1.7.4 Equilibrium Constant Calculations

Calculations involving K_c

• In the equilibrium expression each figure within a square bracket represents the concentration in mol dm^-3
• The units of K_c therefore depend on the form of the equilibrium expression
• Some questions give the number of moles of each of the reactants and products at equilibrium together with the volume of the reaction mixture
• The concentrations of the reactants and products can then be calculated from the number of moles and total volume

Equation to calculate concentration from number of moles and volume

Worked example: Calculating K_c of ethanoic acid

Answer

• Step 1: Calculate the concentrations of the reactants and products

• Step 2: Write out the balanced chemical equation with the concentrations of beneath each substance

• Step 3: Write the equilibrium constant for this reaction in terms of concentration

• Step 4: Substitute the equilibrium concentrations into the expression

• Step 5: Deduce the correct units for K_c

All units cancel out

Therefore, K_c = 4.03

• Note that the smallest number of significant figures used in the question is 3, so the final answer should also be given to 3 significant figures

• Some questions give the initial and equilibrium concentrations of the reactants but products
• An initial, change and equilibrium table should be used to determine the equilibrium concentration of the products using the molar ratio of reactants and products in the stoichiometric equation

Worked example: Calculating K_c of ethyl ethanoate

Answer

• Step 1: Write out the balanced chemical equation with the concentrations of beneath each substance using an initial, change and equilibrium table

• Step 2: Calculate the concentrations of the reactants and products

• Step 3: Write the equilibrium constant for this reaction in terms of concentration

• Step 4: Substitute the equilibrium concentrations into the expression

= 0.28

• Step 5: Deduce the correct units for K_c

All units cancel out

Therefore, K_c = 0.288

Calculations involving K_p

• In the equilibrium expression the p represent the partial pressure of the reactants and products in Pa
• The units of K_p therefore depend on the form of the equilibrium expression

Worked example: Calculating K_p of a gaseous reaction

Answer

• Step 1: Write the equilibrium constant for the reaction in terms of partial pressures

• Step 2: Substitute the equilibrium concentrations into the expression

= 9.1 x 10^-6

• Step 3: Deduce the correct units of K_p

The units of K_p are Pa^-1

Therefore, K_p = 9.1 x 10^-6 Pa^-1

• Some questions only give the number of moles of gases present and the total pressure
• The number of moles of each gas should be used to first calculate the mole fractions
• The mole fractions are then used to calculate the partial pressures
• The values of the partial pressures are then substituted in the equilibrium expression

Worked example: Calculating K_p of hydrogen iodide equilibrium reaction

• Step 1: Calculate the total number of moles

Total number of moles = 1.71 x 10^-3 + 2.91 x 10^-3 + 1.65 x 10^-2

= 2.112 x 10^-2

• Step 2: Calculate the mole fraction of each gas

• Step 3: Calculate the partial pressure of each gas

H₂ = 0.0810 x 100 = 8.10 kPa

I₂ = 0.1378 x 100 = 13.78 kPa

HI = 0.7813 x 100 = 78.13 kPa

• Step 4: Write the equilibrium constant in terms of partial pressure

• Step 5: Substitute the values into the equilibrium expression

= 54.7

• Step 6: Deduce the correct units for K_p

All units cancel out

Therefore, K_p = 54.7

• Other questions related to equilibrium expressions may involve calculating quantities present at equilibrium given appropriate data

Worked example: Calculating partial pressures

Answer

There are equal volumes of reactants A and B in a 1:1 molar ratio.

B therefore also has an equilibrium partial pressure of 0.5

Total pressure = sum of equilibrium (Σ) partial pressures

Therefore, the sum of all the partial pressures must equal to 3 atm

0.5 + 0.5 + p_c = 3 atm

p_c = 2 atm