For C(s) + CO2(g) 2CO(g), K_p = 2.0 atm at a fixed temperature. A gas mixture over excess graphite always has the mole ratio n_CO : n_CO2 = 3 : 1. At what total pressure (in atm, two decimals) does this mixture have Q_p = K_p? The net reaction is forward only below this pressure.

JEE Advanced levelNumerical answerDifficulty 3 of 3ce149

For $C (s) + CO X_{2} (g) 2 CO (g)$ , $K_{p} = 2.0$ atm at a fixed temperature. A gas mixture over excess graphite always has the mole ratio $n_{CO} : n_{CO X_{2}} = 3 : 1$ . At what total pressure (in atm, two decimals) does this mixture have $Q_{p} = K_{p}$ ? The net reaction is forward only below this pressure.

Numerical answer type, answer in atm, tolerance 0.01.

p_{CO} = 0.75 P

and

p_{CO X_{2}} = 0.25 P

Q_{p} = (0.75 P)^{2} / (0.25 P) = 2.25 P

(atm). Setting

2.25 P = 2.0

gives

P = 0.8889

atm, i.e. 0.89 atm. Below this value

Q_{p} < K_{p}

and the reaction goes forward.