Chemical Equilibrium: The Equilibrium Constant and Its Applications

Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical system are equal, resulting in constant concentrations of reactants and products. The equation for a reversible reaction is written with a double arrow (↔), indicating that both directions are possible.

• Dynamic equilibrium: Both forward and reverse reactions continue to occur, but there is no net change in concentrations.

• Equilibrium position: The relative concentrations of reactants and products at equilibrium.

• Example: The synthesis of ammonia via the Haber process: $\mathrm{N_2(g) + 3H_2(g) \leftrightarrow 2NH_3(g)}$

The Equilibrium Constant Expression

The equilibrium constant, K, quantifies the ratio of product and reactant concentrations at equilibrium for a given reaction. It is derived from the law of mass action.

• Generalized reaction: $aA + bB \leftrightarrow cC + dD$

• Equilibrium constant expression: $K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• Concentrations are expressed in molarity (M).

• Each concentration is raised to the power of its coefficient in the balanced equation.

Equilibrium Constants for Gaseous Reactions

For reactions involving gases, equilibrium constants can be expressed in terms of partial pressures (Kp) as well as concentrations (Kc).

• Ideal gas law: $PV = nRT$

• Relationship between Kp and Kc: $K_p = K_c (RT)^{\Delta n}$

• $\Delta n$ is the difference in moles of gaseous products and reactants: $\Delta n = \text{moles of products} - \text{moles of reactants}$

• Example: For the Haber process, $\Delta n = 2 - 4 = -2$

Stoichiometry and Equilibrium

The stoichiometry of a reaction determines the relationship between the rates of disappearance of reactants and appearance of products.

• For $\mathrm{N_2(g) + 3H_2(g) \leftrightarrow 2NH_3(g)}$, hydrogen disappears three times faster than nitrogen due to the coefficients.

• Rate relationship: $\text{Rate of disappearance of H}_2 = 3 \times \text{Rate of disappearance of N}_2$

Achieving Equilibrium

Regardless of whether a reaction starts with only reactants or only products, the system will reach the same equilibrium state, determined by the equilibrium constant and stoichiometry.

• The relative amounts of reactants and products at equilibrium depend on the initial concentrations and the equilibrium constant.

• Example: The concentration of $\mathrm{N_2O_4}$ may decrease or increase to reach equilibrium, depending on the starting conditions.

Evaluating the Equilibrium Constant (Kc)

To determine the equilibrium constant, measure the concentrations of all species at equilibrium and substitute them into the equilibrium expression.

• Initial and equilibrium concentrations are often tabulated for clarity.

• The ratio of product to reactant concentrations remains constant at equilibrium, regardless of initial concentrations.

Species	Initial Concentration (M)	Equilibrium Concentration (M)
Reactant A	Varies	Measured at equilibrium
Reactant B	Varies	Measured at equilibrium
Product C	Varies	Measured at equilibrium
Product D	Varies	Measured at equilibrium
Additional info: Table structure inferred from context; actual values depend on specific reaction studied.

Writing Equilibrium-Constant Expressions

To write an equilibrium-constant expression, use the law of mass action: place product concentrations in the numerator and reactant concentrations in the denominator, each raised to the power of their coefficients.

• Example: For $\mathrm{2NO_2(g) \leftrightarrow N_2O_4(g)}$, $K = \frac{[N_2O_4]}{[NO_2]^2}$

• Practice: Write the equilibrium expression for $\mathrm{H_2(g) + I_2(g) \leftrightarrow 2HI(g)}$

• Answer: $K = \frac{[HI]^2}{[H_2][I_2]}$

Converting Between Kc and Kp

For gaseous reactions, the equilibrium constant can be converted between concentration and pressure units using the ideal gas law and the change in moles of gas.

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

• Where $R$ is the ideal gas constant (0.08206 L-atm/mol-K), $T$ is temperature in Kelvin, and $\Delta n$ is the difference in moles of gaseous products and reactants.

• Example: For the Haber process at 573 K, $\Delta n = -2$

Summary Table: Kc vs. Kp

Type	Expression	Units
Kc	$\frac{[C]^c [D]^d}{[A]^a [B]^b}$	Molarity (M)
Kp	$\frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$	Pressure (atm)
Conversion	$K_p = K_c (RT)^{\Delta n}$	Depends on $\Delta n$

Practice and Application

• Write equilibrium expressions for given reactions.

• Calculate Kc or Kp using measured equilibrium concentrations or partial pressures.

• Convert between Kc and Kp for gaseous reactions.

Additional info: Academic context and table structures were inferred to ensure completeness and clarity. The included image is the textbook cover, directly relevant as it identifies the source and context for the study notes.