Equilibrium Constant K_p for Homogeneous Systems

Specification Reference Physical Chemistry, Equilibrium constant K_p for homogeneous systems 3.1.10.1

Quick Notes

K_p is the equilibrium constant for reactions involving gases, expressed in terms of partial pressures instead of concentrations.
Expression for K_p:

AQA A-Level Chemistry Kp expression showing ratio of product partial pressures to reactant partial pressures, each raised to their stoichiometric powers.

P[A], P[B], P[C], P[D] = Partial pressures of gases (Pa or atm).
a, b, c, d = molar ratios from the balanced equation.
K_p is only affected by temperature.
Catalysts do not affect Kp, but they increase the rate at which equilibrium is reached.

Full Notes

K_p has been outlined in more detail here.
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K_p (Equilibrium Constant for Gases)

The equilibrium constant, K_p, works in the same way as K_c. (see K_c).

It applies to homogeneous gaseous equilibria, where all reactants and products are in the gas phase
K_p is the equilibrium constant expressed in terms of partial pressures of gases

For the General reaction:

AQA A-Level Chemistry general gaseous equilibrium aA(g) + bB(g) reversible reaction to cC(g) + dD(g).

The K_p expression is:

AQA A-Level Chemistry Kp expression showing product partial pressures over reactant partial pressures with powers as stoichiometric coefficients.

Calculating Partial Pressure

The total pressure of a gaseous system at equilibrium is directly related to the number of moles of each gas in the mixture. How much pressure one type of gas contributes to the total pressure of a gaseous system is called its partial pressure. All partial pressures of gases in a system add up to give the total pressure of the system.

It is calculated using:

$AQA A-Level Chemistry formula: partial pressure of a gas equals mole fraction of the gas times total pressure.$

The mole fraction of a gas is the moles of that gas in the mixture compared to moles of all gases. It is calculated using:

$AQA A-Level Chemistry formula: mole fraction of gas A equals moles of gas A divided by total moles of all gases.$

Worked Example

Find K_p for the following system, given the total pressure = 400 kPa and the moles of N₂O₄ and NO₂ at equilibrium are 0.40 and 0.60, respectively.

N₂O₄ (g) ⇌ 2NO₂ (g)

Given:
Total pressure = 400 kPa
Moles of N₂O₄ = 0.40
Moles of NO₂ = 0.60

Calculate mole fractions
X(N₂O₄) = 0.40 / (0.40 + 0.60) = 0.40
X(NO₂) = 0.60 / (0.40 + 0.60) = 0.60
Calculate partial pressures
P(N₂O₄) = 0.40 × 400 = 160 kPa
P(NO₂) = 0.60 × 400 = 240 kPa
Write Kp expression
Kp = (P²[NO₂]) / P[N₂O₄]
Substitute
Kp = (240²) / (160) = 360 kPa

Answer: K_p = 360 kPa.

Effect of Temperature on K_p

K_p only changes with temperature and we can predict the effect of changing temperature on K_p values.

If the forward direction is exothermic (−ΔH): Increasing temperature decreases K_p (shifts equilibrium left).
If the forward direction is endothermic (+ΔH): Increasing temperature increases K_p (shifts equilibrium right).

Effect of Pressure and Concentration on K_p

K_p remains constant when pressure or concentration are changed.
The system shifts equilibrium to restore K_p.

For Example:
For N₂O₄ ⇌ 2NO₂. If the total pressure is increased:
Position of equilibrium shifts to the left (favours direction that produces the fewest moles of gas - see Le Chatelier’s Principle).
More N₂O₄ forms to reduce the total number of gas moles.
K_p stays the same because the ratio of partial pressures will get back to what it was before pressure was increased.

Effect of a Catalyst on Kp

A catalyst does not affect K_p because it does not change equilibrium position.
A catalyst lowers activation energy, so equilibrium is reached faster, but the position of equilibrium remains unchanged.

Summary Table

Factor	Effect on K_p	Explanation
Temperature (Exothermic Reaction)	Decreases	Shifts equilibrium left
Temperature (Endothermic Reaction)	Increases	Shifts equilibrium right
Pressure	No effect	System adjusts equilibrium to restore K_p
Concentration	No effect	System shifts to maintain K_p
Catalyst	No effect	Equilibrium is reached faster, but K_p remains the same

Equilibrium Constant Kp for Homogeneous Systems