Question

3. The water-gas shift reaction (CO + H­₂O à CO₂ + H_­2) occurs in a series of two reactors. An equimolar mixture of steam and CO (stream 1) enters the first reactor. The product stream from the first reactor (stream 3) and an additional stream (stream 3) containing pure steam enter the second reactor. The fractional conversion of CO in the first reactor is 0.610, and the fractional conversion of CO in the second reactor is 0.790. The product stream has a water (steam) mole fraction of 0.210.

1. Draw and fully label a PFD for the process.
2. What is the fractional conversion of CO for the overall process?
3. What is the ratio of the molar flow rate of stream 2 relative to the molar flow rate of stream 1?
4. Put a box around the answers to the questions in b. and c. You will receive 5 points for answering with the correct number of significant digits.

Answer 1

a)

The PFD for the same is given below:

b)

Basis : 100 mol of Stream 1

Moles of CO in stream 1 = 50 mol

Fractional conversion of CO in reactor1 = 0.61

Moles of CO converted in reactor1 = 0.61 X 50 = 30.5 mol

Moles of CO unconverted and entering reactor2 = 50 - 30.5 = 19.5 mol

Fractional conversion of CO in reactor2 = 0.79

Moles of CO converted in reactor2 = 0.79 X 19.5 = 15.405 mol

Total moles of CO converted = 30.5 + 15.405 = 45.905 mol

Fractional conversion of CO for the overall process ; F

F = Total moles converted / Total moles fed

F = 45.905 / 50

F = 0.918 (3 significant digits)

c)

From the reaction stoichiometry;

Moles of CO reacted = Moles of H2O reacted = Moles of CO2 formed = Moles of H2O formed

In reactor 1;

Moles of CO reacted = 30.5 mol

Moles of H2O reacted = Moles of CO2 formed = Moles of H2O formed = 30.5

Total moles in stream 2 = Moles of CO left + Moles of H2O left + Moles of CO2 formed + Moles of H2 formed

Total moles in stream 2 = 19.5 + 19.5 + 30.5 +30.5 = 100 mol

Total moles in stream 1 = 100 mol

Therefore;

The ratio of the molar flow rate of stream 2 relative to the molar flow rate of stream 1; R

R = 100 / 100 = 1.00 (3 significant digits)