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Math Help - balancing chemical reaction

  1. #1
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    balancing chemical reaction[SOLVED]

    question:I'm given the reaction Na_2S_4O_6+H_2O_2 --> Na_2SO_4 +H_2O + H_2SO_4 and I need to find the coefficient in front of each term so that all the variables are balanced. Na is one variable.

    work:I take the homogeneous linear equations which are
    [html]2a-2c=0
    4a-c-e=0
    6a+2-4c-d-4e=0
    2b-2d-2e[/html]So that gives the matrix

    <br />
\left(<br />
\begin{array}{ccccc}<br />
2 & 0 & -2 & 0 & 0 \\<br />
4 & 0 & -1 & 0 & -1 \\<br />
6 & 2 & -4 & -1 & -4 \\<br />
0 & 2 & 0 & -2 & -2 \\<br />
\end{array} \right)

    2 0 -2 0 0
    4 0 -1 0 -1
    6 2 -4 -1 -4
    0 2 0 -2 -2

    when I plug this into matlab I get


    \left| \begin{array}{ccccr}<br />
1 & 0 & 0 & 0 & \frac{-1}{3} \\<br />
0 & 1 & 0 & 0 & \frac{-2}{3} \\<br />
0& 0 & 1 & 0 & -\frac{1}{3} \\<br />
0 & 0 & 0 & 1 & -\frac{1}{3} \end{array} \right|.

    1.0000 0 0 0 -0.3333
    0 1.0000 0 0 -2.3333
    0 0 1.0000 0 -0.3333
    0 0 0 1.0000 -1.3333

    but now I'm not sure how to interpret the results. Since I have 4 equations and 5 unknowns, doesn't that mean one of the coefficients can be any number?
    Last edited by superdude; January 27th 2010 at 09:30 PM. Reason: solved - remove
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