Solid ammonium hydrosulfide is placed in a closed vessel and allowed to decompose at 600 ~K until equilibrium is reached: NH ₄ HS ( s ) NH ₃( g ) + H ₂ S ( g ) If the total pressure of the gas mixture at equilibrium is 20 ~bar , what is the value of K_c for this reaction at 600 ~K ? (Given: R = 0.0833 ~L~bar~K ⁻¹ mol ⁻¹ )

Step-by-step solution

The thermal decomposition of solid ammonium hydrosulfide is given by: NH ₄ HS ( s ) NH ₃( g ) + H ₂ S ( g ) At equilibrium, the gases are produced in a 1:1 molar ratio. Let the partial pressure of each gas be p . Total pressure, P_ total = P_ NH ₃ + P_ H ₂ S = p + p = 2p Given P_ total = 20 ~bar , we have 2p = 20 p = 10 ~bar . The equilibrium constant in terms of partial pressures ( K_p ) is: K_p = P_ NH ₃ P_ H ₂ S = 10 10 = 100 The change in the number of moles of gas is: n_g = (1 + 1) - 0 = 2 The relationship bet