Chemical Equilibrium: Dynamic Nature, Law of Mass Action, and Equilibrium Constants

Chemical Equilibrium

Reversibility of Physical and Chemical Processes

Chemical and physical processes can be classified as reversible or irreversible. Understanding this distinction is essential for studying equilibrium in chemical systems.

• Reversible Processes: These are processes that can proceed in both forward and backward directions under suitable conditions. For example, the melting and freezing of ice.

• Irreversible Processes: These occur in only one direction under normal conditions, such as the frying of an egg.

• Thermodynamics: The spontaneity and reversibility of processes are linked to thermodynamic concepts such as enthalpy change ($\Delta H$) and entropy change ($\Delta S$).

Dynamic Equilibrium

At equilibrium, the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. This state is referred to as dynamic equilibrium because reactions continue to occur in both directions.

• Bridge Analogy: Imagine cars traveling at the same speed in both directions across a bridge. The number of cars on the bridge remains constant, analogous to the constant concentrations at equilibrium.

• Key Point: The system is dynamic, not static; molecules continue to react, but their concentrations remain unchanged.

Representing Chemical Equilibrium

It is crucial to distinguish between what is true and what is not about chemical equilibria. Consider the reaction:

• $\mathrm{N_2O_4(g) \rightleftharpoons 2 NO_2(g)}$

• At equilibrium: $\text{Rate}_f = k_f[\mathrm{N_2O_4}]$ and $\text{Rate}_b = k_b[\mathrm{NO_2}]^2$

• At equilibrium, $\text{Rate}_f = \text{Rate}_b$

Equilibrium Constant ($K_c$)

The equilibrium constant quantifies the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.

• General Expression: For a reaction $aA + bB \rightleftharpoons cC + dD$:

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

• Example: For $\mathrm{N_2(g) + 3 H_2(g) \rightleftharpoons 2 NH_3(g)}$:

$K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

Law of Mass Action

The law of mass action states that the equilibrium constant expression is determined by the stoichiometry of the balanced chemical equation.

• Key Point: Only concentrations of gases and aqueous species are included; pure solids and liquids are omitted.

Relationship Between $K_c$ and $K_p$

For reactions involving gases, equilibrium can be expressed in terms of concentrations ($K_c$) or partial pressures ($K_p$). The ideal gas law relates these quantities:

• $PV = nRT$

• $P = MRT$

• $P/RT = M$

For a general reaction $aA + bB \rightleftharpoons cC + dD$:

$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$

Relating $K_c$ and $K_p$:

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

• $\Delta n$ is the difference in moles of gaseous products and reactants: $\Delta n = (c + d) - (a + b)$

Example Calculation: Converting Between $K_c$ and $K_p$

Given: $2 SO_2(g) + O_2(g) \rightleftharpoons 2 SO_3(g)$, $K_c = 4.08 \times 10^{-3}$ at 1000 K. Calculate $K_p$.

• Use $K_p = K_c (RT)^{\Delta n}$

• Plug in values: $K_p = 4.08 \times 10^{-3} \times (0.0821 \times 1000)^{-1} = 0.335$

Summary Table: Key Equilibrium Concepts

Concept	Definition	Equation
Dynamic Equilibrium	Forward and reverse reaction rates are equal; concentrations remain constant	$\text{Rate}_f = \text{Rate}_b$
Equilibrium Constant ($K_c$)	Ratio of product to reactant concentrations at equilibrium	$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
Equilibrium Constant ($K_p$)	Ratio of product to reactant partial pressures at equilibrium	$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$
Relationship between $K_c$ and $K_p$	Conversion using ideal gas law	$K_p = K_c (RT)^{\Delta n}$

Additional info: Thermodynamic concepts such as enthalpy and entropy are linked to spontaneity and reversibility, and will be covered in later chapters.