I went back and took out my 20 year old HP calculator where I have a program that balances equations using matrices. I guess I should have used it before assuming that the equation needed acidic or basic medium. However, as many of you can see this reaction ends up in an acidic medium due to the formation of phosphoric acid. That and the fact that trimolecular reactions are very rare. Regardless here is a way that you can use matrices and your TI calculator to balance most chemical equations including the one from the post.

__P4 + __H2O + __P2I4 ------> __PH4I + __H3PO4

we produce a matrix as follows where you line up the formulas on the first row, and the elements on the first column, then fill in the table with the number of each element present in each formula. The reactants are input as positive values and products as negative values

P_{4} H_{2}O P_{2}I_{4} PH_{4}I H_{3}PO_{4}

P 4 0 2 -1 -1

H 0 2 0 -4 -3

O 0 1 0 0 -4

I 0 0 4 -1 0

We separate the last column and end up with two matrices

1. Select MATRIX, EDIT, 1 to choose A.

2. Type in 4x4 to signify 4 rows by 4 columns.

3. ENTER each value.

4. Return to Home Screen.

5. Select MATRX, 1 to view A.

Now create a 4x1 matrix B and enter the values for matrix B

1. Select MATRIX, MATH, 1 to retrieve det( command.

2. Retrieve matrix A.

3. Add right paranthese, ), and press ENTER.

det([A]) = -64 this is the coefficient of the last formula (H3PO4)

now calculate [A] ^{-1} {B} det([A])

[A] ^{-1} {B} det([A]) =

This means that our balanced equation is

26 P4 + 256 H2O + 20 P2I4 ? 80 PH4I + 64 H3PO4

all coefficients are divisible by two thus,

13 P4 + 128 H2O + 10 P2I4 ? 40 PH4I + 32 H3PO4

## Comments

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