Equilibrium

Equilibrium refers to the state of a system where no observable or measurable change occurs in the system's properties over time.

Examples of Equilibrium Systems

• A balanced see-saw
• A saturated solution of NaCl

Static and Dynamic Equilibrium

Static Equilibrium: This is when a system is in equilibrium and remains at rest or in a fixed state.
Example: A balanced see-saw.

Dynamic Equilibrium: Occurs during a physical or chemical change that is reversible.
Physical changes result in physical equilibrium, while chemical changes result in chemical equilibrium.
A system is in dynamic equilibrium when both the forward and backward reactions occur at the same rate.

Example: $$ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g) $$

Equilibrium in Reversible Reactions

A reversible reaction proceeds in both forward and reverse directions under appropriate conditions.

Example: $$ \text{NH}_4\text{Cl}(s) \rightleftharpoons \text{NH}_3(g) + \text{HCl}(g) $$

At dynamic equilibrium, the rates of the forward and reverse reactions are equal, leading to constant concentrations of reactants and products.

Properties of a System at Equilibrium

1. The system is in a dynamic state with forward and reverse reactions occurring at equal rates.
2. Equilibrium can be reached starting from reactants only or products only.
3. A closed system is required to establish equilibrium.

Factors Affecting the Position of Equilibrium

The position of equilibrium can be influenced by:

1. Temperature
2. Concentration
3. Pressure (in the case of gases)

Changes in these conditions will disturb the system and shift the equilibrium position, as described by Le Chatelier's Principle.

Le Chatelier’s Principle

This principle states: "If a system at equilibrium is disturbed by a change in temperature, pressure, or concentration, the system adjusts to counteract the effect of the disturbance."

Importance in Industry

• Helps determine optimal conditions for chemical processes
• Minimizes undesirable reverse reactions
• Predicts the outcome of changes in reaction conditions

Effect of Temperature

- For an endothermic reaction: Increasing temperature favors the forward reaction.
- For an exothermic reaction: Increasing temperature favors the backward reaction.

Effect of Concentration

• Increasing reactant concentration or decreasing product concentration shifts equilibrium to the right (forward reaction).
• Increasing product concentration or decreasing reactant concentration shifts equilibrium to the left (backward reaction).

Effect of Pressure (for Gaseous Reactions)

Pressure is directly related to the number of moles of gas present.

• If the forward reaction decreases the number of gas molecules, increasing pressure favors the forward reaction.
• If the forward reaction increases the number of gas molecules, increasing pressure favors the backward reaction.

Effect of Catalyst

A catalyst does not alter the position of equilibrium. However, it increases the rate of both the forward and reverse reactions by lowering the activation energy.

As a result, equilibrium is achieved faster in the presence of a catalyst.

The Haber Process

The Haber process is an industrial method for producing ammonia, NH₃, essential for fertilizer production.

Reaction: $$ \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \quad \Delta H = -96 \text{ kJ/mol} $$

Temperature Choice

The forward reaction is exothermic, so lower temperatures favor ammonia formation. However, extremely low temperatures slow the reaction. A compromise temperature of around 500°C gives a reasonable yield in a short time.

Pressure Choice

The forward reaction reduces the number of gas molecules, so high pressure favors ammonia formation. Industrial processes use around 25 atm.

Catalyst Choice

Finely divided iron is used as a catalyst. It speeds up the reaction and allows equilibrium to be reached faster. The catalyst is used in pellet form to increase surface area.

Equilibrium Constant and Law of Mass Action

Law of Mass Action

At constant temperature, the rate of a chemical reaction is proportional to the product of the active masses (concentrations) of the reactants, each raised to the power of their coefficients in the balanced equation.

For the reaction: $$ aA + bB \rightarrow \text{Products} $$

$$ r \propto [A]^a[B]^b $$
$$ r = k[A]^a[B]^b $$

where \( k \) is the rate constant, and the square brackets indicate concentration in mol·dm^-3.

Equilibrium Constant Expressions

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

The equilibrium constant in terms of concentration is: $$ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} $$

Equilibrium Constant for Gaseous Reactions

For gaseous reactions: $$ aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g) $$

The equilibrium constant in terms of partial pressure is: $$ K_p = \frac{P_C^c \cdot P_D^d}{P_A^a \cdot P_B^b} $$

Note:

• Solids are excluded from the equilibrium constant expressions.
• If \( K_c \) or \( K_p > 1 \), products are favored at equilibrium.
• If \( K_c \) or \( K_p < 1 \), reactants are favored.
• If \( K_c \) or \( K_p = 1 \), neither side is favored — the system is perfectly balanced.