Law of Mass Action
Law of Mass Action
The Law of Mass Action is a principle in chemistry that quantifies the relationship between the rate of a chemical reaction and the concentrations of the reactants. It was formulated by Cato Maximilian Guldberg and Peter Waage in 1864. This law is fundamental to the understanding of chemical equilibrium, reaction kinetics, and the behavior of systems in dynamic balance.
Definition
The Law of Mass Action states that the rate of a chemical reaction at a constant temperature is directly proportional to the product of the molar concentrations of the reactants, each raised to a power equal to the stoichiometric coefficient in the balanced chemical equation.
Mathematical Expression
For a general chemical reaction:
[ aA + bB \rightleftharpoons cC + dD ]
The Law of Mass Action can be expressed by the equilibrium constant expression:
[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} ]
Where:
- ( K_c ) is the equilibrium constant for the reaction when concentrations are used.
- ( [A] ), ( [B] ), ( [C] ), and ( [D] ) are the molar concentrations of the reactants and products at equilibrium.
- ( a ), ( b ), ( c ), and ( d ) are the stoichiometric coefficients of the reactants and products in the balanced equation.
Application in Chemical Equilibrium
The Law of Mass Action is crucial in determining the position of equilibrium in a chemical reaction. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of reactants and products remain constant.
Differences and Important Points
Here's a table summarizing key aspects of the Law of Mass Action:
| Aspect | Description |
|---|---|
| Equilibrium Constant (K) | A numerical value that represents the ratio of product concentrations to reactant concentrations at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. |
| Reaction Quotient (Q) | Similar to the equilibrium constant, but for a reaction that has not yet reached equilibrium. It helps predict the direction in which the reaction will proceed to reach equilibrium. |
| Le Chatelier's Principle | While not part of the Law of Mass Action, it complements it by predicting how changes in concentration, pressure, or temperature will affect the position of equilibrium. |
| Limitations | The Law of Mass Action applies to ideal solutions and gases where the activities can be approximated by concentrations. It may not hold in non-ideal conditions. |
Formulas and Examples
Example 1: Simple Reaction
For the reaction:
[ H_2 + I_2 \rightleftharpoons 2HI ]
The Law of Mass Action gives the equilibrium expression as:
[ K_c = \frac{[HI]^2}{[H_2][I_2]} ]
If at equilibrium, the concentrations are ( [H_2] = 0.1 ) M, ( [I_2] = 0.1 ) M, and ( [HI] = 0.2 ) M, then:
[ K_c = \frac{(0.2)^2}{(0.1)(0.1)} = 4 ]
Example 2: Complex Reaction
For the reaction:
[ 2NO_2 \rightleftharpoons N_2O_4 ]
The equilibrium expression is:
[ K_c = \frac{[N_2O_4]}{[NO_2]^2} ]
If ( [NO_2] = 0.5 ) M and ( [N_2O_4] = 0.1 ) M at equilibrium, then:
[ K_c = \frac{0.1}{(0.5)^2} = 0.4 ]
Conclusion
The Law of Mass Action is a foundational concept in chemistry that helps us understand and predict the behavior of chemical reactions in equilibrium. By knowing the equilibrium constant and the concentrations of reactants and products, one can determine the extent to which a reaction will proceed and how it will respond to changes in conditions.