Question

CO2 can be eliminated and transformed to fuel like CH4 by the following reaction: CO2(g) + 4H2(g) → 2H2O(g) + CH4 (8) Figure below shows 1 mol of CO2 entering at 800 K and reacting with 4 mol of Hz entering at 298 K while the product exits the reactor at 1000 K. 1 mol CO2 800 K Product 1000 K Reactor 4 mol H2 298 K Determine the heat transfer, Q for this process if only 70% conversion of CO2 is achieved.

Answer 1

CO2 fed = 1 mol

H2 fed = 4 mol

CO2 + 4 H2 ---> CH4 + 2 H2O

For 70% conversion of CO2, CO2 reacted = 0.7 mol

From reaction stoichiometry,

H2 reacted = 0.7 × 4 mol = 2.8 mol

CH4 produced = 0.7 mol

H2O produced =( 0.7 × 2) mol = 1.4 mol

Product stream contains:

CO2 = (1-0.7) mol = 0.3 mol

H2 = (4-2.8) mol = 1.2 mol

CH4 = 0.7 mol

H2O = 1.4 mol

Specific heats are:

CO2 at 800 K = 51.392 J/mol K

CO2 at 1000 K = 54.296 J/mol K

H2 at 298 K = 28.6 J/mol K

H2 at 1000 K = 29.96 J/mol K

CH4 at 1000 K = 71.6 J/mol K

H2O at 1000 K = 41.184 J/mol K

Applying the energy balance,

(Energy in) + ( heat added) = (energy leaving )

As energy is given as (no. of moles) × (specific heat) × (temperature)

Energy in = (1 mol × 51.392 J/mol K × 800 K ) + (4 × 28.6 × 800) = 132633.6 J = 132.63 kJ

Energy out = ( 0.3 × 54.296 + 1.2 × 29.96 + 0.7 × 71.6 + 1.4 × 41.184) × 1000 = 160018.4 J = 160.018 kJ

Heat transfer (added) = Q

132.63 + Q = 160.018

Q = 27.3884 kJ