Chapter 15: Chemical Equilibrium – Core Concepts and Problem-Solving Strategies

Chapter 15: Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium is a fundamental concept in general chemistry, describing the state in which the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. This chapter explores the dynamic nature of equilibrium, factors that affect it, and quantitative methods for analyzing equilibrium systems.

Key Topics Overview

• Equilibrium processes

• Factors that affect equilibria

• Equilibrium concepts applied to partially soluble salts

• Dynamic equilibria

• Reaction quotient and shifts

• Le Châtelier’s principle

• Equilibrium constants (Concentration and Pressure)

• Equilibrium concentrations – ICE Table

Equilibrium Processes

Dynamic Nature of Equilibrium

At equilibrium, both the forward and reverse reactions continue to occur, but the concentrations of reactants and products remain constant over time. This is known as dynamic equilibrium.

• Dynamic equilibrium: The condition in which the rate of the forward reaction equals the rate of the reverse reaction.

• Example: In the reaction $N_2O_4(g) \rightleftharpoons 2NO_2(g)$, both $N_2O_4$ and $NO_2$ are constantly interconverting, but their concentrations do not change once equilibrium is reached.

Factors That Affect Equilibria

Le Châtelier’s Principle

Le Châtelier’s Principle states that if a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will shift its equilibrium position to counteract the disturbance.

• Change in concentration: Adding reactants or products shifts equilibrium to consume the added substance.

• Change in temperature: For endothermic reactions, increasing temperature shifts equilibrium toward products; for exothermic reactions, it shifts toward reactants.

• Change in pressure (gases only): Increasing pressure favors the side with fewer moles of gas; decreasing pressure favors the side with more moles of gas.

Equilibrium Concepts Applied to Partially Soluble Salts

Solubility Product Constant ($K_{sp}$)

For salts that are only partially soluble, equilibrium concepts are used to describe the extent of dissolution. The solubility product constant ($K_{sp}$) quantifies the equilibrium between a solid and its ions in solution.

• Example: For $AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)$, $K_{sp} = [Ag^+][Cl^-]$

Equilibrium Constants

Equilibrium Constant Expressions

The equilibrium constant ($K$) expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.

• General form: For $aA + bB \rightleftharpoons cC + dD$:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• For gases: $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$, where $P$ denotes partial pressure.

• Note: Pure solids and liquids are not included in equilibrium expressions.

Relationship Between $K_c$ and $K_p$

For reactions involving gases, $K_p$ and $K_c$ are related by the equation:

$K_p = K_c(RT)^{\Delta n}$

• $R$ = gas constant (0.08206 L·atm·mol−1·K−1)

• $T$ = temperature in Kelvin

• $\Delta n$ = (moles of gaseous products) − (moles of gaseous reactants)

Reaction Quotient and Shifts

Reaction Quotient ($Q$)

The reaction quotient ($Q$) is calculated using the same expression as $K$, but with initial (not equilibrium) concentrations or pressures. Comparing $Q$ to $K$ predicts the direction the reaction will shift to reach equilibrium.

• If $Q < K$, the reaction shifts forward (toward products).

• If $Q > K$, the reaction shifts backward (toward reactants).

• If $Q = K$, the system is at equilibrium.

ICE Tables: Calculating Equilibrium Concentrations

Using ICE Tables

ICE tables (Initial, Change, Equilibrium) are a systematic way to calculate equilibrium concentrations when given initial concentrations and the equilibrium constant.

• Step 1: List initial concentrations.

• Step 2: Define changes in concentration using variables (usually $x$).

• Step 3: Write equilibrium concentrations in terms of $x$.

• Step 4: Substitute into the equilibrium expression and solve for $x$.

Example: For $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$, with initial concentrations $[H_2] = [I_2] = 2.0$ M, $[HI] = 0$ M, and $K_c = 16$:

• Initial: $[H_2] = 2.0$ M, $[I_2] = 2.0$ M, $[HI] = 0$ M

• Change: $-x$ for $H_2$ and $I_2$, $+2x$ for $HI$

• Equilibrium: $[H_2] = 2.0 - x$, $[I_2] = 2.0 - x$, $[HI] = 2x$

• Equilibrium expression: $K_c = \frac{[HI]^2}{[H_2][I_2]} = 16$

• Solve for $x$ to find equilibrium concentrations.

Summary Table: Types of Equilibrium Constants

Constant	System	Expression
$K_c$	Concentration (mol/L)	$K_c = \frac{[products]}{[reactants]}$
$K_p$	Pressure (atm)	$K_p = \frac{(P_{products})}{(P_{reactants})}$
$K_{sp}$	Solubility product	$K_{sp} = [ions]$

End-of-Chapter Problems

Practice problems are essential for mastering equilibrium concepts. Refer to the textbook for problems such as:

• Calculating $K_c$ and $K_p$ from equilibrium concentrations or pressures

• Predicting shifts in equilibrium using Le Châtelier’s Principle

• Using ICE tables to solve for unknown concentrations

• Applying equilibrium concepts to solubility and precipitation

Additional info: These notes are based on the provided slides and summary outline, expanded with standard textbook explanations and examples for clarity and completeness.