How to balance chemical equations using algebraic method?

1 Answer
Jan 18, 2017

Answer:

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.