14-1

Chapter 14: Chemical Equilibrium

The Concept of Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a closed system are equal, resulting in constant concentrations of reactants and products over time. This dynamic state is fundamental to many chemical processes.

• Dynamic Equilibrium: Both forward and reverse reactions continue to occur, but there is no net change in the concentrations of reactants and products.

• Equilibrium Position: The relative concentrations of reactants and products at equilibrium can vary depending on the reaction and conditions.

• Reversibility: Equilibrium can be approached from either direction—starting with reactants or products.

• Example: The reaction $2 ext{HI} (g) \rightleftharpoons ext{H}_2 (g) + ext{I}_2 (g)$ reaches equilibrium when the rate of HI decomposition equals the rate of H2 and I2 recombination.

PhET Simulations: Reversible Reactions

Simulations can help visualize how changing conditions (such as temperature) affect equilibrium. For example, increasing temperature can shift the equilibrium position, changing the relative amounts of reactants and products.

• Observation: When temperature increases, the equilibrium may shift to favor either reactants or products, depending on whether the reaction is endothermic or exothermic (Le Châtelier's Principle).

• Example: In a simulation with A (green) and B (red), increasing temperature may result in more B and less A if the forward reaction is endothermic.

The Law of Mass Action and the Equilibrium Constant

The Law of Mass Action states that for a reversible reaction at equilibrium and constant temperature, the ratio of the concentrations of products to reactants (each raised to the power of their coefficients) is constant. This ratio is called the equilibrium constant.

• General Reaction: $aA + bB \rightleftharpoons cC + dD$

• Equilibrium Constant Expression (Kc):

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

• Units: The units of $K_c$ depend on the reaction stoichiometry, but $K$ itself is often treated as unitless in practice.

• Magnitude: Indicates whether products or reactants are favored at equilibrium.

• Constant at Given Temperature: $K$ does not change unless the temperature changes.

• Interpretation: A large $K$ means products are favored; a small $K$ means reactants are favored.

Homogeneous and Heterogeneous Equilibria

Equilibria can involve species in the same phase (homogeneous) or different phases (heterogeneous).

• Homogeneous Equilibrium: All reactants and products are in the same phase (usually all gases or all aqueous solutions).

• Heterogeneous Equilibrium: Reactants and products are in different phases. Concentrations of pure solids and liquids are not included in the equilibrium expression.

• Example: $\text{CaCO}_3 (s) \rightleftharpoons \text{CaO} (s) + \text{CO}_2 (g)$ — only $[\text{CO}_2]$ appears in $K$.

Equilibrium Constants: $K_c$ and $K_p$

For reactions involving gases, equilibrium constants can be expressed in terms of concentrations ($K_c$) or partial pressures ($K_p$).

• Concentration-based ($K_c$): Uses molarity (mol/L).

• Pressure-based ($K_p$): Uses partial pressures (usually in bar or atm).

• Relationship: $K_p$ and $K_c$ are related by the equation:

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

• Where $R = 0.08314$ bar·L·mol−1·K−1, $T$ is temperature in Kelvin, and $\Delta n$ is the change in moles of gas ($\text{moles of gaseous products} - \text{moles of gaseous reactants}$).

• Example: For $2\text{HI} (g) \rightleftharpoons \text{H}_2 (g) + \text{I}_2 (g)$, $\Delta n = (1+1) - 2 = 0$ so $K_p = K_c$.

Writing Equilibrium Expressions

To write an equilibrium expression:

• Place the product concentrations (or partial pressures) in the numerator, each raised to the power of its coefficient.

• Place the reactant concentrations (or partial pressures) in the denominator, each raised to the power of its coefficient.

• Do not include pure solids or liquids in the expression.

• General Form:

$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ $K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$

• Example: For $\text{N}_2 (g) + 3\text{H}_2 (g) \rightleftharpoons 2\text{NH}_3 (g)$:

$K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$

Table: Initial and Equilibrium Concentrations

The following table illustrates how initial partial pressures and equilibrium concentrations are used to calculate the equilibrium constant for the reaction $\text{H}_2 (g) + \text{I}_2 (g) \rightleftharpoons 2\text{HI} (g)$ at 640 K.

Initial Partial Pressures (bar)	Equilibrium Partial Pressures (bar)	Equilibrium Constant $K_p$
H2: 0 I2: 0 HI: 2.000	H2: 0.090 I2: 0.090 HI: 1.820	67
H2: 2.000 I2: 2.000 HI: 0	H2: 0.936 I2: 0.936 HI: 2.128	67
H2: 1.000 I2: 0.760 HI: 0.331	H2: 0.331 I2: 0.331 HI: 1.324	67
H2: 1.000 I2: 1.000 HI: 0	H2: 0.295 I2: 0.295 HI: 1.410	67

Additional info: The table demonstrates that the value of $K_p$ is constant regardless of the initial concentrations, as long as the system reaches equilibrium at the same temperature.

Summary of Key Equilibrium Equations

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

$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ $K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$ $K_p = K_c (RT)^{\Delta n}$

Concept Check: Interpreting Equilibrium Constants

Given hypothetical reactions and their equilibrium constants, you can predict the relative amounts of reactants and products at equilibrium. For example, a large $K$ value means more products are present at equilibrium, while a small $K$ value means more reactants remain.

• Example: If $K = 10^3$, the reaction strongly favors products; if $K = 10^{-3}$, it favors reactants.

Additional info:

• Le Châtelier's Principle: If a system at equilibrium is disturbed (by changing concentration, pressure, or temperature), the system will shift to counteract the disturbance and restore equilibrium.

• Units for $K_c$ and $K_p$ depend on the reaction and are often omitted for simplicity, but should be considered in calculations.