Chemical Equilibrium - 1 - JEE MCQ

CO(g) + ½ O₂(g)  <====> CO₂(g)
For this reaction, k1 = [CO₂]/[CO][O₂]½
2CO(g) +  O₂(g)  <====> 2CO₂(g)
For this reaction, k₂ = [CO₂]₂/[CO]₂[O₂] = ([CO2]/[CO][O2]½)₂ = (k1)₂
So, k₂ = k₁²
∆G = -RTln keqm
∆G₂/∆G₁ = ln k₁/ln k₁² = 2
∆G₂ = 2∆G₁

Calculation of Degree of Dissociation

Reaction:

CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)

Thermodynamic Data:

• Δ_fG° (in kcal/mol):
  • CO = -32.81
  • CO₂ = -94.26
  • H₂O = -54.64
  • H₂ = 0

Step 1: Calculate Δ_rG°

The change in Gibbs free energy for the reaction is calculated as:

Δ_rG° = Σ Δ_fG° (products) - Σ Δ_fG° (reactants)

Substitute the values:

Δ_rG° = [(-94.26) + (0)] - [(-32.81) + (-54.64)]
Δ_rG° = -94.26 - (-87.45)
Δ_rG° = -94.26 + 87.45 = -6.81 kcal/mol

Convert Δ_rG° to cal/mol:

Δ_rG° = -6.81 × 1000 = -6810 cal/mol

Step 2: Relationship Between Δ_rG° and K

The equilibrium constant (K) is related to Δ_rG° as:

Δ_rG° = -RT ln K

Rearranging for K:

K = e^{-Δ_rG° / RT}

Substitute the values:

• R = 1.987 cal/(mol·K)
• T = 298 K
• Δ_rG° = -6810 cal/mol

K = e^{-(-6810) / (1.987 × 298)}
K = e^{6810 / 591.926}
K = e^11.5 ≈ 9.7 × 10⁴

Step 3: Degree of Dissociation

The equilibrium constant (K) is related to the degree of dissociation (α):

K = α² / (1 - α)²

Given that K is very large (K ≈ 9.7 × 10⁴), this indicates that the degree of dissociation (α) is almost 1, implying nearly complete dissociation.

Final Answer:

The degree of dissociation of CO(g) is approximately 100%.

Correct Option: (a) ≈ 100%

Statement I: The graph shows that as T^-1 increases (temperature decreases), log₁₀K increases, indicating that the equilibrium constant (K) increases with decreasing temperature. This behavior is characteristic of an exothermic reaction.
Statement II: The association of NO₂ to N₂O₄ is indeed exothermic because heat is released during the formation of N₂O₄ from NO₂.

Correct Evaluation:

• Option a: Both Statement I and Statement II are correct, and Statement II is the correct explanation of Statement I. (Correct)
• Option b: Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I. (Incorrect)
• Option c: Statement I is correct, but Statement II is incorrect. (Incorrect)
• Option d: Statement I is incorrect, but Statement II is correct. (Incorrect)

a) Both Statement I and Statement II are correct, and Statement II is the correct explanation of Statement I.