A vessel is initially filled with a mixture of CO ₂ and CO gases having partial pressures of 0.4 atm and 0.2 atm respectively. Excess solid graphite is then added, and the system is allowed to reach equilibrium according to the reaction CO ₂( g ) + C ( s ) 2 CO ( g ) . If the total pressure of the gas mixture at equilibrium is 0.8 atm , the value of K_p for the reaction is:

Step-by-step solution

The given reaction is CO ₂( g ) + C ( s ) 2 CO ( g ) . Let the decrease in pressure of CO ₂ be x . Initial partial pressures: P_ CO ₂ = 0.4 atm P_ CO = 0.2 atm At equilibrium: P_ CO ₂ = 0.4 - x P_ CO = 0.2 + 2x Total pressure at equilibrium is given as 0.8 atm : P_ total = (0.4 - x) + (0.2 + 2x) = 0.8 0.6 + x = 0.8 x = 0.2 atm Substitute x back to find equilibrium partial pressures: P_ CO ₂ = 0.4 - 0.2 = 0.2 atm P_ CO = 0.2 + 2(0.2) = 0.6 atm Now, calculate the equilibrium constant K_p : K_p = (P_ CO )^2 P_ CO ₂ K_