Equilibrium Constant
Equilibrium Constant
In chemistry, the equilibrium constant (denoted as ( K )) is a value that expresses the ratio of the concentrations of products to reactants at equilibrium for a reversible chemical reaction at a given temperature. It provides a quantitative measure of the position of equilibrium and indicates the extent to which a reaction will proceed.
Understanding Chemical Equilibrium
Chemical equilibrium occurs in a reversible reaction when the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products over time. At this point, the reaction has reached a state of balance, although the individual reactants and products continue to react with each other.
The Law of Mass Action
The Law of Mass Action states that, at a given temperature, the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, each raised to a power equal to the coefficient of that substance in the balanced chemical equation.
For a general reaction:
[ aA + bB \rightleftharpoons cC + dD ]
The equilibrium constant expression, according to the Law of Mass Action, is given by:
[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} ]
where:
- ( [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.
Types of Equilibrium Constants
There are different types of equilibrium constants, depending on the nature of the reactants and products:
- ( K_c ): Equilibrium constant for concentrations, used when dealing with solutions.
- ( K_p ): Equilibrium constant for partial pressures, used for gaseous reactions.
- ( K_{sp} ): Solubility product constant, used for sparingly soluble salts.
- ( K_a ): Acid dissociation constant, used for weak acids.
- ( K_b ): Base dissociation constant, used for weak bases.
Important Points and Differences
| Property | ( K_c ) | ( K_p ) |
|---|---|---|
| Definition | Ratio of molar concentrations of products to reactants | Ratio of partial pressures of gaseous products to reactants |
| Units | Depends on the reaction (may be dimensionless) | Usually atm or bar (may be dimensionless) |
| Usage | Primarily for reactions in solution | Primarily for gaseous reactions |
| Relation | ( K_p = K_c(RT)^{\Delta n} ) where ( \Delta n ) is the change in moles of gas | - |
Formulas
For gaseous reactions, the relationship between ( K_c ) and ( K_p ) is given by the equation:
[ K_p = K_c(RT)^{\Delta n} ]
where:
- ( R ) is the ideal gas constant (0.0821 L·atm/mol·K).
- ( T ) is the temperature in Kelvin.
- ( \Delta n ) is the difference in moles of gaseous products and reactants.
Examples
Example 1: Equilibrium Constant for a Reaction
Consider the reaction:
[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) ]
At equilibrium, the concentrations are:
- ( [N_2] = 0.5 ) M
- ( [H_2] = 1.5 ) M
- ( [NH_3] = 1.0 ) M
The equilibrium constant ( K_c ) is:
[ K_c = \frac{[NH_3]^2}{[N_2][H_2]^3} = \frac{1.0^2}{0.5 \cdot 1.5^3} = \frac{1}{0.5 \cdot 3.375} = \frac{1}{1.6875} \approx 0.592 ]
Example 2: Relationship between ( K_c ) and ( K_p )
For the above reaction, if we want to find ( K_p ) at 298 K, we use the formula:
[ K_p = K_c(RT)^{\Delta n} ]
Here, ( \Delta n = 2 - (1 + 3) = -2 ).
[ K_p = K_c(0.0821 \cdot 298)^{-2} \approx 0.592 \cdot (24.5)^{-2} \approx 0.592 \cdot 0.00167 \approx 0.00099 ]
Thus, ( K_p ) is approximately 0.00099 atm(^{-2}).
Understanding the equilibrium constant is crucial for predicting the direction of a reaction and determining the extent to which reactants are converted into products. It is a fundamental concept in chemical thermodynamics and is widely used in various fields such as chemistry, biochemistry, and environmental science.