Balancing Chemical Equations

Date: 02/04/2004 at 20:07:03
From: Aaron
Subject: Balancing chemical equations

I am having trouble balancing very complex chemical equations, like
this one:

HIO3 + FeI2 + HCl -> FeCl3 + ICl + H2O.

After I balance all the elements other than hydrogen and oxygen I
cannot balance the hydrogen and oxygen.

Date: 02/04/2004 at 21:52:50
From: Doctor Rob
Subject: Re: Balancing chemical equations

Thanks for writing to Ask Dr. Math, Aaron!

To balance any chemical equation, put unknowns for the number of
molecules of each compound on both sides:

a*HIO3 + b*FeI2 + c*HCl -> d*FeCl3 + e*ICl + f*H2O.

Then for each element appearing, set the number of atoms on the left
equal to the number of atoms on the right:

H:   a + c = 2*f.
I:   a + 2*b = e.
O:   3*a = f.
Fe:  b = d.
Cl:  c = 3*d + e.

Now solve this system of equations for b, c, d, e, and f in terms of a
by using substitutions and combinations of the above:

   b = (4/5)*a,
   c = 5*a,
   d = (4/5)*a,
   e = (13/5)*a,
   f = 3*a.

Now put a equal to the greatest common denominator of the coefficients
appearing, (a = 5) and evaluate b, c, d, e, and f:

   a = 5,
   b = 4,
   c = 25,
   d = 4,
   e = 13,
   f = 15.

That means that the equation will be balanced if you have

   5 HIO3 + 4 FeI2 + 25 HCl -> 4 FeCl3 + 13 ICl + 15 H2O.

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/