# Homework Help: Chem Eq Balancing - underdetermined system?

1. Nov 28, 2008

### JeffNYC

All relevant data is attached in a .jpeg.

Ultimately, I have 4 equations with 6 unknowns. I found the correct answer through a chem calculator, but I'm wondering how it computed the balanced equation.

Any insight much appreciated!

Jeff

2. Nov 29, 2008

### Staff: Mentor

First of all - that's nothing unusual to have one less equation when balancing. That doesn't stop us from getting to the answer, as we know that all coefficients must be integer and the smallest possible, this condition is strong enough to serve as additional equation.

Second - this equation doesn't make a chemical sense. I understand that's not a problem you have to deal with, but chemically on teh right you should have either H2SO4 (one molecule, one unknown less) or H+ and SO42- - charge must be balanced, that gives you an additional equation.

That's all for now, perhaps more comments later.

3. Nov 29, 2008

### Staff: Mentor

Here comes more. There is plenty of solutions.

2SO2 + 1NO3 + 2H2O -> 4H + 2SO4 + 1NO

3SO2 + 1NO3 + 4H2O -> 8H + 3SO4 + 1NO

3SO2 + 2NO3 + 2H2O -> 4H + 3SO4 + 2NO

and so on.

4. Nov 29, 2008

### JeffNYC

Thanks Borek - any insight into how you arrived at any of those answers?

Jeff

5. Nov 29, 2008

### Staff: Mentor

Brute force. But you may try to start with the set of equations you already have, and assume x1 to be a parameter and check what you get for different integer values of x1.