3.4.2 Equilibria - Equilibrium constant Kc for homogeneous systems

Specification

The equilibrium law

The equilibrium law, sometimes called the law of mass action, says that in a system at equilibrium the activities of the products raised to the powers of their stoichiometric coefficients divided by the activities of the reactants raised to the power of their stoichiometric coefficients is constant at constant temperature.

Although this may seem complicated, the activities can be taken as the concentrations, so for a system at equilibrium:

A + 2B 3C + D

The value of Kc is given by the equilibrium law:

Kc = [C]³[D]/[A][B]²

All concentrations are taken when the system has reached equilibrium, and so given all concentrations, Kc can be calculated, or given Kc and all but one of the concentrations, the final concentration can be calculated.

The units for Kc can also be calculated by replacing each concentration with mols dm^-3 (remembering to take exponents into account) and cancelling out.

top

Calculations involving kc

Calculations involving kc require more of an understanding of reacting moles then actual equilibrium.

The most likely scenario is that you are given the initial moles of a reactant mixture and told how many moles of one of the products is found at equilibrium. You are to use this information to find the equilibrium constant.

If you are given concentrations then the calculation may be a little more complex, but still a matter of working with the number of moles reacting.

For example: The reaction between ethanol and ethanoic acid in the presence of an acid catalyst was allowed to reach equilibrium.

CH₃CH₂OH + CH₃COOH CH₃COOCH₂CH₃ + H₂O

The acid content was analysed by titration and the following data was obtained.

Use the data to calculate the value of the equilibrium constant kc.

The first stage is to fill in the missing values in the table. From the equation for the reaction the ethanol reacts with ethanoic acid in a 1:1 ratio. Hence, if 0.1 - 0.067 = 0.033 moles of ethanoic acid have reacted, then the same moles of ethanol must also have reacted.

The products are formed in a 1:1 ratio (to the reactants) and so the same moles of products must appear as moles of reactants reacting = 0.033.

The table can now be completed:

Kc is calculated using the equilibrium law expression:

kc = [ethyl ethanoate][water]/[ethanol][ethanoic acid]

Note All components are in the same volume and the coefficients of the reaction are 1, then the moles can be treated as concentrations.

kc = [0.033][0.033]/[0.067][0.067]

kc = 0.24 (dimensionless)