Question

How to balance chemical equations using algebraic method?

Answer 1

Here's how you do it.

Explanation:

Assume you must balance the equation

`"CaCO"_3 + "H"_3"PO"_4 → "Ca"_3("PO"_4)_2 + "H"_2"CO"_3`

You first write the equation using letter variables for the coefficients:

`a"CaCO"_3 + b"H"_3"PO"_4 → c"Ca"_3("PO"_4)_2 + d"H"_2"CO"_3`

Then you set up a series of simultaneous equations, one for each element.

`"Ca":color(white)(ml) a color(white)(mml)= 3c`
`"C":color(white)(mll)acolor(white)(mmll) = color(white)(mmm)d`
`"O": color(white)(m)3a + 4b = 8c +3d`
`"H": color(white)(mmmll)3b = color(white)(mmll)2d`
`"P": color(white)(mmmml)b = 2c`

Now you solve the five simultaneous equations.

It looks almost impossible, but we know that the coefficients must be integers.

Let's set `c = 1`.

Then `color(white)(l) a = 3` and

`color(white)(mmll)d = a = 3`

`color(white)(mmll)b = 2c = 2`

So `a = 3`; `b = 2`; `c = 1`; `d = 3`

The balanced equation is

`"3CaCO"_3 + "2H"_3"PO"_4 → "Ca"_3("PO"_4)_2 + "3H"_2"CO"_3`

Here's a useful equation on balancing equations by the algebraic method.