A closed vessel contains CO ₂ gas and excess solid graphite. The system is allowed to reach equilibrium at a temperature where the equilibrium constant K_p for the reaction CO ₂( g ) + C ( s ) 2 CO ( g ) is 1.8 atm . If the total pressure of the gas mixture at equilibrium is 0.8 atm , the initial partial pressure of CO ₂ before any reaction occurred is:

Step-by-step solution

Let the equilibrium partial pressure of CO be y . The total equilibrium pressure is 0.8 atm , so the equilibrium partial pressure of CO ₂ is (0.8 - y) . The equilibrium constant is given by: K_p = (P_ CO )^2 P_ CO ₂ Substitute the known values: 1.8 = y^2 0.8 - y 1.44 - 1.8y = y^2 y^2 + 1.8y - 1.44 = 0 Solving this quadratic equation: y = -1.8 + (1.8)^2 - 4(1)(-1.44) 2 y = -1.8 + 3.24 + 5.76 2 y = -1.8 + 3 2 = 0.6 atm Thus, at equilibrium: P_ CO = 0.6 atm P_ CO ₂ = 0.8 - 0.6 = 0.2 atm The reaction is CO ₂( g ) + C (