Calculate Kc for The Following Reaction Given Kp

When studying chemical equilibrium, it's often necessary to convert between the equilibrium constant expressed in terms of concentrations (Kc) and that expressed in terms of pressures (Kp). This guide explains how to calculate Kc from Kp, including the formula, assumptions, and practical examples.

Introduction

In chemical equilibrium, the equilibrium constant can be expressed in two ways:

Kc: The equilibrium constant in terms of concentrations of the reactants and products.
Kp: The equilibrium constant in terms of partial pressures of the gaseous reactants and products.

For reactions involving only gaseous species, Kc and Kp are related through the ideal gas law. This relationship allows chemists to convert between these two forms of the equilibrium constant.

Formula

The relationship between Kc and Kp is given by:

Kc = Kp × (RT)Δn

Where:

Kc = Equilibrium constant in terms of concentrations
Kp = Equilibrium constant in terms of pressures
R = Universal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹)
T = Temperature in Kelvin
Δn = Change in the number of moles of gas (products - reactants)

This formula accounts for the conversion between concentration and pressure units, as well as the temperature dependence of the equilibrium.

Calculation Steps

Determine the value of Kp for your reaction.
Measure or estimate the temperature (T) in Kelvin.
Calculate Δn (the change in the number of moles of gas).
Use the universal gas constant (R = 0.0821 L·atm·K⁻¹·mol⁻¹).
Plug these values into the formula: Kc = Kp × (RT)Δn.

For reactions where Δn = 0 (equal numbers of moles of reactants and products), Kc = Kp.

Example Calculation

Consider the reaction: 2H₂(g) + O₂(g) ⇌ 2H₂O(g)

Given:

Kp = 0.015 atm²
Temperature (T) = 500 K

Step 1: Calculate Δn

Reactants: 2 moles H₂ + 1 mole O₂ = 3 moles

Products: 2 moles H₂O

Δn = 2 - 3 = -1

Step 2: Plug values into the formula

Kc = 0.015 × (0.0821 × 500)^(-1)

Kc = 0.015 × (41.05)^(-1)

Kc = 0.015 / 41.05 ≈ 0.000365

The equilibrium constant in terms of concentrations (Kc) is approximately 0.000365.

FAQ

What is the difference between Kc and Kp?: Kc is expressed in terms of concentrations, while Kp is expressed in terms of partial pressures. They are related through the ideal gas law.
When should I use Kc instead of Kp?: Use Kc when dealing with reactions involving solutions or when concentration units are more convenient. Use Kp for reactions involving gases.
What units are used for Kc and Kp?: Kc has units of (mol/L)^Δn, while Kp has units of atm^Δn, where Δn is the change in the number of moles of gas.
Can I convert Kp to Kc for reactions with solids or liquids?: No, the conversion formula only applies to reactions involving gaseous species. Solids and liquids do not contribute to the gas phase.
What if my reaction has Δn = 0?: If Δn = 0, then Kc = Kp because the (RT)Δn term becomes 1, and the conversion factors cancel out.