Law of Chemical Equilibrium Tutorial

Key Concepts

• Law of Chemical Equilibrium states that at any given temperature, the value of the mass-action expression, Q, for a given reaction at equilibrium is a constant.
• This constant value is known as the equilibrium constant and has the symbol K
• At equilibrium: Q = a constant = K

  The relationship Q = K is known as the equilibrium condition.

• For homogeneous systems in the gas phase or in aqueous solutions, the expression for K is the same as the mass-action expression.
• For heterogeneous systems in which a solid or liquid is present, the expression for K is a simplified version of the mass-action expression

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Writing Equilibrium Constant Expressions (Expressions for K): Homogeneous Systems

Consider the following reaction at equilibrium:

aA_(g) + bB_(g) ⇋ cC_(g) + dD_(g)

The mass-action expression, Q, for this reaction is:

At equilibrium the rate of the forward reaction is the same as the rate of the reverse reaction so that the concentration of each species remains constant, that is:

[C] = a constant
[D] = a constant
[A] = a constant
[B] = a constant

The expression for the equilibrium constant, K, is the same as the mass-action expression, Q, that is:

Similarly, if all the species were present in aqueous solution, the chemical reaction could be represented as

aA_(aq) + bB_(aq) ⇋ cC_(aq) + dD_(aq)

The mass-action expression, Q, for this reaction is:

At equilibrium the rate of the forward reaction is the same as the rate of the reverse reaction so that the concentration of each species remains constant, that is:

[C] = a constant
[D] = a constant
[A] = a constant
[B] = a constant

And once again, the expression for the equilibrium constant, K, is the same as the mass-action expression, Q, that is:

Writing Equilibrium Constant Expressions (Expressions for K): Heterogeneous Systems

But what happens if one of the reactants or products is a solid?

aA_(aq) + bB_(aq) ⇋ cC_(s) + dD_(aq)

The mass-action expression, Q, for this reaction is:

The concentration of the solid, C_(s), is always the same! Even if the system is NOT at equilibrium, the concentration of C_(s) will still not change.
The concentration of a solid is fixed by its density, that is, the amount of solid substance in a given volume is always the same at constant temperature and pressure, so the concentration of a solid is a constant.
We could then re-write the mass-action expression as:

And, at equilibrium:

Q/[C]^c = a constant/a constant
          = K (the equilibrium constant)

So, the expression for the equilibrium constant is:

Similarly, if one of the reactants or products is a liquid, the concentration of the liquid species does not change.
The concentration of a liquid is also fixed by its density, that is, the amount of liquid substance in a given volume at constant temperature and pressure, is always the same, so the concentration of a liquid is a constant.

So, for the reaction

aA_(aq) + bB_(l) ⇋ cC_(aq) + dD_(aq)

The mass-action expression, Q, for this reaction is:

but since [B] is always constant because B is a liquid, we can re-write the expression as:

and at equilibrium,

Q[B]^b = a constant × a constant
= constant
= K (the equilibrium constant)

So the expression for the equilibrium constant, K, is

Worked Examples: Writing Equilibrium Constant Expressions

Reactions Involving Aqueous Species

1. All species are present in aqueous solution eg:

   Ag⁺_(aq) +2NH_3(aq) ⇋ Ag(NH₃)₂⁺_(aq)

   K =	[Ag(NH3)2+]
   	[Ag+][NH3]2

2. Solvent, such as water, takes part in reaction, eg:

   NH_3(aq) + H₂O_(l) ⇋ NH₄⁺_(aq) + OH^-_(aq)

   K =	[NH4+][OH-]
   	[NH3]

   The concentration of the water as solvent is said to be constant and is incorporated into the value of K.

3. A solid is present in the reaction, eg

   Pb²⁺_(aq) + 2I^-_(aq) ⇋ PbI_2(s)

   K =	1
   	[Pb2+][I-]2

   The concentration of the solid is said to be constant and is incorporated into the value of K.

Reactions Involving Gases

1. All species are present as gases, eg:

   CO_(g) + 2H_2(g) ⇋ CH₃OH_(g)

   K =	[CH3OH]
   	[CO][H2]2

2. A solid is present in the reaction, eg:

   CaCO_3(s) ⇋ CaO_(s) + CO_2(g)

   K = [CO₂]

   The concentration of solids are said to be constant and are incorporated into the value of K.