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Equilibrium composition
Posted Aug 27, 2013, 5:08 p.m. EDT Version 4.2, Version 4.2a 1 Reply
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Can anyone help me solve this problem. I am not sure what I am doing wrong here.
CH4 + CO2 <=> 2 CO + 2 H2 (equilibrium reaction)
Assuming batch reactor constant volume and initially we have 1 mole of CH4 1 mole of CO2 and 2 mole of H2.
Kequilibrium is 1250.
Pressure 1 atm
volume 1 m^3
Temperature 1252
How can I calculate the equilibrium composition of this reaction.
CH4 + CO2 <=> 2 CO + 2 H2 (equilibrium reaction)
Assuming batch reactor constant volume and initially we have 1 mole of CH4 1 mole of CO2 and 2 mole of H2.
Kequilibrium is 1250.
Pressure 1 atm
volume 1 m^3
Temperature 1252
How can I calculate the equilibrium composition of this reaction.
1 Reply Last Post Aug 29, 2013, 3:18 a.m. EDT
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Posted:
1 decade ago
First of all, this is not a Comsol related problem, but a fundamental chemical equilibrium exercise. But I'll try to reply.
An ideal das law applies surprisingly well also here. You need to go very high pressures before deviations from it are significant.
pV = nRT => n = (pV)/(RT) = 9.73 mol if T = 1252 K.
This is the total amount in the gas phase at the equilibrium. I assume that the reaction takes place in the gas phase.
K = [CO]^2*[H2]^2/([CH4]*[CO2]) where the brackets denote the partial pressure of the species. If the ideal gas applies p ~ n for each species. I denote the amount of reacted CO with x :
K = (2x)^2*(2 + 2x)^2/(1 - x)^2 <=> sqrt(K) = (4x + 4x^2)/(1 - x)
The roots are x = -10.67 and x = 0.8286; the former is not possible. Hence at equilibrium you should have
CH4: 0.1714 mol
CO2: 0.1714 mol
CO: 1.6572 mol
H2: 3.6572 mol
Yet, the sum is only 5.6572 mol. Hence, experimental conditions and the equilibrium constant do not agree. Or my assumptions are not valid.
An ideal das law applies surprisingly well also here. You need to go very high pressures before deviations from it are significant.
pV = nRT => n = (pV)/(RT) = 9.73 mol if T = 1252 K.
This is the total amount in the gas phase at the equilibrium. I assume that the reaction takes place in the gas phase.
K = [CO]^2*[H2]^2/([CH4]*[CO2]) where the brackets denote the partial pressure of the species. If the ideal gas applies p ~ n for each species. I denote the amount of reacted CO with x :
K = (2x)^2*(2 + 2x)^2/(1 - x)^2 <=> sqrt(K) = (4x + 4x^2)/(1 - x)
The roots are x = -10.67 and x = 0.8286; the former is not possible. Hence at equilibrium you should have
CH4: 0.1714 mol
CO2: 0.1714 mol
CO: 1.6572 mol
H2: 3.6572 mol
Yet, the sum is only 5.6572 mol. Hence, experimental conditions and the equilibrium constant do not agree. Or my assumptions are not valid.