The Reaction Quotient

The reaction quotient, Q, is the ratio of products and reactants in a system at any point in the reaction
The equilibrium constant (K) the ratio of products and reactants in a system at equilibrium
Q and K are defined by an expression that relates the products’ and reactants’ concentrations (c) or partial pressures (P)
Consider the generic equation:

aA + bB ⇌ cC + dD

Where a, b, c, and d represent stoichiometric coefficients and A, B, C, and D represent chemical species

The expressions for Q_c and K_c are:

$Q_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}$ $K_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}$

[A] indicates the concentration of species A in mol/L

The expressions for Q_P and K_P are:

$Q_{p} = \frac{{(P_{C})}^{c} {(P_{D})}^{d}}{{(P_{A})}^{a} {(P_{B})}^{b}}$ $K_{p} = \frac{{(P_{C})}^{c} {(P_{D})}^{d}}{{(P_{A})}^{a} {(P_{B})}^{b}}$

P_A indicates the partial pressure of species A in atm

Solids and pure liquids are omitted from all of these expressions as their concentrations and partial pressures do not depend on the amount of substance present
As a reversible reaction proceeds towards equilibrium, the value of Q approaches K such that at equilibrium Q = K

Worked example

2ZnS (s) + 3O₂(g) ⇌ 2ZnO (s) + 2SO₂(g)

Write the equilibrium expression for the equilibrium constant, K_c, for the reaction above?

Answer:

For the generic equation

aA + bB ⇌ cC + dD

The equilibrium expression for K_c is

$K_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}$

Solids are not included in an equilibrium expression as their concentrations are constant
So, ZnS(s), ZnO(s), and their corresponding stoichiometric coefficients will not be written in the equilibrium expression
Therefore the equilibrium expression for K_c becomes

$K_{c} = \frac{{[{SO}_{2}]}^{2}}{{[O_{2}]}^{3}}$

When solving for Q we substitute in values for concentration or partial pressure any point during the reaction, but when solving for K we substitute values for concentration or partial pressure for the system at equilibrium
Both Q and K are unitless values
The value of K is the same for a given reversible reaction regardless of the initial amounts of each species but it is temperature dependant and will vary with changes in temperature

Exam Tip

Remember, an equilibrium constant only expresses the state of a system at equilibrium.

When writing a K_c or Q_c expression, always be sure to include the brackets, as brackets around a species represent the concentration of that species. However, when writing a K_P or Q_P expression never use brackets as this expression involves partial pressures not concentrations.

Note that the AP Chemistry exam equation and constant sheet only includes the equations for K_c and K_P. We need to remember that the equations for Q_c and Q_P follow the same format.

The Reaction Quotient (College Board AP Chemistry)

Revision Note