Chemical Equilibrium: Principles and Manipulation (Chapter 6 Study Notes)

Chapter 6: Chemical Equilibrium

Overview

This chapter introduces the concept of chemical equilibrium, focusing on equilibrium constants, their manipulation, and the thermodynamic principles that govern equilibrium. Key topics include:

• The Equilibrium Constant and How to Manipulate It

• Equilibrium Constants

• Equilibrium and Thermodynamics

• Solubility Product

• Complex Formation

• Protic Acids and Bases

• Strengths of Acids and Bases

Equilibrium Constant

Definition and Expression

The equilibrium constant, K, quantifies the ratio of concentrations of products to reactants at equilibrium for a given chemical reaction. For the general reaction:

aA + bB ⇌ cC + dD

The equilibrium constant is given by:

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

• K > 1: The reaction is favored; products predominate at equilibrium.

• Concentrations of solutes are expressed in moles per liter (M).

• Concentrations of gases are expressed in bars.

• Pure solids, pure liquids, and solvents are omitted from the equilibrium expression because their activities are unity.

• Standard state of a species:

  • Solutes: 1 M

  • Gases: 1 bar (105 Pa)

  • Solids and liquids: pure solid or liquid

Manipulation of Equilibrium Constants

Rules for Manipulating Equilibrium Constants

Equilibrium constants can be manipulated based on how reactions are combined or reversed:

• Reversing a reaction: The new equilibrium constant is the reciprocal of the original value.

• Adding reactions: The equilibrium constant for the overall reaction is the product of the individual equilibrium constants.

• Adding n reactions: The overall equilibrium constant is the product of n individual constants.

Examples

• For the reaction: HA ⇌ H+ + A-

  • $K_1 = \frac{[H^+][A^-]}{[HA]}$

• If reversed: H+ + A- ⇌ HA

  • $K_1' = \frac{[HA]}{[H^+][A^-]} = \frac{1}{K_1}$

• If two reactions are added:

  • HA ⇌ H+ + A- ($K_1$)

  • HA + C ⇌ H+ + CH+ ($K_2$)

  • Sum: HA + C ⇌ H+ + CH+ + A-

  • $K_3 = K_1 K_2 = \frac{[H^+][A^-]}{[HA]} \cdot \frac{[H^+][CH^+]}{[HA][C]} = [A^-][CH^+]/[HA][C]$

Worked Example: Combining Equilibrium Constants

Given:

• NH4+ + OH- ⇌ NH3 + H2O ($K_1 = 1.8 \times 10^{-5}$)

• NH3 + H2O ⇌ NH4+ + OH- ($K_2 = 5.6 \times 10^{-10}$)

To find the equilibrium constant for the sum of reactions, multiply the individual constants:

$K = K_1 \cdot K_2$

Additional info: This principle is widely used in analytical chemistry to calculate overall equilibrium constants for multi-step reactions.

Equilibrium and Thermodynamics

Thermodynamic Control of Equilibrium

Chemical equilibrium is governed by the thermodynamics of the reaction. Both the heat absorbed or released (enthalpy) and the degree of disorder (entropy) of reactants and products contribute to whether a reaction is favored or disfavored.

• Enthalpy (ΔH): The heat released or absorbed during a reaction at constant pressure.

• Entropy (S): The measure of disorder or randomness in a system.

Enthalpy

• Enthalpy change, ΔH: The heat released or absorbed when the reaction occurs at constant pressure.

• Standard enthalpy change, ΔHo: The heat absorbed when all reactants and products are in their standard states.

• Example: $ΔH^o = -74.85 \text{ kJ/mol}$ at 25°C for $H^+ (aq) + Cl^- (aq) \rightarrow HCl (aq)$

• If $ΔH^o$ is negative, the reaction is exothermic (heat is released).

• If $ΔH^o$ is positive, the reaction is endothermic (heat is absorbed).

Entropy

• Entropy, S: A measure of the disorder of a substance. Greater disorder means higher entropy.

• In general, gases have higher entropy than liquids, which have higher entropy than solids.

• Ions in aqueous solution are usually more disordered than in their solid salt form.

• Example: $ΔS^o = +76.4 \text{ J/(K·mol)}$ at 25°C for $KCl (s) \rightarrow K^+ (aq) + Cl^- (aq)$

Summary Table: Thermodynamic Quantities

Quantity	Symbol	Description	Significance
Enthalpy Change	ΔH	Heat absorbed or released at constant pressure	Negative: exothermic; Positive: endothermic
Entropy Change	ΔS	Change in disorder/randomness	Positive: increased disorder; Negative: decreased disorder

Additional info: The interplay of enthalpy and entropy determines the spontaneity of a reaction, as described by the Gibbs free energy equation: $ΔG = ΔH - TΔS$.