Question

Public concern about the increase in carbon dioxide (CO2) in the atmosphere has led to numerous proposals to sequester or eliminate CO2. An inventor believes he has developed a new catalyst that can make the following gas phase reaction proceed with 40% conversion of CO2: CO2(g) + H2(g) > H2O(g) + CH4(g)

The source of H2 for the reaction would be from the electrolysis of water using electricity generated from solar cells. Assume that 1.5 mole of CO2 enter the reactor at 700 °C together with 4 mol of H2 at 100 °C. At what temperature do the exit gases leave the reactor? Assume that the system is at steady state, the reactor is perfectly insulated, and no work is involved

Answer 1

reaction is:

CO₂ + H₂ = H₂O + CH₄

conversion = 0.4 of carbon dioxide

CO₂ entering = 1.5 moles

H₂ entering = 4 moles

extent of reaction = (no. of initial moles*conversion)/stoichiometric coefficient

considering extent of CO2 as its conversion is given

extent = (1.5*0.4)/1 = 0.6

CO₂ left after reaction = 1.5 - 0.6 = 0.9 moles

H₂ left = 4 - 0.6 = 3.4 moles

H₂O formed = 0.6*1 = 0.6 moles

CH₄ formed = 0.6*1 = 0.6 moles

It is given that the reactor is insulated, hence reaction is carried out adiabatically. Also, no work is involved. Assuming heat capacity does not vary over the temperature range

the following will be the equation of energy balance over an adiabatic reactor:

Q - W_s + (M*C_p*T)_reactants = (M*C_p*T)products

Q = W_s = 0

(M*C_p*T)_reactants = (M*C_p*T)products

(1.5*0.0227*(700-25)) + (4*7.25*(100-25)) = (0.6*4.186*(T - 25)) + (0.6*0.14125*(T - 25))

Cp is is kJ/molK (found from internet)

M = molar mass

T = outlet temperature of gas

solving for T we get,

T = 871.568 Kelvin

T = 598.418 Celsius