Short-cut tech. for balancing a chemical eq.

Example:

aCaCO₃ + bH₃PO₄ → cCa₃(PO₄)₂ + dH₂CO₃

Set up a series of simultaneous equations, one for each element.

Ca: a=3c

C: a=d

O: 3a+4b=8c+3d

H: 3b=2d

P: b=2c

Let’s set c=1

Then a=3 and

d = a = 3

b = 2c = 2

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

The balanced equation is

3CaCO₃ + 2H₃PO₄ → Ca₃ (PO₄)₂ + 3H₂CO₃