Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide as CO + 2H₂ ⇌ CH₃OH. CO and H₂ are charged to a reactor and the reaction proceeds to equilibrium at 453 K and 2 atm. The reaction equilibrium constant, which depends only on the temperature, is 1.68 at the reaction conditions. The mole fraction of H₂ in the product is 0.4. Assuming ideal gas behaviour, the mole fraction of methanol in the product is ____ (rounded off to 2 decimal places).

Question

Accepted Answer

The correct answer is 0.28 to 0.34. GATE 2025 official key: 0.28 to 0.34. K_p = y_MeOH/(y_CO·y_H2²·P²) ⇒ 1.68 = y_MeOH/(y_CO×0.16×4), so y_MeOH ≈ 1.075·y_CO. With y_CO+0.4+y_MeOH=1, solving gives y_CO≈0.289 and y_MeOH≈0.311.