Homogeneous Equilibria

Quick Notes

• Homogeneous Equilibria involve substances in the same phase (e.g., all gases or all solutes in a solution).
• For gaseous reactions, equilibrium constants can be expressed as:
  • K_c – in terms of concentrations (mol/L)

• K_p – in terms of partial pressures (atm)

• K_p and K_c are related by:
  K_p = K_c (RT)^Δn
  where:
  • R = 0.0821 L·atm/mol·K
  • T = temperature in Kelvin
  • Δn = moles of gaseous products − moles of gaseous reactants

Full Notes

What is Homogeneous Equilibrium?

A homogeneous equilibrium refers to a reversible reaction where all reacting species are in the same phase – typically gases or aqueous solutions.

Example: Nitrogen and hydrogen to ammonia

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

All species are gases = homogeneous equilibrium in gas phase.

6.4.1 Equilibrium Constant in Gaseous Systems

In gaseous equilibria, we can express the equilibrium constant in two main forms:

Up to now, we’ve been expressing equilibrium constants using concentrations of reactants and products – this is called K_c.

But for reactions involving gases, it’s often more convenient to express the equilibrium constant in terms of partial pressure instead. That’s when we use K_p.

The Ideal Gas Equation

To understand how pressure and concentration are related, we start with the ideal gas equation:

pV = nRT

This can be rearranged to:

p = (n/V) × RT

Here:

• p is pressure (in pascals or bar)
• n is number of moles
• V is volume
• R is the gas constant (0.0831 bar·L/mol·K)
• T is temperature in Kelvin

So, since n/V is just concentration, you can also say:

p = concentration × RT

Meaning p is proportional to concentration (at a constant temperature).

This relationship helps us convert between concentration (for K_c) and pressure (for K_p).

This means that we can use partial pressures of each gas type in an equilibrium mixture instead of concentration. When we do, the equilibrium constant is referred to as K_p.

For the General reaction:

The K_p expression is:

where:

• P[A], P[B], P[C], P[D] are the partial pressures of each gas.
• a, b, c, d are the stoichiometric coefficients from the balanced equation.

Example: The Reaction Between Hydrogen and Iodine

Let’s look at the reaction:

H₂(g) + I₂(g) ⇌ 2HI(g)

In terms of concentration: K_c = [HI]² / ( [H₂] [I₂] )

In terms of partial pressures: K_p = (p_HI)² / ( p_H2 × p_I2 )

Since p = [gas] × RT, if we substitute that into the equation, the RT terms cancel out — and we find that:

K_p = K_c

This happens here because the number of gas molecules is the same on both sides (1 + 1 → 2). But that’s not always the case.

When K_p ≠ K_c

Let’s take another example:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

In this case, there are 4 moles of gas on the left and 2 on the right. This difference matters.

For this reaction: K_p = (p_NH3)² / ( p_N2 × (p_H2)³ )

If we convert that into K_c using the gas law, we get:

K_p = K_c × (RT)^Δn

Where:

• Δn = (moles of gas in products) – (moles of gas in reactants)

So here, Δn = 2 − 4 = −2

That means K_p = K_c × (RT)⁻²

So K_p and K_c are not equal unless Δn = 0.

General Formula for Gaseous Reactions

For any reaction like:

aA + bB ⇌ cC + dD

Where:

• Δn = (c + d) − (a + b)

In other words, change in number of moles of gaseous products minus gaseous reactants

Important Points to Remember

• Always specify the balanced chemical equation when giving a value for K_p or K_c, because changing the equation changes the value!
• Use bar as the unit of pressure when calculating K_p.
• R = 0.0831 bar·L/mol·K if pressure is in bar and concentration is in mol/L
• K_p and K_c may or may not be equal — it all depends on Δn.

Summary

• Homogeneous equilibria involve species in the same phase
• Gaseous equilibria can be written as K_c or K_p
• K_p relates to K_c through K_p = K_c (RT)^Δn
• When Δn = 0 then K_p equals K_c