7.3 - Reaction Quotient & Equilibrium Constant
The concept of the reaction quotient (Q)
The reaction quotient, denoted as Q, is a measure that describes the relative concentrations of reactants and products in a chemical reaction at any given time. It provides a snapshot of the reaction's progress before it reaches equilibrium, helping to predict the direction in which the reaction will proceed.
Understanding Q and its significance
- Relative concentrations - Q is calculated using the concentrations of reaction species (reactants and products) at a specific moment during the reaction.
- Gas phase alternative - For reactions involving gases, Q can also be expressed in terms of partial pressures, denoted as Qp, instead of concentrations.
- Dynamic indicator - Q helps determine whether a reaction is at equilibrium or if it will shift toward reactants or products to reach equilibrium.
This concept is critical because it allows chemists to monitor reactions in real-time and understand how far a system is from achieving a balanced state.
The equilibrium constant (Kc and Kp) and its relationship to Q
The equilibrium constant is a value that describes the ratio of products to reactants at equilibrium, a state where the rates of the forward and reverse reactions are equal. It is denoted as Kc when using concentrations and Kp when using partial pressures for gas-phase reactions. The reaction quotient (Q) becomes equal to the equilibrium constant (K) when the system reaches equilibrium.
Key relationship between Q and K
- Equilibrium condition - At equilibrium, the reaction quotient equals the equilibrium constant: Kc = Q for concentrations, and Kp = Qp for partial pressures.
- Direction prediction - If Q is less than K, the reaction will proceed forward to form more products. If Q is greater than K, the reaction will shift backward to form more reactants.
- Constant value - Kc and Kp are specific to a given reaction at a particular temperature, unlike Q, which varies as the reaction progresses.
This relationship is fundamental to understanding how reactions behave over time and under different conditions.
Writing expressions for Q and K using concentrations and partial pressures
For a general reversible reaction of the form a A + b B ⇄ c C + d D, the expressions for the reaction quotient (Q) and equilibrium constant (K) are derived using the law of mass action. This law states that at equilibrium, the ratio of the concentrations (or partial pressures) of products to reactants, each raised to the power of their stoichiometric coefficients, is constant at a given temperature.
Expression for the reaction quotient and equilibrium constant using concentrations (Kc and Q)
Where:
- [C], [D], [A], [B] = Molar concentrations of the respective species (in mol/L)
- c, d, a, b = Stoichiometric coefficients of the products and reactants in the balanced equation
At equilibrium, Q equals Kc, reflecting the stable ratio of products to reactants.
Expression for gas-phase reactions for partial pressures (Kp and Qp)
Where:
- PC, PD, PA, PB = Partial pressures of the respective gases (typically in atmospheres or bars)
- c, d, a, b = Stoichiometric coefficients from the balanced equation
Similarly, at equilibrium, Qp equals Kp, indicating the reaction has reached a balanced state in terms of pressure.
These expressions are essential tools for quantifying the extent of a reaction and determining equilibrium conditions.
Exclusions of certain substances in Q and K expressions
When writing expressions for Q and K, not all substances involved in a reaction are included. Some species have concentrations or partial pressures that do not change with the amount of substance present, and thus, they are excluded from these calculations.
Substances excluded from Q and K
- Solids - The concentration of a solid is constant because its density does not change with the amount present. Therefore, solids are not included in Q or K expressions.
- Pure liquids - Like solids, pure liquids have a fixed concentration independent of the amount, so they are also excluded from these expressions.
This exclusion simplifies calculations and focuses on the species whose concentrations or pressures directly influence the reaction's progress toward equilibrium.