Chemical Equilibrium: Principles, Expressions, and Calculations

Chemical Equilibrium

Basic Concepts

Chemical equilibrium is a fundamental concept in chemistry describing the state in which the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products over time.

• Reversible reactions do not go to completion; they can proceed in both directions.

• Symbolically, a reversible reaction is represented as: $aA_{(g)} + bB_{(g)} ightleftharpoons cC_{(g)} + dD_{(g)}$

• At equilibrium, rateforward = ratereverse.

• This state is called dynamic equilibrium, where the overall composition of the reaction mixture remains constant.

Basic Concepts from Kinetics

Kinetics helps us understand how equilibrium is established. The rates of the forward and reverse reactions change over time until they become equal at equilibrium.

• Graphical representation shows concentrations of reactants decreasing and products increasing until equilibrium is reached.

• Example reaction: $aA_{(g)} + bB_{(g)} ightleftharpoons cC_{(g)} + dD_{(g)}$

• Equilibrium can be established from either direction (starting with reactants or products).

Establishing Equilibrium

Equilibrium can be reached whether the system starts with reactants or products. The final equilibrium concentrations will be the same, regardless of the starting point.

• Equilibrium constants only include gases and aqueous solutions.

• Example: $2SO_2(g) + O_2(g) ightleftharpoons 2SO_3(g)$ Graphs show how concentrations change over time until equilibrium is established.

The Equilibrium Constant

Definition and Expression

The equilibrium constant quantifies the ratio of product concentrations to reactant concentrations at equilibrium for a given reaction.

• For a general reaction: $aA_{(g)} + bB_{(g)} ightleftharpoons cC_{(g)} + dD_{(g)}$

• The rates of the forward and reverse reactions are equal at equilibrium: $Rate_f = Rate_r$

• The equilibrium constant ($K_c$) is defined as: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• This expression is valid for all reactions involving gases and aqueous solutions.

Properties of the Equilibrium Constant

The equilibrium constant has several important properties that affect how it is used in calculations and predictions.

• If the reaction is reversed, $K_c$ becomes $1/K_c$.

• If the reaction is multiplied by a factor $n$, $K_c$ is raised to the power $n$.

• If reactions are added, the equilibrium constant for the overall reaction is the product of the individual $K_c$ values.

Examples and Applications

• Example 1: Write equilibrium constant expressions for the following reactions: - $PCl_5 ightleftharpoons PCl_3 + Cl_2$ $K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]}$ - $H_2 + I_2 ightleftharpoons 2HI$ $K_c = \frac{[HI]^2}{[H_2][I_2]}$

Graphical Representation of Equilibrium

Graphs illustrate how concentrations of reactants and products change over time, eventually reaching constant values at equilibrium.

• Starting with reactants: concentrations of reactants decrease, products increase.

• Starting with products: concentrations of products decrease, reactants increase.

Key Terms

• Dynamic equilibrium: The state in which the forward and reverse reaction rates are equal, and concentrations remain constant.

• Equilibrium constant ($K_c$): A ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients in the balanced equation.

• Reversible reaction: A reaction that can proceed in both the forward and reverse directions.

Summary Table: Equilibrium Constant Properties

Operation	Effect on $K_c$
Reverse reaction	$K_c' = 1/K_c$
Multiply reaction by $n$	$K_c' = (K_c)^n$
Add reactions	$K_c' = K_{c1} \times K_{c2}$

Example Calculation

• For the reaction $2SO_2(g) + O_2(g) ightleftharpoons 2SO_3(g)$, if equilibrium concentrations are $[SO_2] = 0.344 M$, $[O_2] = 0.172 M$, $[SO_3] = 0.056 M$, then: $K_c = \frac{[SO_3]^2}{[SO_2]^2[O_2]}$

Additional info:

• Equilibrium can be established from either direction, and the final equilibrium concentrations are independent of the initial conditions.

• Equilibrium constants are dimensionless and depend on temperature.