Question

How do you balance `Ca + P -> Ca_2P_3`?

Answer 1

`color(red)(2)Ca+color(red)(3)P rarr color(red)(1)Ca_2P_3`

Explanation:

Assume:
`color(white)("XXX")color(red)(x)Ca+color(red)(y)P rarr color(red)(z)Ca_2P_3`

Based on `Ca`
[1]`color(white)("XXX")x-2z=0`
Based on `P`
[2]`color(white)("XXX")y-3z=0`

In order to find the ratio of `(x:y:z)` we will arbitrarily set one of our variables to `1`; later we may need to adjust our ratios to get integer results.

In order to see how this works in the general case I have chosen to use `x=1`

From [1] with `x=1`
[3]`color(white)("XXX")z=1/2`
From [2] with `z=1/2`
[4]`color(white)("XXX")y=3/2`

So the ratio of components is
`color(white)("XXX")(1,3/2,1/2)`

Since we want integer factors we will multiply all terms by `2` to clear all fractions, giving:
`color(white)("XXX")(x:y:z) = (2:3:1)`