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These notes were written for the old IB syllabus (2009). The new IB syllabus for first examinations 2016 can be accessed by clicking the link below.

### 17.2 - The equilibrium law

17.2.1 - Solve homogenous equilibrium problems using the expression for Kc. Calculate Kc given all equilibrium concentrations. Given Kc and other appropriate concentrations, find an equilibrium concentration. Kp and Ksp are not required nor is use of the quadratic expression

#### The equilibrium law

The value of Kc can be expressed for a general reaction:

 A + 2B 3C + D

Kc = ([C]3[D])/([A][B]2)

The concentrations of the products (each to the power of their coefficient) over the concentrations of the reactants (each to the power of their coefficient).

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.

#### Solving problems

This usually involves working with teh stoichiometry of a reaction to determine either the concentrations at equilibrium, or using the concentrations at equilibrium to work out the equilibrium constant.

If we are given the equation:

N2O4(g) 2NO2(g)

And we are told that 2 moles of N2O4(g) are introduced into a 1dm3 flask at a given temperature and left to establish equilibrium. At equilibrium it is found that only 1.2 moles of N2O4(g) gas remain.

From this we can determine the equilibrim constant at the given temperature by looking at the coefficients of the balanced equation and working out the molar quantities of each gas at equilibrium.

Initially - moles of N2O4(g) = 2, therefore concentration = 2 mol dm-3

Initially - moles of NO2(g) = 0

@ equilibrium - moles of N2O4(g) = 1.2, therefore concentration = 1.2 mol dm-3

@ equilibrium - moles of NO2(g) = 1.6 (this comes from doubling the 0.8 moles of N2O4(g) reacted, according to the stoichiometry of the balanced equation), therefore concentration = 1.6 mol dm-3

The we substitute values into the equilibrium law equation to obtain Kc.

Kc = [NO2(g)]2/[N2O4(g)] = (1.6)2/1.2 = 2.13

This procedure is sometimes called ICE after the three steps.

• 1. Initial moles
• 2. Concentrations
• 3. Equilibrium moles and concentrations

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