15.6Calculating and Using Equilibrium Constants

The idea

• Calculate K from equilibrium concentrations.
• Use Q versus K to predict the direction of shift.

If a problem gives equilibrium concentrations, substitute them into the expression and compute K. If it gives initial amounts and one equilibrium amount, use an ICE table: initial, change, equilibrium. The changes are in the stoichiometric ratio. Let x be the change for a coefficient of 1, and 2x or 3x where the coefficient demands it. Then K is written entirely in x, or the known equilibrium value fills in one line of the table.

The reaction quotient Q has the same form as K but uses current concentrations, not necessarily equilibrium ones. If Q < K, the forward reaction is faster in the sense that the mixture must make more products to reach equilibrium. If Q > K, the reverse reaction is favored. If Q = K, the system is at equilibrium. Q is the tool for “which way does it go?” before you do the full algebra.

Worked path

At equilibrium, [N₂O₄] = 0.20 M and [NO₂] = 0.040 M for N₂O₄ ⇌ 2 NO₂. Find K.

1. Observe

   K = [NO₂]² / [N₂O₄].

Check yourself