A question of...Maths! 3

[AndreChE]

I have a %vol and a %wt composition of a mixture.

I want to calculate the molecular weight of each component.

%vol %wt
Component A 34.8 33.9
Component B 56.8 56.3
Component C 6.0 6.9
Component D 1.0 1.1
Component E 1.4 1.8

Can someone help me? I am trying with a 6 equations system but the last one is not correct, 5 equations for each component and the other...I don't know. I have tried the sums but I don't get anything..

Thank you,
AndreChE

 

[TD2K]

I'm assuming this is a gas mixture so I can assume vol% = mol%. If it's a liquid or solid, my numbers will not be correct.

If it is a gas, I get the following:

Cmpt A is 4.1759
Cmpt B is 4.2490
Cmpt C is 4.9300
Cmpt D is 4.7157
Cmpt E is 5.5123

These are (to coin a phrase), the lowest common factor for MWs. If all of these are multiplied by the same number, eg 10, you would get the same wt% when you converted from vol% to wt%.

On the other hand, with those MWs, they could be various sour H2 streams.

 

[joerd]

You need the average mol. wt of the mixture (or mol. flow and mass flow, then average mol. wt = mass flow/mol flow). The problem is now not "scaled", so you can calculated the relative MW of each component relative to the average mol wt, by comparing vol%(A)*MW(A) with wt%(A) for each component. You can set this up in e.g. Excel by guessing a MW for each component, and then have the solver minimize the total error.
[tt]
%vol %wt Mol. wt. %vol*MWi %wt*MWtot squared error
Component A 34.8 33.9 0.97 33.90 33.90 1.E-10
Component B 56.8 56.3 0.99 56.30 56.30 3.E-10
Component C 6 6.9 1.15 6.90 6.90 4.E-12
Component D 1 1.1 1.10 1.10 1.10 4.E-15
Component E 1.4 1.8 1.29 1.80 1.80 2.E-13
TOTAL ERROR 4.E-10
Av. mw 1
[/tt]
If you use an average MW of say 30, the table becomes:
[tt]
%vol %wt Mol. wt. %vol*MWi %wt*MWtot squared error
Component A 34.8 33.9 29.22 1017 1017 1.E-07
Component B 56.8 56.3 29.74 1689 1689 2.8E-07
Component C 6 6.9 34.50 207 207 4.1E-09
Component D 1 1.1 33.00 33 33 1.9E-11
Component E 1.4 1.8 38.57 54 54 1.9E-10
TOTAL ERROR 4E-07
Av. mw 30
[/tt]

Cheers,
Joerd

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Guidoo]

I also gave it a try, but you end up with four independent equations for five unknowns. So you can't solve the system unless you provide additional information such as the average molecular weight of the mixture.

By the way, I had to assume that this is a gas mixture at low pressures (so compressibility z is about 1 for all components, and vol% is same as mol%). Otherwise I would end-up with five more unknowns...

This confirms the post by Joerd above.

 

[AndreChE]

joerd

How do you do that in Excel?

 

[Montemayor]

AndreChE:

I would leave well enough alone. You've had 3 good responses to what is a classic student problem in chemistry (not math) and now you not only want a documented answer but also in Excel.

Where are the "thank you" 's? Where are the red flags?

Art Montemayor
Spring, TX

 

[AndreChE]

Montemayor

This is not a typical chemistry student problem...believe me!

This is a PIONA... not pure components. It is a problem without a simple solution.

A lot of equations, implicit ones...not a typical chemistry student. General parafins (iso and normal), olefins, naftenics and aromatics!

Thank you all. In this part you are right and I am sorry for that.

AndreChE