A86: Re: Chem86 Equation Balancing!!


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A86: Re: Chem86 Equation Balancing!!



Ok.  (If you like this and have any influence in getting excepting people
into college I'm applying this year.... :)

numbers after the elements are the numbers that are usually in subscript
like H2O (water)
numbers separated by a space infront of the molecule is the number of
molecules like 2 H2O (two water molecules)

I'll start with a simple equation.  (As far as I can tell it works for all
very complex ones too)
(I'll use x, y, and z as variables to show the number of the molecules
needed to balance)
H3PO3 -> H3PO4 + PH3
--or with the added variables--
x H3PO3 -> y H3PO4 + z PH3


In this equation we have H, P, and O.
The equation then breaks down to 3 separate parts because it has three
separate elements:
(The "->" are replaced with "=")

for H:
x*3 = y*3 + z*3
for P:
x*1 = y*1 + z*1
for O:
x*3 = y*4 + z*0

See, the number that is multiplied by x, y, or z is the amount of the
element in the molecule that the equation is for.

I then change them into:
x*3 - y*3 - z*3 = 0
x*1 - y*1 - z*1 = 0
x*3 - y*4 - z*0 = 0

All three variables in the three equations stand for the same number by the
nature of this problem.  But there is an infinite amount of numbers that
could fit into the three variables :(

To solve that problem I plug 1 into x which makes only one possibility to y
and z.
so now the equations become:
- y*3 - z*3 = 3
- y*1 - z*1 = 1
- y*4 - z*0 = 3

Now we all know how to solve those equations for y and z. (The hard part is
getting around a singular matrix which I think I have an idea of how to do
but it's been awhile since I've done matrix math)

using the first and last equations y= -.75 and z= -.25
The negative sign only comes out because of the side of the equation the y
and z are from so I'll use the abs value of .75 and .25

So now:
x= 1
y= .75
z= .25

Now all the numbers should be divided by the smallest number (.25)

So now we get:
x= 4
y= 3
z= 1

So now if we plug them back into the original equation we get:

4 H3PO3 -> 3 H3PO4 + 1 PH3

The properly balanced equation :-)

now a complex equation: (by my standards)
(using a,b,c,d,e as the variables)
Fe2(SO4)3 + NH3 + H2O -> Fe(OH)3 + (NH4)2SO4
a                        b         c             d                   e
that becomes
3Fe
a*2 =d*1
S
a*3 = e*1
2O
a*12 + c*1 = d*3 + e*4
4N
b*1 = e*2
1H
b*3 + c*2 = d*3 + e*8

so:
a=1 (set value ahead of time)
b= 6 (remember to take the abs)
c= 6
d= 2
e= 3

If plugged in this gives the correctly balanced formula.

Do you see my method now?
________
Eli Allen
eallen@mail.bcpl.lib.md.us


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