Question

An isobaric reactor is fed an equimolar mixture of carbon monoxide (CO) and steam (H₂O) at 400 K and 1 bar. If 60% of the H₂O is converted to H₂ through the following reaction, calculate how much heat must be added to the reactor in kJ/mol H₂ produced if the product stream leaves the reactor at 700 K. Assume ideal gas behavior for all species.

CO_(g) + H₂O_(g) → CO_2(g) + H_2(g)

Answer 1

The reaction is

CO_(g) + H₂O_(g) → CO_2(g) + H_2(g)

The reactor is isobaric which means the pressure will remain constant

Let initially we have 1 mole of each reactants

The conversion is 60% which means that after reaction the mixture will have

0.4 moles of each CO and H2O

0.6 moles of each CO2 and H2

Now heat capacities of each are as follows

CO = 28.12

H2O = 32.218

H2 = 29.1

CO2 = 22.24

So heat before the start will be

Moles of reactants X heat capacity X temperature

CO = 1 X 28.12 X 400 = 11248

H2O = 29.1 X 400 = 11640

Total = 22888 Joules

After reaction

reactants = 0.4 X 22888 X 700 / 400= 16021.6 Joules

CO2 = 0.6 X 22.24 X 700 = 9340.8 J

H2 = 0.6 X 29.1 X 700 = 12222 Joules

so total heat = 37584.4 Joules

Heat required = 37584.4 - 22888= 14696.4 Joules