Chemical Equilibrium: Principles, Calculations, and Applications

Module 5.1: What is an Equilibrium?

Chemical Equilibrium

Chemical equilibrium occurs in a reversible chemical reaction when the concentrations of reactants and products remain constant over time. This does not mean the reactions have stopped, but rather that the rates of the forward and reverse reactions are equal.

• Dynamic Equilibrium: Molecules continue to react to form products and reactants, but the overall concentrations do not change.

• Reversibility: The reaction is reversible, meaning both forward and reverse reactions occur.

• Rate Equality: At equilibrium, 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 present at equilibrium, and their concentrations remain constant.

Catalysts and Equilibrium

Catalysts increase the rate at which equilibrium is reached but do not affect the position of equilibrium or the equilibrium constant.

• Effect: Catalysts lower the activation energy for both forward and reverse reactions equally.

• Thermodynamics: Catalysts do not change the thermodynamic properties of the reaction.

Example: Automotive catalytic converters use catalysts to speed up the conversion of exhaust gases into less harmful substances without altering the equilibrium composition.

Module 5.2: K and Q

Standard State

The standard state of a substance is a reference point used to calculate properties under standard conditions.

• Gases and Solids: 1 atm pressure and a specified temperature, usually 25°C.

• Solutions: 1 M concentration.

The Activity of a Chemical

Activity is a measure of the 'effective concentration' of a species in a mixture.

• Pure solids and liquids: Activity = 1

• Gases: Activity = partial pressure / 1 atm

• Ions in solution: Activity = concentration / 1 M

• Standard State: Activity of a chemical at standard state is 1

The Reaction Quotient (Q)

The reaction quotient, Q, is calculated using the same expression as the equilibrium constant, K, but with current (not necessarily equilibrium) concentrations or pressures.

• Expression: For a general reaction $aA + bB \rightleftharpoons cC + dD$, $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Calculating the Equilibrium Constant (K)

At equilibrium, Q becomes K, and the system's free energy change ($\Delta G$) is zero.

• At equilibrium: $Q = K$

• Gibbs Free Energy: $\Delta G = 0$

Rules for Equilibrium Constants

• Reversing the Equation: Invert the equilibrium constant ($K_{reverse} = 1/K_{forward}$)

• Multiplying Coefficients: If the coefficients in the equation are multiplied by a factor n, raise the equilibrium constant to the nth power ($K_{new} = K^n$)

• Combining Equations: When adding two or more chemical equations, multiply their equilibrium constants to obtain the overall equilibrium constant.

Relationship between Q and K

The comparison of Q and K determines the direction in which a reaction will proceed to reach equilibrium.

• If Q < K: The reaction will proceed forward (products will be formed).

• If Q > K: The reaction will proceed in reverse (reactants will be formed).

• If Q = K: The reaction is at equilibrium.

Module 5.3: ICE Tables

Using ICE Tables for Equilibrium Amounts

ICE tables (Initial, Change, Equilibrium) are used to organize and calculate the concentrations or pressures of species in a reaction as it approaches equilibrium.

	A	B	C	D
Initial	[A]	[B]	[C]	[D]
Change	-ax	-bx	+cx	+dx
Equilibrium	[A]-ax	[B]-bx	[C]+cx	[D]+dx

ICE Table Example: Gaseous Reaction

Suppose nitrogen gas reacts with oxygen gas to form nitrogen monoxide. If the equilibrium constant is 0.10, and initial partial pressures of both gases are 0.200 atm, the ICE table helps determine the equilibrium pressure of oxygen after the reaction.

• Set up the ICE table: Assign x to the change in pressure.

• Apply the equilibrium constant expression: Solve for x and calculate the new equilibrium pressures.

ICE Table Example: Dinitrogen Tetraoxide Decomposition

Dinitrogen tetraoxide gas decomposes into nitrogen dioxide. Given $K_c = 0.36$ and an initial concentration of $0.100$ M nitrogen dioxide, use the ICE table to find the equilibrium concentration of dinitrogen tetraoxide.

• Set up the ICE table: Assign x to the change in concentration.

• Apply the equilibrium constant expression: Solve for x and calculate the equilibrium concentrations.

ICE Table Approximations

When the value of x added or subtracted is less than 5% of the initial amount, it can be neglected for simplification.

• Valid when: K is very large or very small, so changes are minimal.

ICE Table Example: Hydrogen Sulfide Decomposition

Hydrogen sulfide gas decomposes into hydrogen gas and sulfur gas. Given $K_c = 1.67 \times 10^{-7}$ and an initial amount of $0.0125$ moles of hydrogen dissolved, use the ICE table to find the equilibrium concentration of hydrogen.

• Set up the ICE table: Assign x to the change in concentration.

• Apply the equilibrium constant expression: Solve for x and calculate the equilibrium concentrations.

Module 5.4: Le Chatelier's Principle

Le Chatelier’s Principle

Le Chatelier’s Principle states that if a chemical system at equilibrium is disturbed, the system will shift in a direction that minimizes the disturbance and restores equilibrium.

• Disturbances: Changes in concentration, pressure, or temperature.

• System Response: The system shifts to counteract the change.

Le Chatelier’s Principle: Changing Concentration

Adding or removing reactants or products causes the equilibrium to shift to restore balance.

• Add Reactant: System shifts right (toward products).

• Add Product: System shifts left (toward reactants).

Example: For $N_2O_4(g) \rightleftharpoons 2NO_2(g)$, adding $NO_2$ shifts the reaction left, favoring $N_2O_4$ formation.

Le Chatelier’s Principle: Changing Pressure

Changing the pressure affects equilibrium involving gases. The system shifts toward the side with fewer moles of gas when pressure increases, and toward more moles when pressure decreases.

• Increase Pressure: Shift toward fewer moles of gas.

• Decrease Pressure: Shift toward more moles of gas.

Le Chatelier’s Principle: Changing Temperature

Temperature changes affect the equilibrium constant and the position of equilibrium, depending on whether the reaction is exothermic or endothermic.

• Exothermic Reaction: Decreasing temperature increases K (products favored); increasing temperature decreases K (reactants favored).

• Endothermic Reaction: Increasing temperature increases K (products favored); decreasing temperature decreases K (reactants favored).

Example: For $N_2O_4(g) + \text{heat} \rightleftharpoons 2NO_2(g)$, adding heat shifts the reaction right, favoring $NO_2$ formation and increasing K.

Van't Hoff Plot

The Van't Hoff plot is a graphical method to analyze the temperature dependence of the equilibrium constant. It is based on the Van't Hoff equation:

• $\ln K = -\frac{\Delta H^\circ}{R} \cdot \frac{1}{T} + \frac{\Delta S^\circ}{R}$

• Plotting $\ln K$ versus $1/T$ yields a straight line, where the slope is $-\Delta H^\circ/R$ and the intercept is $\Delta S^\circ/R$.

Application: Used to determine enthalpy and entropy changes from experimental equilibrium data.

Additional info: Some explanations and equations have been expanded for clarity and completeness based on standard General Chemistry curriculum.