Chemical Equilibrium Notes

Chemical Reactions

Based on the direction of their occurrence, chemical reactions are of two types:

Irreversible Reactions:

Reactants are converted into products, but products cannot be converted back into reactants.
These reactions are unidirectional (Reactants → Products).
Represented by a single arrow mark (→).
Reactions proceed almost to completion, where reactants are almost completely converted into products.
Examples:
- Precipitation reactions
- Ionic reactions
- Explosive reactions
- Strong acid-strong base neutralization reactions
- Combustion reactions
Examples with chemical equations:
- 2KClO3(s) → 2KCl(s) + 3O2(g)
- NH4NO2(s) → N2(g) + 2H2O(g)
- C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H_2O(g)
- 2Mg(s) + O_2(g) → 2MgO(s)
- HCl(aq) + NaOH(aq) → NaCl(aq) + H_2O(l)
- H2(g) + F2(g) → 2HF(g)
- H2(g) + Cl2(g) → 2HCl(g)

Reversible Reactions:

Both forward and backward reactions occur simultaneously under given experimental conditions.
Forward reaction: Reactants giving rise to products.
Reverse (or backward) reaction: Products giving rise to reactants.
Represented by a pair of half-headed arrows pointing in opposite directions (⇌).
Reactants \rightleftharpoons Products
Do not go to completion.
Most reversible reactions are carried out in closed vessels.
Examples with chemical equations:
- H2(g) + I2(g) \rightleftharpoons 2HI(g)
- PCl5(g) \rightleftharpoons PCl3(g) + Cl_2(g)
- 2NO2(g) \rightleftharpoons N2O_4(g)
- N2(g) + O2(g) \rightleftharpoons 2NO(g)
- 2SO2(g) + O2(g) \rightleftharpoons 2SO_3(g)
- CaCO3(s) \rightleftharpoons CaO(s) + CO2(g)
- CH3COOH(l) + C2H5OH(l) \rightleftharpoons CH3COOC2H5(l) + H_2O(l)

Equilibrium State:

The state at which the rate of the forward reaction equals the rate of the reverse reaction in a reversible reaction.
Chemical equilibrium is considered a dynamic equilibrium because both forward and reverse reactions continue to take place simultaneously.
Equilibrium is established in:
- A reversible reaction
- A closed vessel
In the beginning of a reversible reaction, the rate of the forward reaction is higher due to a higher concentration of reactants.
As time progresses, the rate of the forward reaction decreases as the concentration of reactants decreases.
Initially, the rate of the backward reaction is zero because the concentration of products is zero.
As time progresses, the rate of the backward reaction increases as the concentration of products increases.
At equilibrium, the rate of the forward reaction equals the rate of the backward reaction, leading to no further change in the concentrations of reactants or products.
At equilibrium, the concentrations of reactants and products may not be equal but remain constant.

Characteristics of Chemical Equilibrium:

The rate of the forward reaction equals the rate of the reverse reaction.
The concentrations of reactants and products remain unchanged with time.
Observable properties (pressure, concentration, density, color) also remain unchanged with time.
Attainment of chemical equilibrium can be recognized by the constancy in macroscopic properties.
Equilibrium is dynamic in nature; both forward and reverse reactions occur simultaneously at equal rates.
A catalyst does not alter the state of equilibrium or composition but speeds up the attainment of equilibrium.
Chemical equilibrium can be established from either side of the reversible reaction.
Chemical equilibrium can be homogeneous or heterogeneous and also ionic or molecular.
Factors such as pressure, concentration, temperature, and presence of inert gas influence the position of equilibrium.
At equilibrium, the change in Gibbs free energy (\Delta G) is zero (\Delta G = 0).
At equilibrium, entropy (\Delta S) is maximum.
Equilibrium does not indicate how long it takes for a reaction to attain equilibrium.
Once equilibrium is reached, it continues forever until conditions are altered.
At equilibrium, the concentration of reactants may be equal to, less than, or more than the concentration of products.

Law of Mass Action:

Stated by C.M. Guldberg and P. Wage in 1863.
Gives the relation between the rate of a reaction and the concentration of the reactants.
The rate of a chemical reaction at a given temperature and instant is proportional to the product of the active masses of the reactants.
Applicable to all reactions (reversible and irreversible) in the gas or liquid phase.
For a reaction aA + bB \rightleftharpoons cC + dD, the equilibrium constant k_c is given by:
- kc = \frac{[C]^c [D]^d}{[A]^a [B]^b} = \frac{kf}{k_b}
  - Where:
    - k_f = forward reaction rate constant
    - k_b = backward reaction rate constant
Equilibrium constant k_c = (product of the concentration of products) / (product of the concentration of reactants).
Partial pressure of a gas = (mole fraction of gas) × (total pressure).
kp = \frac{pC^c pD^d}{pA^a pB^b} = \frac{kf}{k_b}
- Where:
  - k_p = equilibrium constant in terms of partial pressure
  - k_c = equilibrium constant in terms of molar concentration
Active mass = (number of moles) / (volume in liters). Considered for gas or liquid.
The active mass of a solid is unity, regardless of its mass.

Types of Chemical Equilibrium:

Based on the physical states of substances:

Homogeneous Equilibrium:

All reactants and products are present in the same physical state (same phase).
Examples:
- 2SO2(g) + O2(g) \rightleftharpoons 2SO_3(g)
- N2(g) + 3H2(g) \rightleftharpoons 2NH_3(g)
- CH3COOC2H5(l) + H2O(l) \rightleftharpoons CH3COOH(l) + C2H_5OH(l)
- CH3COOH(l) \rightleftharpoons CH3COO^-(l) + H^+(l)

Heterogeneous Equilibrium:

Reactants and products are in different physical states (different phases).
Examples:
- CaCO3(s) \rightleftharpoons CaO(s) + CO2(g)
- NH4HS(s) \rightleftharpoons NH3(g) + H_2S(g)
- Fe(s) + 4H2O(g) \rightleftharpoons Fe3O4(s) + 4H2(g)

Relationship Between Kp and Kc:

kp = kc (RT)^{\Delta n}
- Where:
  - R = gas constant
  - T = absolute temperature
  - \Delta n = change in the number of moles = nP - nR (moles of gaseous products – moles of gaseous reactants)
Case (i): If nP = nR, then \Delta n = 0, and kp = kc. Example: H2 + I2 \rightleftharpoons 2HI
Case (ii): If nP > nR, then \Delta n > 0, and kp > kc. Example: PCl5 \rightleftharpoons PCl3 + Cl_2
Case (iii): If nP < nR, then \Delta n < 0, and kp < kc. Example: N2 + 3H2 \rightleftharpoons 2NH_3

Units of the Equilibrium Constant:

Unit of k_c = (mol \cdot lit^{-1})^{\Delta n}
Unit of k_p = (atmosphere)^{\Delta n}

Examples for Writing kc and kp Expressions and Their Units:

I) H2(g) + I2(g) \rightleftharpoons 2HI(g)
- kc = \frac{[HI]^2}{[H2][I2]}, No unit for kc
- kp = \frac{p{HI}^2}{p{H2} \times p{I2}}, No unit for k_p
II) 2SO2(g) + O2(g) \rightleftharpoons 2SO_3(g)
- kc = \frac{[SO3]^2}{[SO2]^2[O2]}, k_c = lit \cdot mol^{-1}
- kp = \frac{p{SO3}^2}{p{SO2}^2 p{O2}}, kp = atm^{-1}
III) CaCO3(s) \rightleftharpoons CaO(s) + CO2(g)
- kc = [CO2], k_c = mol \cdot lit^{-1}
- kp = p{CO2}, kp = atm

Characteristics of Equilibrium Constant (kp or kc):

The value of k depends on the nature of the reaction.
The value of k will be constant for a given reaction at a given temperature.
The value of k depends on the temperature of the reaction.
The value of k is independent of concentration and pressure.
The value of k is independent of the presence of a catalyst and the presence of inert gas.
The value of k depends on the stoichiometry of the equation.
The value of k depends on the mode of writing the equilibrium reaction.

Le Chatelier's Principle:

The effect of change of pressure, concentration, and temperature on equilibrium was studied by Henry Lewis Le Chatelier in 1885 and F. Braun.
If a system at equilibrium is subjected to a stress, the system shifts the equilibrium to reduce or nullify the stress.

Effect of Concentration:

An increase in the concentration of reactants or a decrease in the concentration of products favors the shift of equilibrium towards the products side, increasing the rate of the forward reaction.
An increase in the concentration of products or a decrease in the concentration of reactants favors the shift of equilibrium towards the reactants side, increasing the rate of the backward reaction.

Effect of Pressure:

Pressure has no effect on equilibrium if \Delta v or \Delta n = 0, where np = nr. Example: H2(g) + I2(g) \rightleftharpoons 2HI(g)
Pressure has an effect on equilibrium if \Delta v \neq 0 or \Delta n \neq 0, where np \neq nr. When pressure increases, equilibrium shifts to decrease volume or less mole number, and vice versa. Example: N2(g) + 3H2(g) \rightleftharpoons 2NH_3(g)
Pressure change shows no marked effect on equilibrium reactions in the solution or solid phase.

Effect of Temperature:

Increasing the temperature of the equilibrium system favors endothermic reactions, and decreasing the temperature favors exothermic reactions.

Effect of Catalyst:

A catalyst has no net effect on equilibrium. It helps the system to attain equilibrium faster by increasing both the forward and backward reaction rates equally.

Examples:

Synthesis of Ammonia by Haber's Process:

N2(g) + 3H2(g) \rightleftharpoons 2NH_3(g) + \text{heat}, \Delta H = -92.0 \text{ kJ}
Favorable conditions for high yield of NH_3:
- High pressure: 200 atm
- Low temperature: 773 K
- Catalyst: Fe
- Promoter: small amount of molybdenum or Al2O3 and K_2O

Manufacture of H2SO4 by the Contact Process:

2SO2(g) + O2(g) \rightleftharpoons 2SO_3(g) + \text{Heat}; \Delta H = -189 \text{ kJ}
Favorable conditions for higher yield of SO_3:
- High pressure: 1.5 – 1.7 atm
- Low temperature: 673 K
- Catalyst: V2O5 or platinized asbestos

Formation of NO:

N2(g) + O2(g) \rightleftharpoons 2NO(g) - \text{heat}
- High temperature
- No effect of pressure

Melting of Ice:

H2O(s) + \text{heat} \rightleftharpoons H2O(l)
- High temperature
- High pressure

Multiple Choice Questions and Answers

The provided answers are included in the original document and thus not listed again here