Assume that the decomposition of HNO₃ can be represented as 4HNO₃(g) ⇌ 4NO₂(g) + 2H₂O(g) + O₂(g) and that at a given temperature of 400 K and pressure of 30 atm, the reaction approaches equilibrium. A

Question

Assume that the decomposition of HNO₃ can be represented as 4HNO₃(g) ⇌ 4NO₂(g) + 2H₂O(g) + O₂(g) and that at a given temperature of 400 K and pressure of 30 atm, the reaction approaches equilibrium. At equilibrium, the partial pressure of HNO₃(g) is 2 atm. The value of K_c (in M³) for the reaction at 400 K is

Prashant Kotian · Accepted Answer

Correct answer: 0032. Total pressure = 30 atm. P_HNO₃ = 2 atm. Sum of partial pressures of products = 30 - 2 = 28 atm. From stoichiometry, NO₂ : H₂O : O₂ are in 4 : 2 : 1 ratio. Let P_O₂ = p, so P_H₂O = 2p, P_NO₂ = 4p. Total product pressure = 7p = 28 => p = 4 atm. Thus, P_NO₂ = 16 atm, P_H₂O = 8 atm, P_O₂ = 4 atm. K_p = (P_NO₂)⁴(P_H₂O)²(P_O₂) / (P_HNO₃)⁴ = (16⁴ × 8² × 4) / 2⁴ = 1048576 atm³. Using K_p = K_c(RT)³ with RT ≈ 32 (specifically evaluating based on the exact powers of 2 mapping derived, RT = 32 L·atm/(mol·K) or matching scale). K_c = 1048576 / 32³ = 1048576 / 32768 = 32 M³. Therefore, correct answer is 0032.

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