Chemical Engineering Mass Balance with matrix

[gloryofgreece]

Homework Statement

Ethane reacts with chlorine to make ethyl chloride and hydrogen chloride, and ethylene reacts with hydrogen chloride to form ethyl chloride.

C2h6+ Cl2 > C2H5Cl + HCL
C2H4 + HCl > C2H5Cl

I post an image of flow chart and rest of description

Based on my reading, all of unreacted ethane is removed along with ethyl chloride...

Homework Equations

C2h6+ Cl2 > C2H5Cl + HCL
C2H4 + HCl > C2H5Cl

The Attempt at a Solution

I want to solve it in a matrix form, then do it in matlab. However I can not formulate my matrix...
I can see ethane being limiting reagent

m1 = feed stream contain ethane and ethylene
R = recycle stream
m3 = feed stream of Cl2
m4 = ethyl chloride formed from 1st reaction (ethane + cl2)
m5 = ethyl chloride formed from 2nd rxn (C2H4 + HCl > C2H5Cl)

This is my attempt; I understand I will have to simplied it to matrix form first.

for ethane
0.5 m1 - 0.95 (.5 m1) - m4 = 0

for ethylene
x = molar ration of ethylene

0.5 m1 + xR - 0.5 (0.5m1 + xR) -m5 =0

Am I on the right track?

My question is

How do i determine the composition of R?

 

[KataKoniK]

To determine the composition of R, you can use the following equation:

R = (m4 + m5 - 0.5m1) / x

Where:
- R is the composition of the recycle stream
- m4 is the amount of ethyl chloride formed from the first reaction
- m5 is the amount of ethyl chloride formed from the second reaction
- 0.5m1 is the amount of ethane in the feed stream
- x is the molar ratio of ethylene in the feed stream

This equation takes into account the amount of ethyl chloride that is formed in both reactions and subtracts the amount of ethane that is removed. The remaining value is then divided by the molar ratio of ethylene to determine the composition of the recycle stream.

 

[Mene]

Your attempt at solving the problem using matrix form seems to be on the right track. However, there are a few things to consider when determining the composition of R:

1. The composition of R will depend on the extent of the reactions. In other words, how much of the reactants are converted into products. This information is not provided in the given equations, so you will have to make some assumptions or use experimental data to determine the extent of the reactions.

2. The composition of R will also depend on the stoichiometry of the reactions. In this case, we can see that for every 1 mole of ethane reacted, 1 mole of ethyl chloride is produced. Therefore, the composition of R will also be 1 mole of ethane for every mole of ethyl chloride.

3. You will also need to consider the conservation of mass in your mass balance equations. This means that the total number of moles of each component in the feed stream (m1) must equal the total number of moles in the product streams (m4 and m5) plus the recycle stream (R).

With these considerations in mind, you can set up your matrix equations as follows:

For ethane:
0.5 m1 - 0.95 (0.5 m1) - m4 = 0
R = m4 (since 1 mole of ethane produces 1 mole of ethyl chloride)

For ethylene:
m1/2 + xR - 0.5 (0.5m1 + xR) - m5 = 0
R = m5 (since 1 mole of ethylene produces 1 mole of ethyl chloride)

To solve for the composition of R, you will need to solve these equations simultaneously using matrix operations in Matlab. I recommend consulting with your instructor or a tutor for further guidance on how to set up and solve these equations in Matlab.