Chemical Equilibrium and Le Châtelier’s Principle: Concepts, Calculations, and Applications

Chemical Equilibrium

Introduction to Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. This state is dynamic, meaning reactions continue to occur, but there is no net change in concentrations.

• Dynamic Equilibrium: Both forward and reverse reactions proceed at equal rates.

• Equilibrium Constant (K): Quantifies the ratio of product to reactant concentrations at equilibrium.

Equilibrium Constant Expressions

The equilibrium constant expression depends on the balanced chemical equation. For a general reaction:

$aA + bB \rightleftharpoons cC + dD$

The equilibrium constant in terms of concentration ($K_c$) is:

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

• Only aqueous and gaseous species are included; pure solids and liquids are omitted.

Practice Problem: Calculating $K_c$

Given: 1 mol X and 2 mol Y in a 4.0 L container. The reaction is:

$\text{X (aq)} + 2\text{Y (aq)} \rightleftharpoons 3\text{Z (aq)}$

• Calculate initial concentrations: $[X]_0 = \frac{1}{4.0} = 0.25\ \text{M}$, $[Y]_0 = \frac{2}{4.0} = 0.50\ \text{M}$

• At equilibrium, use given or calculated concentrations to find $K_c$:

$K_c = \frac{[Z]^3}{[X][Y]^2}$

Additional info: Insert equilibrium concentrations as provided in the full problem statement.

Equilibrium Constant in Terms of Pressure ($K_p$)

For reactions involving gases, the equilibrium constant can also be expressed in terms of partial pressures ($K_p$):

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

• $R$ = 0.08206 L·atm/(mol·K)

• $\Delta n$ = moles of gaseous products - moles of gaseous reactants

Example: For $2\text{CO (g)} \rightleftharpoons \text{C (s)} + \text{CO}_2 (g)$, $\Delta n = 1 - 2 = -1$

Practice Problem: $K_p$ Calculation

Given $K_c$ at 800 K and the reaction above, calculate $K_p$ using the formula above.

Le Châtelier’s Principle

Definition and Application

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.

• Concentration: Adding/removing reactants or products shifts equilibrium to consume/produce the changed species.

• Pressure/Volume: For gaseous systems, increasing pressure (decreasing volume) shifts equilibrium toward the side with fewer moles of gas.

• Temperature: Increasing temperature favors the endothermic direction; decreasing favors exothermic.

Examples and Applications

• Adding CO2 to CaCO3 ⇌ CaO + CO2: Adding CO2 shifts equilibrium left, increasing CaCO3 (solid).

• Doubling Concentrations: If all concentrations are doubled and the system remains at equilibrium, the reaction likely involves a solid product (e.g., $A(aq) + B(aq) \rightleftharpoons AB(s)$), since solids are not included in $K_c$ expressions.

Practice Problem: Industrial Reduction of Nickel(II) Oxide

Given: $\text{NiO (s)} + \text{CO (g)} \rightleftharpoons \text{Ni (s)} + \text{CO}_2 (g)$, $K = 6.0 \times 10^2$ at 1000 K. If $P_{CO} = 0.640$ atm and $P_{CO_2} = 0.803$ atm, will NiO be reduced?

• Calculate reaction quotient $Q = \frac{P_{CO_2}}{P_{CO}}$ and compare to $K$.

• If $Q < K$, reaction proceeds forward (NiO is reduced).

Solubility Guidelines

Solubility Rules for Common Ionic Compounds

Solubility rules help predict whether an ionic compound will dissolve in water. The following table summarizes key rules and exceptions:

Soluble Ionic Compounds	Important Exceptions
NO3-, CH3COO-	None
Cl-, Br-, I-	Compounds of Ag+, Hg22+, Pb2+
SO42-	Compounds of Sr2+, Ba2+, Hg22+, Pb2+

Important Exceptions
S2-	NH4+, alkali metal cations, Ca2+, Sr2+, Ba2+
CO32-, PO43-	NH4+, alkali metal cations
OH-	Alkali metal cations, NH4+, Ca2+, Sr2+, Ba2+

Equilibrium Shifts: Visualizing Changes

Concentration Changes

For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, adding more $H_2$ increases the rate of the forward reaction, temporarily increasing $NH_3$ production until a new equilibrium is established.

• Equilibrium Expression: $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

• At the instant $H_2$ is added, the forward rate > reverse rate.

• As the system re-equilibrates, $[N_2]$ decreases and $[NH_3]$ increases.

Key Point: The value of $K_c$ does not change with concentration changes; only temperature changes affect $K_c$.

Pressure and Volume Changes

• Decreasing volume (increasing pressure) shifts equilibrium toward the side with fewer moles of gas.

• For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, decreasing volume favors $NH_3$ formation (4 mol gas → 2 mol gas).

Temperature Changes

• For endothermic reactions ($\Delta H > 0$), increasing temperature shifts equilibrium right (products favored).

• For exothermic reactions ($\Delta H < 0$), increasing temperature shifts equilibrium left (reactants favored).

Summary Table: Effects of Disturbances on Equilibrium

Disturbance	System Response
Add reactant	Shifts toward products
Remove reactant	Shifts toward reactants
Increase pressure (decrease volume)	Shifts toward fewer moles of gas
Increase temperature (endothermic)	Shifts toward products
Increase temperature (exothermic)	Shifts toward reactants

Key Terms and Concepts

• Equilibrium Constant ($K_c$, $K_p$): Quantifies the ratio of products to reactants at equilibrium.

• Le Châtelier’s Principle: Predicts the direction of shift in response to disturbances.

• Solubility Rules: Guidelines for predicting ionic compound solubility in water.

• Reaction Quotient ($Q$): Used to predict the direction a reaction will proceed to reach equilibrium.

Additional info: For full problem solutions, insert provided equilibrium concentrations or pressures as needed. These notes provide the conceptual framework and formulas required for solving typical equilibrium and Le Châtelier’s Principle problems in General Chemistry.