# 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:

 Q = [C]c[D]d[A]a[B]b

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

So

 Q = [a constant]c[a constant]d[a constant]a[a constant]b = a constant = equilibrium constant = K

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

 K = [C]c[D]d[A]a[B]b

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:

'
 Q = [C]c[D]d[A]a[B]b

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

So

 Q = [a constant]c[a constant]d[a constant]a[a constant]b = a constant = equilibrium constant = K

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

 K = [C]c[D]d[A]a[B]b

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## 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:

 Q = [C]c[D]d[A]a[B]b

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:

 Q   [C]c = [D]d     [A]a[B]b

And, at equilibrium:

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

So, the expression for the equilibrium constant is:

 K = [D]d     [A]a[B]b

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:

 Q = [C]c[D]d[A]a[B]b

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

 Q[B]b = [C]c[D]d[A]a

and at equilibrium,

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

So the expression for the equilibrium constant, K, is

 K = [C]c[D]d[A]a

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## Worked Examples: Writing Equilibrium Constant Expressions

Reactions Involving Aqueous Species

1. All species are present in aqueous solution eg:
Ag+(aq) +2NH3(aq) ⇋ Ag(NH3)2+(aq)

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

2. Solvent, such as water, takes part in reaction, eg:
NH3(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) ⇋ PbI2(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) + 2H2(g) ⇋ CH3OH(g)

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

2. A solid is present in the reaction, eg:
CaCO3(s) ⇋ CaO(s) + CO2(g)

K = [CO2]

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

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