Question

Some of the reactions and their equilibrium constants K_c are given. Choose the reaction which proceeds rarely at the given temperature.

• A. 2H₂(g) + O₂(g) ⇌ 2H₂0(g); K_c = 2.4×10⁴⁷ at 500K
• B. H₂(g) + I₂(g) ⇌ 2HI(g); K_c = 57.0 at 700K
• C. H₂(g) + Cl₂(g) ⇌ 2HCI(g); K_c = 4.0×10³¹at 300K
• D. N₂(g) + O₂(g) ⇌ 2N0(g); K_c = 4.8×10³¹ at 298K
• E. H₂(g) + Br₂(g) ⇌ 2HBr(g); K_c = 5.4×10¹⁸ at 300K

Answer 1

The Correct Option is D

The equilibrium constant \( K_c \) indicates the tendency of a reaction to proceed in the forward direction. A very large value of \( K_c \) indicates that the reaction proceeds almost completely in the forward direction, while a very small value of \( K_c \) indicates that the reaction proceeds very rarely in the forward direction.

Given the equilibrium constants for the reactions:

(A) \( K_c = 2.4 \times 10^{47} \) at 500K: This is a very large value, so the reaction proceeds easily.
(B) \( K_c = 57.0 \) at 700K: This is a moderate value, indicating a reaction that proceeds but not extensively.
(C) \( K_c = 4.0 \times 10^{31} \) at 300K: This is also a large value, indicating the reaction proceeds with a high degree.
(D) \( K_c = 4.8 \times 10^{-31} \) at 298K: This is a very small value, indicating the reaction proceeds very rarely.
(E) \( K_c = 5.4 \times 10^{18} \) at 300K: This is a large value, indicating the reaction proceeds easily.

Since option (D) has the smallest equilibrium constant, it represents the reaction that proceeds rarely at the given temperature.

The correct option is (D) : N₂(g) + O₂(g) ⇌ 2N0(g); K_c = 4.8×10³¹ at 298K

Answer 2

To determine which reaction proceeds rarely, we need to examine the equilibrium constant (K_c). A very small value of K_c implies that the reaction favors the reactants and proceeds very little toward the formation of products. Let’s analyze the given K_c values:

• 2H₂ + O₂ ⇌ 2H₂O; K_c = 2.4×10⁴⁷ → Proceeds extensively 
• H₂ + I₂ ⇌ 2HI; K_c = 57.0 → Moderate extent
• H₂ + Cl₂ ⇌ 2HCl; K_c = 4.0×10³¹ → Proceeds extensively
• N₂ + O₂ ⇌ 2NO; K_c = 4.8×10^-31 → Very low, proceeds rarely
• H₂ + Br₂ ⇌ 2HBr; K_c = 5.4×10¹⁸ → Proceeds extensively

Correct Answer: N₂(g) + O₂(g) ⇌ 2NO(g); K_c = 4.8×10^-31 — This reaction proceeds rarely at 298 K.