Reaction Quotient and Equilibrium Constant
Quick Notes
- Q is the reaction quotient: the ratio of product/reactant concentrations (or partial pressures) at any point in the reaction.
- K is the equilibrium constant: the ratio of product/reactant concentrations when the system is at equilibrium.
- Comparing Q to K tells the direction the reaction will shift in:
- If Q < K → reaction shifts right (toward products)
- If Q > K → reaction shifts left (toward reactants)
- If Q = K → system is at equilibrium
- Qc uses concentrations (mol L−1), Qp uses partial pressures (atm).
- Pure solids and liquids are excluded from the expression.
Full Notes
What Is the Reaction Quotient (Q)?
The reaction quotient (Q) is a snapshot of a reaction’s progress. It is calculated by using concentration values at a specific point in time, which might not be equilibrium values.
For the general reaction:
The expression is:
What Is the Equilibrium Constant (K)?
The equilibrium constant (Kc or Kp) uses the same form as Q, but only applies at equilibrium.
The general form for a homogeneous reaction is:
The expression is:
- Square brackets [ ] represent concentration in mol dm⁻³.
- Each term is raised to the power of its stoichiometric coefficient from the balanced equation.
- K is constant at a given temperature and does not change unless temperature changes.
Rules for Writing Q and K Expressions
- Include only gases and aqueous species.
- Don’t include pure solids and pure liquids, since their concentration (or 'activity') does not change.
- Coefficients in the balanced equation become exponents.
Kc and Kp
In AP Chemistry, you'll encounter two main types of equilibrium constants:
Kc – based on concentrations (mol/L)
Kp – based on partial pressures (used for gases)
Both express the position of equilibrium, but they are calculated differently depending on the type of data provided.
What the value of K tells us:
K = 1
The system is balanced. Neither the forward nor reverse reaction is favored — concentrations of reactants and products are comparable.
K > 1
The equilibrium favors products. At equilibrium, the mixture contains a higher proportion of products than reactants — the forward reaction is favored.
K < 1
The equilibrium favors reactants. There are more reactants than products in the mixture — the reverse reaction is favored.
In short: the magnitude of K gives insight into which side of the reaction is dominant at equilibrium.
Kc (Equilibrium Constant based on Concentration)
For the general reaction:
The expression is:
- [A], [B], [C], [D] are equilibrium concentrations in mol dm⁻³.
- a, b, c, and d are the balancing numbers from the equation.
Kp (Equilibrium Constant based on Partial Pressures)
The equilibrium constant, Kp, works in the same way as Kc.
It applies to homogeneous gaseous equilibria, where all reactants and products are in the gas phase and is expressed in terms of partial pressures of all gases present.
Kp for the general reaction:
The expression is:
Calculating Partial Pressures and Mole Fractions
The total pressure of a gaseous system at equilibrium is directly related to the number of moles of each gas in the mixture. How much pressure one type of gas contributes to the total pressure of a gaseous system is called its partial pressure. All partial pressures of gases in a system add up to give the total pressure of the system.
It is calculated using:
The mole fraction of a gas is the moles of that gas in the mixture compared to moles of all gases. It is calculated using:
Comparing Q and K
The reaction quotient (Q) can be compared to the equilibrium constant (K) to predict the direction in which a reversible reaction will proceed.
It’s important to compare like with like — for example, Qc must be compared with Kc, and Qp with Kp. Mixing types (e.g., comparing Qc with Kp) is not valid.
If Q = K,
the system is at equilibrium. The rates of the forward and reverse reactions are equal, and the concentrations of all species remain constant.
However, If Q ≠ K,
the system is not at equilibrium. The reaction will proceed in the direction that moves Q toward K.
- If Q < K → the reaction shifts forward (toward products).
- If Q > K → the reaction shifts backward (toward reactants).
For the reaction N2(g) + 3H2(g) ⇌ 2NH3(g) with K = 0.50, the instantaneous concentrations are [N2] = 0.20 M, [H2] = 0.60 M, and [NH3] = 0.10 M. Determine the direction of shift.
- Write the expressions
K = [NH3]2 / ( [N2] [H2]3 )
Q = [NH3]2 / ( [N2] [H2]3 ) - Compute Q with current concentrations
Q = (0.10)2 / (0.20 × (0.60)3)
Q ≈ 0.010 / 0.0432 ≈ 0.231 - Compare Q and K
Q = 0.231 and K = 0.50 → Q < K
Direction: Since Q < K, the reaction shifts right (toward products), producing more NH3 until equilibrium is reached.
Exam Note
On the AP exam you will not be asked to convert between Kc and Kp, and mixed phase equilibria (solid + gas + aqueous) are avoided.
Summary
- Q shows reaction position at any point; K shows position at equilibrium.
- Qc is based on concentrations, Qp on pressures.
- Compare Q and K to predict direction of shift.
- Expressions exclude solids and pure liquids, and use coefficients as exponents.