Equilibrium Constant, K, and Temperature Chemistry Tutorial

Key Concepts

• K is the symbol given to the equilibrium constant for a chemical reaction.¹

  For the general reaction:

  reactants ⇋ products     ΔH = ? kJ mol^-1

  K_c can be represented as :

  Kc =	[products] [reactants]

• The value of the equilibrium constant, K, for a given reaction is dependent on temperature.
• If ΔH is positive, reaction is endothermic, then:

  (a) K increases as temperature increases

  (b) K decreases as temperature decreases

• If ΔH is negative, reaction is exothermic, then:

  (a) K decreases as temperature increases

  (b) K increases as temperature decreases

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Introduction

Imagine a reaction in which the gaseous reactants A_(g) and B_(g) react in a sealed vessel to produce the gaseous products C_(g) at a constant temperature.
The result is an equilibrium reaction which can be represented by the following chemical equation:

The mass-action expression for this reaction is:

At equilibrium the value of the mass-expression is a constant, that is,

Q = a constant

At constant temperature, the equilibrium concentrations of A_(g), B_(g) and C_(g) do not appear to change because the rate of the forward reaction is the same as the rate of the reverse reaction.

Effect of Heating on the Value of the Equilibrium Constant, K

What happens if we heat the reaction mixture after it reaches equilibrium?

Remember that chemical reactions themselves either absorb energy (endothermic reactions) or release energy (exothermic reactions).

If our reaction is endothermic, it absorbs energy, so energy (enthalpy, ΔH) can be considered as a reactant in the chemical equilibrium equation:

When the equilibrium mixture is heated, by Le Chatelier's Principle, the equilibrium position will shift to the right to consume some of the additional heat.

This means that when the reaction mixture reaches equilibrium again, the concentration of each reactant will have decreased by an amount x, while the concentration of the product will have increased by an amount x.

We can summarise these changes in concentration of each species in a R.I.C.E. (or I.C.E.) table as shown below:

Let's compare the relative values of the equilibrium constant before and after heating the reaction mixture:

We can see that K' will be a larger number than K because:

• the value of the numerator has increased (from [C_(g)] to [C_(g)] + x)
• and the value of the denominator has decreased (from [A_(g)][B_(g)] to {([A_(g)] - x)([B_(g)] - x)}
• and a larger number divided by a smaller number results in a larger number

If a reaction is endothermic, the value of the equilibrium constant increases when the reaction mixture is heated.

Endothermic reaction: increasing temperature, increases the value of K

Compare what happens to the value of the equilibrium constant when an exothermic reaction is heated.

An exothermic reaction releases energy, so energy (enthalpy, ΔH) can be considered as a product in the chemical equilibrium equation:

When the equilibrium mixture is heated, by Le Chatelier's Principle, the equilibrium position will shift to the left to consume some of the additional heat.

This means that when the reaction mixture reaches equilibrium again, the concentration of each reactant will have increased by an amount x, while the concentration of the product will have decreased by an amount x.
We can represent these changes in a R.I.C.E. Table as shown below:

Let's compare the relative values of the equilibrium constant before and after heating the reaction mixture:

We can see that K' will be a smaller number than K because:

• the value of the numerator has decreased from [C_(g)] to ([C_(g)] - x)
• and the value of the denominator has increased from [A_(g)][B_(g)] to {([A_(g)] + x)([B_(g)] + x)}
• and a smaller number divided by a larger number results in a smaller number

If a reaction is exothermic, the value of the equilibrium constant decreases when the reaction mixture is heated.

Exothermic reaction: increasing temperature, decreases the value of K

Effect of Cooling on the Value of the Equilibrium Constant, K

If our reaction is endothermic, it absorbs energy, so energy (enthalpy, ΔH) can be considered as a reactant in the chemical equilibrium equation:

When the equilibrium mixture is cooled, that is heat is removed, by Le Chatelier's Principle, the equilibrium position will shift to the left to produce some additional heat.

This means that when the reaction mixture reaches equilibrium again, the concentration of each reactant will have increased by an amount x, while the concentration of the product will have decreased by an amount x.

We can summarise these changes in concentration of each species in a R.I.C.E. (or I.C.E.) table as shown below:

Let's compare the relative values of the equilibrium constant before and after cooling the reaction mixture:

We can see that K' will be a smaller number than K because:

• the value of the numerator has decreased from [C_(g)] to ([C_(g)] - x)
• and the value of the denominator has increased from [A_(g)][B_(g)] to {([A_(g)] + x)([B_(g)] + x)}
• and a smaller number divided by a larger number results in a smaller number

If a reaction is endothermic, the value of the equilibrium constant decreases when the reaction mixture is cooled.

Endothermic reaction: decreasing temperature, decreases the value of K

If our reaction is exothermic, it releases energy, so energy (enthalpy, ΔH) can be considered as a product in the chemical equilibrium equation:

When the equilibrium mixture is cooled, that is heat is removed, by Le Chatelier's Principle, the equilibrium position will shift to the right to produce some additional heat.

This means that when the reaction mixture reaches equilibrium again, the concentration of each reactant will have decreased by an amount x, while the concentration of the product will have increased by an amount x.

We can summarise these changes in concentration of each species in a R.I.C.E. (or I.C.E.) table as shown below:

Let's compare the relative values of the equilibrium constant before and after cooling the reaction mixture:

We can see that K' will be a larger number than K because:

• the value of the numerator has increased (from [C_(g)] to [C_(g)] + x)
• and the value of the denominator has decreased (from [A_(g)][B_(g)] to {[A_(g)] - x}{[B_(g)] - x})
• and a larger number divided by a smaller number results in a larger number

If a reaction is exothermic, the value of the equilibrium constant increases when the reaction mixture is cooled.

Exothermic reaction: decreasing temperature, increases the value of K

Worked Example: Predict the Value for an Equilibrium Constant, K, at a Different Temperature

Question: The decomposition of N₂O_4(g) to produce NO_2(g) is an endothermic chemical reaction which can be represented by the following chemical equation:

N₂O_4(g) ⇋ 2NO_2(g)

At 25°C the value of the equilibrium constant, K_c is 4.7 × 10^-3.

Predict whether the equilibrium constant for this reaction at 100°C will be greater than, less than, or equal to 4.7 × 10^-3.

Solution: (based on the StoPGoPS approach to problem solving)

Worked Example: Use Equilibrium Constant Values at Different Temperatures to Predict Relative Value of ΔH

Question: Consider the synthesis of I₃^-_(aq) from the reactants I_2(aq) and I^-_(aq) as shown by the following chemical equation:

I_2(aq) + I^-_(aq) ⇋ I₃^-_(aq)

The reaction was carried out at a number of different temperatures and the equilibrium constant, K_c, was calculated for each temperature as shown in the table below:

Is this reaction exothermic or endothermic?

Solution: (based on the StoPGoPS approach to problem solving)