3.6.3 The Equilibrium Constant, Kc

Equilibrium expression & constant

• The equilibrium expression 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

          the K_c is defined as follows:

Equilibrium expression linking the equilibrium concentration of reactants and products at equilibrium

• Solids are ignored in equilibrium expressions
• The K_c of a reaction is specific and only changes if the temperature of the reaction changes

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

Answer

Step 1: Calculate the concentrations of the reactants and products

• • [CH₃COOH (l)] =
  • [C₂H₅OH (l)] =
  • [CH₃COOC₂H₅ (l)] = 
  • [H₂O (l)] = 

Step 2: Write the equilibrium constant for this reaction in terms of concentration

• • K_c = 

Step 3: Substitute the equilibrium concentrations into the expression

• • K_c = 

Step 4: Deduce the correct units for K_c 

• • K_c = 
  • All units cancel out

Therefore, K_c = 4.03

• Some questions give the initial and equilibrium concentrations of the reactants but not the 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

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

• • [CH₃COOC₂H₅ (l)] = 
  • [H₂O (l)] = 
  • [CH₃COOH (l)] =
  • [C₂H₅OH (l)] =

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

• • K_c = 

Step 4: Substitute the equilibrium concentrations into the expression

• • K_c = 

Therefore, K_c = 0.28

Estimating the position of equilibrium

• The magnitude of K_c indicates the relative concentrations of reactants and products in the mixture

  • If K_c is very large (Kc >>1) the equilibrium lies to the RHS so the reaction mixture contains mostly products

  • If K_c is very small (Kc << 1) the equilibrium lies to the LHS so the reaction mixture contains mostly reactants

  • If K_c is close to 1 the mixture contains a similar concentration of both reactant and products