Equilibrium Constants, Kc & Kp (Cambridge International AS Chemistry)

Equilibrium Constant: Concentrations

Equilibrium expression & constant

• The equilibrium expression is an expression that links the equilibrium constant, K_c, to the concentrations of reactants and products at equilibrium taking the stoichiometry of the equation into account
• So, for a given reaction:

aA + bB ⇌ cC + dD

• K_c is defined as:

$K_{c} = \frac{[ \mathrm{C} ]^{c} [ \mathrm{D} ]^{d} }{[ \mathrm{A} ]^{a} [ \mathrm{B} ]^{b} }$

• Where:

  • [A] and [B] are the equilibrium concentrations of A and B, in mol dm^-3
  • [C] and [D] are the equilibrium concentrations of C and D, in mol dm^-3
  • a, b, c and d are the respective number of moles of each reactant and product

• Solids are ignored in equilibrium expressions

• The K_c of a reaction is specific and only changes if the temperature of the reaction changes

Worked Example Deduce the equilibrium expression for the following reactions:

1. Ag⁺ (aq) + Fe²⁺ (aq) $\rightleftharpoons$ Ag (s) + Fe³⁺ (aq)
2. N₂ (g) + 3H₂ (g) $\rightleftharpoons$ 2NH₃ (g)
3. 2SO₂ (g) + O₂ (g) $\rightleftharpoons$ 2SO₃ (g)

Answer

1. Ag⁺ (aq) + Fe²⁺ (aq) $\rightleftharpoons$ Ag (s) + Fe³⁺ (aq)

K_c = $\frac{[ Fe^{3 +} ( \text{aq} ) ]}{[ Fe^{2 +} ( \text{aq} ) ] [ Ag^{+} ( \text{aq} ) ]}$

1. N₂ (g) + 3H₂ (g) $\rightleftharpoons$ 2NH₃ (g)

K_c = $\frac{[ NH_{3} ( \mathrm{g} ) ]^{2}}{[ \mathrm{N}_{2} ( \mathrm{g} ) ] [ \mathrm{H}_{2} ( \mathrm{g} ) ]^{3}}$

1. 2SO₂ (g) + O₂ (g) $\rightleftharpoons$ 2SO₃ (g)

K_c = $\frac{[ SO_{3} ( \mathrm{g} ) ]^{2}}{[ SO_{2} ( \mathrm{g} ) ]^{2} [ \mathrm{O}_{2} ( \mathrm{g} ) ]}$

Mole Fraction & Partial Pressure

Spec point — 7.1.5

Partial pressure

• For reactions involving mixtures of gases, the equilibrium constant K_p is used as it is easier to measure the pressure than the concentration for gases
• The partial pressure of a gas is the pressure that the gas would have if it was in the container all by itself
• The total pressure is the sum of the partial pressure:

P_total= P_A+ P_B+ P_C+ .......

• P_total = total pressure

  • P_A, P_B, P_C = partial pressures

How partial pressures contribute to total pressure

Partial pressures can be added together to calculate the total pressure

Mole fraction

• The mole fraction of a gas is the ratio of moles of a particular gas to the total number of moles of gas present

$\mathrm{Mole} \mathrm{fraction}=\frac{\mathrm{number} \mathrm{of} \mathrm{moles} \mathrm{of}a\mathrm{particular} \mathrm{gas}}{\mathrm{total} \mathrm{number} \mathrm{of} \mathrm{moles} \mathrm{of} \mathrm{all} \mathrm{the} \mathrm{gases} \mathrm{in} \mathrm{the} \mathrm{mixture}}$

• To calculate the partial pressures of each gas the following relationship can be used:

$\mathrm{Partial} \mathrm{pressure}=\mathrm{mole} \mathrm{fraction}\times\mathrm{total} \mathrm{pressure}$

• The sum of the mole fractions should add up to 1.00, while the sum of the partial pressures should add up to the total pressure

Equilibrium Constant: Partial Pressures

Equilibrium expressions involving partial pressures

• Equilibrium expressions in terms of partial pressures are written similarly to those involving concentrations, with a few differences:

Comparing K_p and K_c expressions

The process of writing the expressions is similar, but there is a different presentation and different information required

Worked Example Deducing equilibrium expressions of gaseous reactions

Deduce the equilibrium expression for the following reactions:

1. N₂ (g) + 3H₂ (g) $\rightleftharpoons$ 2NH₃ (g)
2. N₂O₄ (g) $\rightleftharpoons$ 2NO₂ (g)
3. 2SO₂ (g) + O₂ (g) $\rightleftharpoons$ 2SO₃ (g)

Answer

1. N₂ (g) + 3H₂ (g) $\rightleftharpoons$ 2NH₃ (g)

K_p = $\frac{p^{2}\mathrm{NH}_{3}}{p^{3}H_{2}\times pN_{2}}$

1. N₂O₄ (g) $\rightleftharpoons$ 2NO₂ (g)

K_p = $\frac{p^{2}NO_{2}}{pN_{2}O_{4}}$

1. 2SO₂ (g) + O₂ (g) $\rightleftharpoons$ 2SO₃ (g)

K_p = $\frac{p^{2}\mathrm{SO}_{3}}{p^{2}\mathrm{SO}_{2}\times pO_{2}}$