Equilibrium Constant and Reaction Quotient Example Problem

In chemistry, the reaction quotient Q relates the amounts of products and reactants in a chemical reaction at a given point in time. If the reaction quotient is compared with the equilibrium constant, the direction of the reaction may be known. This example problem demonstrates how to use the reaction quotient to predict the direction of a chemical reaction towards equilibrium.
Problem:
Hydrogen and Iodine gas react together to form hydrogen iodide gas. The equation for this reaction is
H₂(g) + I₂(g) ↔ 2HI(g)
The equilibrium constant for this reaction is 7.1 x 10² at 25 °C. If the current concentration of gases are
[H₂]₀ = 0.81 M
[I₂]₀ = 0.44 M
[HI]₀ = 0.58 M
what direction will the reaction shift to reach equilibrium?
Solution
To predict the direction of equilibrium of a reaction, the reaction quotient is used. The reaction quotient, Q, is calculated in the same way as the equilibrium constant, K. Q uses the current or initial concentrations instead of the equilibrium concentrations used to calculate K.

• If Q < K, there there are more reactants present that at equilibrium and reaction will shift to the right.
• If Q > K, then there are more products present than equilibrium and the reaction will need to produce more reactants shifting the reaction to the left.
• If Q = K, then the reaction is already at equilibrium and there will be no shift.

Step 1 - Find Q
Q = [HI]₀²/[H₂]₀·[I₂]₀
Q = (0.58 M)²/(0.81 M)(0.44 M)
Q = 0.34/.35
Q = 0.94
Step 2 - Compare Q to K
K = 7.1 x 10² or 710

Q = 0.94

Q is less than K

Answer:
The reaction will shift to the right to produce more hydrogen iodide gas to reach equilibrium.