Equilibrium

1. Introduction to Equilibrium

Equilibrium is a state where the rates of the forward and reverse processes are equal, resulting in no net change in the macroscopic properties of the system. It is a dynamic equilibrium, not a static state.

2. Equilibrium in Physical Processes

Equilibrium can be established for physical processes like phase changes and dissolution, but only in a closed system.

Examples of Physical Equilibria:

Solid-Liquid Equilibrium: e.g., Ice ⇌ Water at 273K. The temperature at which this occurs at 1 atm is the normal melting point.
Liquid-Vapour Equilibrium: e.g., Water(l) ⇌ Water(g). The pressure exerted by the vapor at equilibrium is the vapour pressure.
Solid-Vapour Equilibrium: e.g., I₂(s) ⇌ I₂(g). This process is known as sublimation.
Dissolution Equilibrium: In a saturated solution, a dynamic equilibrium exists between the undissolved solid and the dissolved solute. For gases, this is governed by Henry’s Law.

3. Equilibrium in Chemical Processes

Chemical reactions can also reach a state of dynamic equilibrium where the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant. This state can be approached from either direction.

4. Law of Chemical Equilibrium & Equilibrium Constant (K_c)

The Law of Chemical Equilibrium states that for a reversible reaction at a given temperature, a specific ratio of product concentrations to reactant concentrations has a constant value.

For a general reaction: aA + bB ⇌ cC + dD

The Equilibrium Constant (K_c) is expressed as:

K_c = [C]^c[D]^d / [A]^a[B]^b

The value of K_c is constant at a given temperature but depends on how the reaction is balanced.

5. Homogeneous and Heterogeneous Equilibria

Homogeneous Equilibria

All reactants and products are in the same phase. For gases, the equilibrium constant can be expressed in terms of partial pressures (K_p).

The relationship between K_p and K_c is:

K_p = K_c(RT)^Δn

where Δn = (moles of gaseous products) – (moles of gaseous reactants).

Heterogeneous Equilibria

Reactants and products are in more than one phase. The concentrations of pure solids and pure liquids are considered constant and are omitted from the equilibrium constant expression.

For example, for CaCO₃(s) ⇌ CaO(s) + CO₂(g):

K_p = p_CO₂

6. Applications of Equilibrium Constants

Predicting the Extent of a Reaction

If K_c > 10³: Reaction proceeds nearly to completion.
If K_c < 10⁻³: Reaction rarely proceeds.
If 10⁻³ < K_c < 10³: Appreciable concentrations of both reactants and products exist.

Predicting the Direction of a Reaction (Reaction Quotient, Q)

The Reaction Quotient (Q) is calculated like K, but with non-equilibrium concentrations.

If Q < K: Reaction proceeds in the forward direction.
If Q > K: Reaction proceeds in the reverse direction.
If Q = K: The system is at equilibrium.

7. Factors Affecting Equilibria (Le Chatelier’s Principle)

                Le Chatelier’s Principle: When a system at equilibrium is subjected to a change, it will adjust itself to counteract the effect of the change.
            

Concentration: Adding a substance shifts equilibrium to consume it; removing a substance shifts equilibrium to produce it.
Pressure (for gases): Increasing pressure shifts equilibrium to the side with fewer moles of gas. Decreasing pressure shifts it to the side with more moles.
Temperature: Increasing temperature favors the endothermic direction. Decreasing temperature favors the exothermic direction. Temperature is the only factor that changes the value of K.
Catalyst: A catalyst increases the rate of both forward and reverse reactions equally. It helps reach equilibrium faster but does not change the equilibrium position or the value of K.

8. Ionic Equilibrium in Solution

This section deals with equilibria involving ions in solution, focusing on acids, bases, and salts.

Acids and Bases Concepts

Arrhenius: Acids produce H⁺ in water; bases produce OH⁻ in water.
Brønsted-Lowry: Acids are proton (H⁺) donors; bases are proton acceptors. This introduces the idea of conjugate acid-base pairs.
Lewis: Acids are electron-pair acceptors; bases are electron-pair donors. This is the most general definition.

The pH Scale & Ionic Product of Water

Water autoionizes: 2H₂O ⇌ H₃O⁺ + OH⁻. The ionic product of water (K_w) is:

K_w = [H₃O⁺][OH⁻] = 1.0 x 10⁻¹⁴ at 298K

The pH scale is a logarithmic measure of acidity:

pH = -log[H₃O⁺]

At 298K: Acidic (pH < 7), Neutral (pH = 7), Basic (pH > 7).

Weak Acids/Bases and Ionization Constants

Weak electrolytes only partially ionize. The extent of ionization is given by the ionization constant, K_a for acids and K_b for bases. A larger K value means a stronger acid/base.

For a conjugate acid-base pair:

K_a × K_b = K_w

Common Ion Effect

The dissociation of a weak electrolyte is suppressed by the addition of a strong electrolyte containing a common ion. This is an application of Le Chatelier's principle.

Buffer Solutions

A buffer solution resists changes in pH. It is typically a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid).

The pH of an acidic buffer is given by the Henderson-Hasselbalch equation:

pH = pK_a + log([Salt]/[Acid])

Solubility Equilibria

For sparingly soluble salts, an equilibrium exists between the solid salt and its dissolved ions.

The Solubility Product Constant (K_sp) is the equilibrium constant for this process. For a salt M_xX_y:

K_sp = [M^p+]^x[X^q-]^y

A smaller K_sp value indicates lower solubility. The solubility can be further decreased by the common ion effect.