Equilibrium

reversible reaction: a reaction that proceeds in both forward and backward directions. Usually written with double arrows:

2 NaCl (aq) + K₂SO₄ (aq)  Na₂SO₄ (aq) + 2 KCl (aq)

dynamic chemical equilibrium: reaction is happening in both directions, but the changes balance each other, so the concentrations of reactants & products remain constant. At equilibrium:
rate_{forward reaction} = rate_{reverse reaction}

Assuming the rate laws involve all of the compounds in the equation, the rate laws for the equation above would be:

rate_forward = k_forward [NaCl]² [K₂SO₄]

rate_reverse = k_reverse [NaCl]² [K₂SO₄]

equilibrium constant (K_eq): a constant that describes the equilibrium of a chemical reaction at a specific temperature.

K_eq > 1 means more products than reactants (equilibrium lies to right)

K_eq < 1 means less products than reactants (equilibrium lies to left)

equilibrium expression: a mathematical expression relating the concentrations of the products and reactants at equilibrium. The equilibrium expression is of the form:

For example, in the reaction:

2A + 4B 3C + 5D

two molecules of A react with 4 molecules of B to produce 3 molecules of C and 5 molecules of D.

The products are 3 molecules of C (meaning that C appears 3 times in the equilibrium expression) and 5 molecules of D (so it appears 5 times). The reactants are 2 molecules of A (appears twice) and 4 molecules of B (appears 4 times).

The equilibrium expression would therefore be:

This simplifies to:

Note that concentrations only make sense for solutions, which means only chemicals that exist in aqueous solutions (aq) or gases (g) will appear in the equilibrium constant. Solids (s), precipitates (ppt), and pure liquids (l) do not appear in the equilibrium expression.

K_eq is a constant, but has different values at different temperatures.

reaction quotient (Q): the value of  at any time, not just at equilibrium. I.e., at equilibrium, Q = K_eq.

Le Châtlier’s principle: if a reaction is at equilibrium, the reaction will resist any change with a corresponding change that shifts the reaction back to its equilibrium.

For example, suppose we had the reaction:

A + B  C + D

with K_eq = 1. Suppose [A] = 0.5M, [B] = 4M, [C] = 1M, and [D] = 2M. This is a correct set of concentrations, because

If we added more A to make the concentration 2M, Le Chatlier’s principle predicts that the reaction will compensate by “moving to the right,” producing more C and D.

In fact, the new denominator is (2)(4) = 8, which means [C] and/or [D] must increase so that the product of [C][D] (the numerator) also equals 8.

Le Châtlier’s principle and temperature: Changing the temperature shifts the equilibrium by changing the value of K_eq. However, Le Châtlier’s principle correctly predicts the effects of adding heat, by putting heat into the reaction as either a reactant or a product.

For example, in the following reaction at 25°C:

H₂ (g) + Cl₂ (g) 2 HCl (g) + 92.3

heat is a product. This means that at higher temperatures, the additional heat will shift the equilibrium to the left, resulting in more H₂ and Cl₂ and less HCl.