How do I use the algebraic method to balance the equation CaCO₃ + H₃PO₄ → Ca₃(PO₄)₂ + H₂CO₃?

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Answer 1 · 2014-09-16T22:00:19

The balanced equation is #"3CaCO"_3 + "2H"_3"PO"_4 → "Ca"_3("PO"_4)_2 + "3H"_2"CO"_3#

You 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": a = 3c#
#"C": a = d#
#"O": 3a + 4b = 8c +3d#
#"H": 3b = 2d#
#"P": 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 #a = 3# and

#d = a = 3#

#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#