10.00 L CO2 0.886 mol H2 0.443 mol H2O 0.713 mol 550 K

10.00 L CO2 0.886 mol H2 0.443 mol H2O 0.713 mol 550 K

A mixture of 0.886 mol of CO2, 0.443 mol of H2,

and 0.713 mol of H2O is placed in a 10.00 L vessel.

The following equilibrium is established at 550 K:

CO2(g) + H2(g) ⇌ CO(g) + H2O(g)

a) Calculate the initial partial pressures of CO2, H2, and H2O.

b) At equilibrium P_H2 = 182 kPa,

calculate the equilibrium partial pressures of CO2, CO, and H2O.

c) Calculate Kp for the reaction.

d) Calculate Kc for the reaction.

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[참고] 평형 상수 (equilibrium constant), K

[ https://ywpop.tistory.com/7136 ]

a) Calculate the initial partial pressures of CO2, H2, and H2O.

전체 몰수, n_tot

= 0.886 + 0.443 + 0.713

= 2.042 mol

PV = nRT 로부터,

( 참고 https://ywpop.tistory.com/3097 )

전체 압력, P_tot = n_tot RT / V

= (2.042) (0.08206) (550) / (10.00)

= 9.216 atm

돌턴의 분압법칙

P_a = X_a × P_tot

( 참고 https://ywpop.tistory.com/48 )

CO2의 분압 = (0.886 / 2.042) × 9.216

= 3.999 atm

H2의 분압 = (0.443 / 2.042) × 9.216

= 1.999 atm

H2O의 분압 = (0.713 / 2.042) × 9.216

= 3.218 atm

b) At equilibrium P_H2 = 182 kPa,

calculate the equilibrium partial pressures of CO2, CO, and H2O.

H2의 분압을 atm으로 환산하면,

182 kPa × (1 atm / 101.325 kPa) = 1.796 atm H2

H2의 분압 = 1.999 atm – x = 1.796 atm 이므로,

x = 1.999 – 1.796 = 0.203 atm

CO2(g) + H2(g) ⇌ CO(g) + H2O(g) 평형에서,

CO2 : H2 : CO : H2O = 1 : 1 : 1 : 1 계수비 이므로,

반응물의 분압이 x만큼 감소하면,

생성물의 분압은 x만큼 증가한다.

( 참고 https://ywpop.tistory.com/20883 )

( 참고 https://ywpop.tistory.com/22994 )

CO2의 분압 = 3.999 – 0.203 = 3.796 atm

CO의 분압 = 0 + 0.203 = 0.203 atm

H2O의 분압 = 3.218 + 0.203 = 3.421 atm

c) Calculate Kp for the reaction.

Kp = [(P_CO) (P_H2O)] / [(P_CO2) (P_H2)]

= [(0.203) (3.421)] / [(3.796) (1.796)]

= 0.1019

= 0.102

d) Calculate Kc for the reaction.

Kc = Kp / (RT)^Δn

( 참고 https://ywpop.tistory.com/6523 )

Δn = 기체 생성물들의 몰수 – 기체 반응물들의 몰수

= 2 – 2 = 0 이므로,

Kc = Kp = 0.102

[ 관련 예제 https://ywpop.tistory.com/22805 ] CO(g) + H2O(g) ⇌ CO2(g) + H2(g) 500℃ equilibrium constant 3.9

[키워드] CO2(g) + H2(g) ⇌ CO(g) + H2O(g) 평형 기준, CO2 + H2 ⇌ CO + H2O 평형 기준