Chemical Equilibrium Concepts

Overview of Chemical Equilibrium in Homogeneous Reactions

• Dynamic Equilibrium: Dynamic Equilibrium is a condition in which the forward and reverse reaction rates are identical, leading to steady concentrations despite continuous reactions.

  infoNote

  Dynamic Nature: While concentrations remain unchanged, equilibrium is dynamic because reactions occur continuously.

• Significance: A firm grasp of equilibrium is crucial for anticipating reaction behaviours and in the development of industrial processes such as those in pharmaceuticals and materials synthesis.

Establishing Equilibrium

• Conditions for Equilibrium:

  • Closed System: No exchange of matter with the external environment.
  • Stable Temperature: Required to maintain an equilibrium state.

• Energy and Reaction Kinetics:

  • Activation Energy: The minimum energy necessary for a reaction to proceed.
  • Transition State Theory: Provides insight into how reactants form high-energy transition states before transforming into products.

Key Terms Definitions

• Homogeneous Reaction: A reaction in which all reactants and products exist in the same phase.

• Dynamic Equilibrium: Elucidates how molecular dynamics help maintain stable concentrations through ongoing reactions.

• Equilibrium Constant ($K_{eq}$): A dimensionless value that is key to predicting the direction and extent of reactions.

  chatImportant

  Equilibrium Constant ($K_{eq}$): Crucial for forecasting reaction outcomes.

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

  Example Calculation:

  • Consider the reaction $A + B \leftrightarrow C + D$:
    • Compute the numerator: $([C]^c [D]^d)$ = $(2)^2 \times (2)^1 = 8$.
    • Compute the denominator: $([A]^a [B]^b)$ = $(1)^1 \times (1)^1 = 1$.
    • Calculate $K_{eq}$: $\frac{8}{1} = 8$.

Application of Homogeneous Equilibria in Real-World Processes

• Haber-Bosch Process: Applies equilibrium principles to efficiently synthesise ammonia by managing factors such as pressure and catalyst.
• Diverse Applications: Equilibrium principles are also utilised in various processes to optimise reaction conditions and enhance yields.

Deriving the Equilibrium Expression

Equilibrium Expression

• Definition: The ratio of product concentrations to reactant concentrations at equilibrium for a reversible reaction.
• Importance: Integral for predicting chemical behaviour by indicating concentration balance tendencies.

Derivation Process

Step-by-Step Guide:

• 1. Start with a Balanced Chemical Equation
  • Ensure reactants and products have balanced atoms.
• 2. Formulate the Equilibrium Expression
  • Use concentrations: [A], [B] for reactants; [C], [D] for products.
• 3. Apply Stoichiometric Coefficients
  • Include coefficients as exponents:
    $K_{eq} = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

Worked Examples

Example 1: Synthesis of Ammonia

• Balanced Equation: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$
• Derivation of $K_{eq}$:
  • $K_{eq} = \frac{[NH_3]^2}{[N_2][H_2]^3}$

Common Misconceptions

Calculating the Equilibrium Constant

Steps for Calculation

• Step 1: Write the balanced chemical equation.

  chatImportant

  Correct balancing is fundamental. Errors in balancing impact $K_{eq}$ accuracy.

• Step 2: Arrange initial and equilibrium concentration data in a table format for clarity.

• Step 3: Formulate and resolve the equilibrium expression.

Example Problems

• Example 1: Reaction $A_2 + B_2 \rightleftharpoons 2 AB$
  • Determine $K_{eq}$ using initial concentration data.

Predicting Reaction Directions Using $K_{eq}$

Magnitude of $K_{eq}$

• $K_{eq} >> 1$: Indicates product predominance.
• $K_{eq} << 1$: Indicates reactant predominance.
• $K_{eq} \approx 1$: A balanced state, with neither reactants nor products favoured.

Using Reaction Quotient (Q)

• Reaction Quotient (Q): The ratio of products to reactants at any point, utilised to assess a system's proximity to equilibrium.

  chatImportant

  Comparing Q with $K_{eq}$ is vital for predicting directional shifts.

Examples and Exercises

Example 1: Industrial ammonia synthesis using the Haber process.

Exercise: Calculate Q for specified initial conditions to discern reaction directionality.

• Solution: For the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ with initial concentrations $[N_2] = 0.5 M$, $[H_2] = 1.5 M$ and $[NH_3] = 0.1 M$, calculate: $Q = \frac{[NH_3]^2}{[N_2][H_2]^3} = \frac{(0.1)^2}{(0.5)(1.5)^3} = \frac{0.01}{1.6875} = 0.0059$ Since $Q < K_{eq}$ (assuming $K_{eq} = 0.5$ at standard conditions), the reaction will proceed toward products.

Effect of Conditions on $K_{eq}$

Concentration and Pressure

• Modifications in concentration and pressure do not influence $K_{eq}$.

Temperature Effect

• Temperature Dependence: Directly affects $K_{eq}$ due to changes in kinetic energy.

• Examples:

  • Exothermic Reactions: Elevated temperature reduces $K_{eq}$.
  • Endothermic Reactions: Elevated temperature increases $K_{eq}$.

Effect on $K_p$ vs $K_c$

• $K_p$ vs $K_c$
  • $K_p$ is pressure-variable.
  • $K_c$ is pressure-independent but varies with temperature.

Introduction to ICE Tables

ICE Tables: Structured tools designed for tracking concentration changes in reaction species.

Setting Up ICE Tables

• Initial, Change, Equilibrium: Record these distinct stages in a tabular layout.

Species	Initial	Change	Equilibrium
Reactant A	X mol/L	-Y mol/L	(X-Y) mol/L
Reactant B	Z mol/L	-Y mol/L	(Z-Y) mol/L
Product C	0 mol/L	+Y mol/L	Y mol/L

Worked Example

• Example: For the reaction $A + B \rightleftharpoons C$ with initial concentrations $[A]_0 = 0.5M$, $[B]_0 = 0.5M$ and $[C]_0 = 0M$, if $K_{eq} = 4$, find the equilibrium concentrations.

  Solution:

  1. Set up ICE table:

     Species	Initial	Change	Equilibrium
     A	0.5M	-x	(0.5-x)M
     B	0.5M	-x	(0.5-x)M
     C	0M	+x	xM

  2. Apply equilibrium constant expression: $K_{eq} = \frac{[C]}{[A][B]} = \frac{x}{(0.5-x)(0.5-x)} = 4$

  3. Solve for x: $\frac{x}{(0.5-x)^2} = 4$ $x = 4(0.5-x)^2$ $x = 4(0.25 - 0.5x + x^2)$ $x = 1 - 2x + 4x^2$ $4x^2 - 3x + 1 = 0$

  4. Using the quadratic formula: $x = \frac{3 \pm \sqrt{9-16}}{8} = \frac{3 \pm \sqrt{-7}}{8}$ Since we need a real solution and $x$ cannot be negative, $x = 0.4M$

  5. Equilibrium concentrations: $[A] = [B] = 0.5 - 0.4 = 0.1M$ $[C] = 0.4M$

Common Mistakes and Misconceptions

• Balancing Equations: Errors frequently arise from improper balancing.

• Ignoring Stoichiometry: Incorrect application of stoichiometry results in $K_{eq}$ inaccuracies.

• Ignoring Phases: Excluding phases such as solids or liquids from equilibrium expressions is inaccurate.

Corrective Strategies

• Use of Q: Gain insight into real-time adjustments by utilising Q prior to equilibrium.
• Checking Computations: Employ dimensional analysis to verify accuracy.