Chem Eq Balancing - underdetermined system?

[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

 

[Borek]

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 the right you should have either H₂SO₄ (one molecule, one unknown less) or H⁺ and SO₄^2- - charge must be balanced, that gives you an additional equation.

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

 

[Borek]

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.

 

[JeffNYC]

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

Jeff

 

[Borek]

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.