Efficiently Solving a Complex System of Equations in Chemical Engineering

[robbondo]

Homework Statement

qa+2qb=10.158
4qa+6qb=200d
2qa+(7/2)qb=c
2qa+3qb=100d
3.76qc+100d=89.842

Solve for a,b,c,d,q

Homework Equations

The Attempt at a Solution

I desperately want to avoid solving this system of equations by hand. This if for a chemical engineering class and solves a molecular balance of a chemical process. This seems soooo tedious, I would like to find a program to solve it. All of the solvers I have found seem to not work for equations where I have the unkowns multiplied by each other and will only let me equations like 5a + 6b ... not 5qa + 6bc ... HELP! Any suggestions?

 

[Defennder]

Well first of all, you can't solve this for numerical values for all 5 unknowns. That's because equations 4 and 2 differ by a factor of 2. Meaning to say your final answers for all the unknowns will be expressed in terms of one of these variables.

I have no college background in chemistry (only high school) so I can't help with the chemistry part, but you might want to double-check the question to see if you can come up with 5 equations which are not combinations of each other.

 

[HallsofIvy]

Yes, you really have only 4 independent equations. But that's plausible- there is no "one" answer to this- what ever the correct numbers for a molecule are, you could double them and get the same formulas for 2 molecules which must also satisfy these equations.

What you can do is solve the equations for 4 of the variables, in terms of the fifth. Then choose that fifth variable as the smallest integer that makes the other four variables integers.

 

[robbondo]

Crud... that's why the program gave me the answer in terms of q. Thanks a lot, I didn't catch that.