A closed vessel contains excess CaCO3(s), CaO(s) and C(s) at a fixed temperature, so that two equilibria hold together: CaCO3(s) CaO(s) + CO2(g) with K_p1 = 0.35 atm, and C(s) + CO2(g) 2CO(g) with K_p2 = 1.7 atm. Calculate the total gas pressure in atm at equilibrium, correct to two decimal places.

JEE Advanced levelNumerical answerDifficulty 3 of 3ce101

A closed vessel contains excess $CaCO X_{3} (s)$ , $CaO (s)$ and $C (s)$ at a fixed temperature, so that two equilibria hold together: $CaCO X_{3} (s) CaO (s) + CO X_{2} (g)$ with $K_{p 1} = 0.35$ atm, and $C (s) + CO X_{2} (g) 2 CO (g)$ with $K_{p 2} = 1.7$ atm. Calculate the total gas pressure in atm at equilibrium, correct to two decimal places.

Numerical answer type, answer in atm, tolerance 0.01.

Because

CaCO X_{3}

and

CaO

are both present,

p_{CO X_{2}} = K_{p 1} = 0.35

atm. The second equilibrium then fixes

p_{CO}^{2} = K_{p 2} p_{CO X_{2}} = 1.7 \times 0.35 = 0.595

, so

p_{CO} = 0.7714

atm. Total pressure

= 0.35 + 0.7714 = 1.1214

atm.