Write An Expression For The Equilibrium Constant

Writing an Expression for the Equilibrium Constant: A Comprehensive Guide

The equilibrium constant, denoted as K, is a crucial concept in chemistry that quantifies the relative amounts of reactants and products present at equilibrium in a reversible reaction. Understanding how to write the expression for the equilibrium constant is fundamental to predicting the direction of a reaction and calculating the concentrations of species at equilibrium. This comprehensive guide will walk you through the process, covering various scenarios and providing practical examples.

Understanding Equilibrium and the Equilibrium Constant

Before diving into the intricacies of writing equilibrium constant expressions, let's refresh our understanding of chemical equilibrium. A reversible reaction reaches equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant, although the reaction continues at a microscopic level.

The equilibrium constant, K, is a ratio that relates the concentrations of products to the concentrations of reactants at equilibrium. A large value of K indicates that the equilibrium lies far to the right (favoring products), while a small value of K indicates that the equilibrium lies far to the left (favoring reactants). K is temperature-dependent; changing the temperature will alter the value of K.

Writing the Equilibrium Constant Expression: The Law of Mass Action

The expression for the equilibrium constant is derived from the Law of Mass Action. This law states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, each raised to a power equal to its stoichiometric coefficient in the balanced chemical equation. For the general reversible reaction:

aA + bB ⇌ cC + dD

where a, b, c, and d are the stoichiometric coefficients, the equilibrium constant expression is:

K = ([C]^c[D]^d) / ([A]^a[B]^b)

Notice the following crucial aspects:

• Products in the Numerator: The concentrations of the products (C and D) are in the numerator.
• Reactants in the Denominator: The concentrations of the reactants (A and B) are in the denominator.
• Stoichiometric Coefficients as Exponents: The stoichiometric coefficients from the balanced equation become exponents in the equilibrium constant expression.
• Pure Solids and Liquids are Ignored: The concentrations of pure solids and pure liquids are considered constant and are omitted from the expression. This is because their effective concentrations do not change significantly during the reaction.
• Aqueous and Gaseous Species Included: Only the concentrations of aqueous (aq) and gaseous (g) species are included in the expression.

Examples of Equilibrium Constant Expressions

Let's illustrate the process with some examples:

Example 1: The Haber-Bosch Process

The Haber-Bosch process, used for ammonia synthesis, is represented by the following equation:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

The equilibrium constant expression is:

K = ([NH₃]²) / ([N₂][H₂]³)

Example 2: Dissolution of a Slightly Soluble Salt

Consider the dissolution of silver chloride (AgCl):

AgCl(s) ⇌ Ag⁺(aq) + Cl^-(aq)

Since AgCl is a pure solid, it is omitted from the expression:

K_sp = [Ag⁺][Cl^-]

Note that this specific equilibrium constant is called the solubility product constant, K_sp.

Example 3: A Reaction with Multiple Phases

The reaction between hydrogen gas and iodine vapor to produce hydrogen iodide gas:

H₂(g) + I₂(g) ⇌ 2HI(g)

The equilibrium constant expression is:

K = [HI]² / ([H₂][I₂])

Example 4: Reaction Involving Water

Consider the acid dissociation of acetic acid (CH₃COOH):

CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO^-(aq) + H₃O⁺(aq)

Water, being the solvent, is usually omitted from the equilibrium expression (unless the concentration of water changes significantly, which is rare). Therefore:

K_a = [CH₃COO^-][H₃O⁺] / [CH₃COOH]

This specific equilibrium constant is called the acid dissociation constant, K_a.

Dealing with Partial Pressures: K_p

For gas-phase reactions, the equilibrium constant can also be expressed in terms of partial pressures instead of concentrations. This is denoted as K_p. For the general reaction:

aA(g) + bB(g) ⇌ cC(g) + dD(g)

The K_p expression is:

K_p = (P_C^cP_D^d) / (P_A^aP_B^b)

where P_A, P_B, P_C, and P_D are the partial pressures of the respective gases at equilibrium. The relationship between K_c (equilibrium constant in terms of concentrations) and K_p is given by:

K_p = K_c(RT)^Δn

where:

• R is the ideal gas constant
• T is the temperature in Kelvin
• Δn is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants)

Heterogeneous Equilibria

Reactions involving multiple phases (solid, liquid, gas, aqueous) are known as heterogeneous equilibria. As mentioned earlier, pure solids and liquids are omitted from the equilibrium constant expression because their concentrations remain essentially constant. Only the concentrations of gaseous and aqueous species are included.

Applications of the Equilibrium Constant

The equilibrium constant is a powerful tool with several applications in chemistry:

• Predicting the Direction of a Reaction: By comparing the reaction quotient (Q) to the equilibrium constant (K), we can predict whether a reaction will proceed to the right (towards products) or to the left (towards reactants). If Q < K, the reaction will proceed to the right; if Q > K, the reaction will proceed to the left; and if Q = K, the reaction is at equilibrium.

• Calculating Equilibrium Concentrations: Knowing the value of K and the initial concentrations of reactants, we can calculate the equilibrium concentrations of all species involved in the reaction using an ICE (Initial, Change, Equilibrium) table.

• Understanding Reaction Spontaneity (Gibbs Free Energy): The equilibrium constant is related to the Gibbs Free Energy (ΔG) change of a reaction through the following equation:

ΔG = -RTlnK

A negative ΔG indicates a spontaneous reaction under standard conditions.

Conclusion

Writing the expression for the equilibrium constant is a fundamental skill in chemistry. By understanding the Law of Mass Action and the rules for including or omitting different species, you can accurately represent the equilibrium state of a reversible reaction. This knowledge is essential for predicting reaction direction, calculating equilibrium concentrations, and understanding the thermodynamics of chemical reactions. Mastering this concept will significantly enhance your understanding of chemical equilibrium and its diverse applications in various fields.