Equilibrium from initial concentrations

Equilibrium concentrations can be calculated from the equilibrium constant for the reaction IF all initial concentrations are known.

One method that can be used in solving such problems is outlined below:

Write the expression for K that applies to the given system.
Take note of the direction in which reaction will occur to reach equilibrium.
If the mixture contains only reactants, the forward reaction occurs in reach equilibrium.
If the mixture contains only products, the reverse reaction occurs to reach equilibrium.

Deduce expressions for the equilbrium concentrations in terms of initial concentrations and the change due to the reaction occuring to reach equilibrium.

2NO2(g N2O4(g)  NO2(g)  N2O4(g)
initial
 0.100
(given)
 0
(given)
change
 -2x  +x
equilibrium
 0.100 - 2x  x
Construct an ICE table (one way to do this)
The rows should be labelled initial, change and final (equilibrium).
There should be a column for each component appearing in K.

Enter given data.
For components having no "initial concentration" mentioned in the problem, enter 0.

Deduce expressions for changes.
Take x as the change in concentration of one substance.
Express the changes in the other substances appearing in K in terms of x.
Changes are positive if the substance is formed in the reaction to reach equilibrium.
Changes are negative if the substance is consumed in the reaction to reach equilibrium.
The ratio of the changes is the same as the ratio of the coefficients in the balanced reaction equation.

Deduce expressions for equilibrium concentrations
equilibrium concentration = initial concentration + change in concentration

Solve for x. 
The solution for x depends on the form of the resulting equation. In this section you will see three examples of different forms. The maths can get quite complicated. Don't worry about this. It is the chemistry in steps 1-6 that should be emphasized.