Chemical Equilibrium

Equilibrium is a state of the system in which there is no observable change in properties with time. Equilibrium can be classified into two types:
1. Physical equilibrium 2. Chemical equilibriium

Physical Equilibrium

The equilibrium set up in physical process such as the melting of ice, evaporation of water, etc. is called physical equilibrium. It is of four types:

1. Solid-liquid equilibrium: Solid is in equilibrium with liquid of the same substance at its melting point.
   Ice ⇌ Water at 273K and 1 atm

2. Liquid-gas equilibrium: Liquid is in equilibrium with gas.
   Water ⇌ Vapour

3. Solid-solution equilibrium: Solid is in equilibrium with the solution.
   Sugar (solid) ⇌ Sugar (solution)

4. Solid-gas equilibrium: Solid is in equilibrium with gas.
   Iodine crystal ⇌ Iodine vapour

Chemical Equilibrium

The equilibrium set up in a chemical process is called chemical equilibrium.
H₂ + I₂ ⇌ 2HI
CaCO₃ ⇌ CaO + CO₂

Reversible and irreversible reactions

The reaction in which the product can give back the reactant under suitable condition is called a reversible reaction.
H₂ + I₂ ⇌ 2HI
N₂ + 3H₂ ⇌ 2NH₃

The reaction in which the product can’t be converted back into reactant is called irreversible reaction.
Zn + H₂SO₄(aq) → ZnSO₄ + H₂
AgNO₃ + NaCl → AgCl + NaNO₃

Differences between reversible and irreversible reaction

Homogeneous and heterogeneous equilibrium

When the reactant and product are present in same phase, the equilibrium is homogeneous.
N₂(g) + O₂(g) ⇌ 2NO(g)
H₂(g) + Cl₂(g) ⇌ 2HCl(g)

When the reactant and product are present in a different phase, the equilibrium is heterogeneous.
CaCO₃(s) ⇌ CaO(s) + CO₂(g)

Dynamic nature of chemical equilibrium

Let us consider a general reaction in a closed vessel
A + B ⇌ C + D

In the beginning, the concentration of reactants A and B are maximun whereas the concentration of C and D are zero. Therefore the rate of forward reaction is high. As the reaction proceeds, the concentration of A and B goes on decreasing and the concenration of C and D goes on increasing. Here, the rate of forward reaction decreases and the rate of backward reaction increases. Finally, a stage will be reached in which the rate of forward reaction will be equal to the rate of backward reaction. At this stage, the concentration of A, B, C and D becomes equal. This is called the dynamic nature of chemical equilibrium.
Chemical equilibrium may be defined as the state of reversible reaction at which the concentration of reactant and product doesn’t change with time.

characteristics of chemical equilibrium

• Chemical equilibrium is dynamic in nature i.e. rate of forward reaction is equal to the rate of backward reaction.
• The concentration of reactant and product remains constant.
• Chemical equilibrium is possible only in a closed vessel.
• Catalyst helps to attain equilibrium fast but has no effect on the rate of reaction.
• Chemical equilibrium is characterized by a constant called equilibrium constant (k).

Law of mass action

It states that “The rate at which the substance reacts is directly proportional to the active mass and the rate of chemical reaction is directly proportional to the product of the active mass of reactants”.
Active mass means the molar concentration of reactant expressed in mol/lit and it is written by enclosing it with a square bracket.

Let us consider a general reversible reaction
aA + bB ⇌ cC + dD

According to the law of mass action,
Rate of forward reaction (R_f) α [A]^a [B]^b
R_f = K_f [A]^a [B]^b
where K_f is the rate constant for the forward reaction

Rate of backward reaction (R_b) α [C]^c [D]^d
R_b = K_b [C]^c [D]^d

where K_b is the rate constant for the backward reaction. [A],[B],[C] and [D] are the molar concentration of the species A, B, C and D respectively.

At equilibrium,
Rate of forward reaction(R_f) = Rate of backward reaction(R_b)

Kf\ [A]^{a}[B]^{b} = Kb\ [C]^{c}[D]^{d} \\ \frac{Kf}{Kb} = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}} \\ Kc = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}

where Kc is the equilibrium constant in terms of molar concentration.

The equilibrium constant is defined as the ratio of rate constant of the forward reaction to the rate constant of the backward reaction or the ratio of the product of the active mass of product to the product of the active mass of reactant in which each active mass is raised to the power of its stoichiometric coefficient of the balanced chemical reaction.
Equivalent constant in terms of partial pressure (Kp).

From ideal gas equation,
PV = nRT
P = (n/V) RT

\begin {align*} {}Molar\ concentration\ (C) &= \frac{number\ of\ moles\ (n)}{Volume\ in\ litre\ (V)} \\ P &= CRT\\ so,\ P\ &\alpha\ C \\ Hence,\ Kp &= \frac{[Pc]^{c}\ [Pd]^{d}}{[Pa]^{a}\ [Pb]^{b}} \end {align*}

where Pa, Pb, Pc and Pd are the partial pressure of A, B, C and D respectively.

Characteristics of equilibrium constant

• It is fixed for a particular reaction at a particular temperature.
• It is independent of the concentration of chemical species.
• It is independent of the use of catalyst.
• It depends upon temperature.

Relation between Kc and Kp

For a given reversible reaction,
aA + bB ⇌ cC + dD

From the law of mass action,
Equilibrium constant in terms of molar concentration

Kc = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}[/latex]

Equilibrium constant in terms of partial pressure

Kp = \frac{[Pc]^{c}\ [Pd]^{d}}{[Pa]^{a}\ [Pb]^{b}}

From ideal gas equation,
PV = nRT
P = (n/V) RT
P = CRT where C is molar concentration
Pa =CaRT, Pb = CbRT, Pc = CcRT, Pd = DdRT

Kp = \frac{[CcRT]^{c}\ [CdRT]^{d}}{[CaRT]^{a}\ [CbRT]^{b}}\\ Kp = \frac{[Cc]^{c}\ [RT]^{c}\ [Cd]^{d}\ [RT]^{d}}{[Ca]^{a}\ [RT]^{a}\ [Cb]^{b}\ [RT]^{b}}\\ Kp = \frac{[C]^{c}\ [D]^{d}}{[A]^{a}\ [B]^{b}}\ [RT]^{(c+d)-(a+b)}\\ Kp = Kc\ [RT]^{(c+d)-(a+b)}\\ Kp = Kc\ [RT]^{\Delta n}

where Δn= number moles of gaseous product – number of moles of gaseous reactant.

For a reaction, N₂ + 3H₂ ⇌ 2NH₃
Δn = 2 – (1+3) = -2
Kp = Kc [RT]^-2

• If the number of moles of gaseous reactant and product is the same, i.e. Δn = 0, then Kp = Kc
  H2 + I2 ⇌ 2HI

• If the number of moles of gaseous reactant is greater than gaseous product, Δn < 0, Kp < Kc
  2SO₂ + O₂ ⇌ 2SO₃

• If the number of moles of gaseous reactant is less than gaseous product, Δn > 0, Kp > Kc
  PCl₅ ⇌ PCl₃ + Cl₂

Solved numerical

1. Write down the relationship between Kp and Kc for the reaction: N₂ + O₂ ⇌ 2NO
solution:

Δn = 2-2 = 0
K_p = K_c[RT]^Δn
K_p = K_c[RT]⁰
K_p = K_c

2. What will be the expression for Kc in the following reaction?
i. 2SO₂ + O₂ ⇌ 2SO₃

Kc = \frac{[SO_{3}]^{2}}{[SO_{2}]^{3}\ [O_{2}]}

ii. CaCO₃ ⇌ CaO + CO₂
Kc = [CO₂]

Le-Chatelier’s principle

It states that “When a system in equilibrium is subjected to a change in temperature, pressure, volume and concentration, the equilibrium shifts in such a direction to neutralize the effect of the change”.

Applications in chemical equilibria

1. Effect of change in temperature: When the temperature is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the direction where heat is absorbed. That is an increase in temperature favours the endothermic side of the reaction.
When the temperature is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the direction where heat is released. That is a decrease in temperature favours the exothermic side of the reaction.

2. Effect of change in pressure: When pressure is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the direction where volume is decreased.
When pressure is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the direction where volume is increased.

3. Effect of change in concentration: When concentration is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction.
When concentration is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

Application to physical equilibria

1. In physical equilibrium
Melting of ice: Ice + Heat ⇌ Water

• Effect of change in temperature: This reaction is endothermic in forward direction. When the temperature is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction. When the temperature is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

• Effect of change in pressure: For a given mass, ice has more volume than water. When pressure is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction. When pressure is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

2. In chemical equilibrium
N₂ + 3H₂ ⇌ 2NH₃ + 22kcal
or, N₂ + 3H₂ ⇌ 2NH₃, ΔH = – 22kcal

i. Effect of change in temperature: This reaction is exothermic in forward direction. When the temperature is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the forward direction. When the temperature is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

ii. Effect of change in pressure: The volume of the reactant is greater than the product. When pressure is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction. When pressure is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards backward direction.

iii. Effect of change in concentration: When the concentration of reactants is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction.
When the concentration of reactants is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

Formation of NH₃ is favored by

i. Low temperature
ii. High pressure
iii. High concentration of N₂ and H₂

N₂ + O₂ + heat ⇌ 2NO

i. Effect of change in temperature: This reaction is endothermic in forward direction. When the temperature is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction. When the temperature is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

ii. Effect of change in pressure: Since the volume of reactant is equal to the volume of product, there is no effect in the change in pressure.

iii. Effect of change in concentration: When the concentration of reactants is increased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards forward direction.
When the concentration of reactants is decreased, equilibrium is disturbed. To neutralize the effect of change, it is shifted towards the backward direction.

Solved Numerical

Predict the favourable condition for forward reaction in following reaction.

a. 4NH₃ + 5O₂ ⇌ 4NO + 6H₂O + Heat
Ans: The favourable conditions are:
i. Low temperature
ii. Low pressure
iii. High concentration

b. SO₂ + O₂ ⇌ SO₃ + Heat
Ans: The favourable conditions are:
i. Low temperature
ii. High pressure
iii. High concentration

Some Important Questions

1. State law of mass action and Le-Chatlier’s principle.
2. Derive the relationship between Kp and Kc.
3. Application of Le-Chatlier’s principle in Haber’s and Contact process.
4. What will be the expression for Kc in the following reaction?
   a. 2SO₂ + O₂ ⇌ 2SO₃
   b. CaCO₃ ⇌ CaO + CO₂
   c. PCl₅ ⇌ PCl₃ + Cl₂
   d. N₂+ O₂ ⇌ 2NO
   e. H₂ + I₂ ⇌ 2HI
5. Write down the relationship between Kp and Kc for the reaction.
   a. N₂ + O₂ ⇌ 2NO
   b. PCl₅ ⇌ PCl₃ + Cl₂
   c. N₂ + 3H₂ ⇌ 2NH₃
   d. 2SO₂ + O₂ ⇌ 3SO₂
6. Predict the favourable condition for the forward reaction in the following:
   a. 4NH₃ + 5O₂ ⇌ 4NO + 6H₂O + Heat
   b. PCl₅ + Heat ⇌ PCl₃ + Cl₂
   c. SO₂ + O₂ ⇌ SO₃ + Heat