# Balancing Equations ```Balancing Equations
Balancing a chemical equation refers to the skill (or art) of
making sure that all atoms that are written on the left of a
chemical reaction as reactants are also present on the right
side of the equation as products.
Since many of the problems you will see in this class require
you to start with a balanced chemical equation, this is a skill
you must learn now and will use over and over of the course
of the year.
Balancing Equations
Balancing a chemical equation isn’t that hard to do, it is a
simple trial
trial-and-error
and error process that is repeated for each
element in the equation until all elements are balanced.
After you get the hang of it it can even be kind of fun as you
fi
figure
outt a way tto puzzle
l th
through
bl
Balancing Equations
Example 1. Balance the following chemical equation:
FeCl3(aq) + AgNO3(aq) = AgCl(s) + Fe(NO3)3(aq)
The (aq) and the (s) refer to the physical form of the
chemical
h i l and
d we will
ill talk
b t that
th t more in
i chapter
h t 4,
4 for
f
now the physical descriptors can be ignored.
To balance the equation the only change you can make is to
change the coefficient in front of a molecule. You cannot
change any of the subscripts in a molecule because that
changes the chemical to a different substance.
? FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = ? AgCl(s)
g ( ) + ? Fe(NO
( 3)3((aq)
q)
Fe
1
0
0
1
So pick an element and make sure you have the same
number of atoms of that element on both sides of the equation.
are there on each side of the equation?
One Fe both sides of the equations so it is already balanced!
That means the coefficients for FeCl3 and Fe(NO3)3 can be
set to 1.
1 FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = ? AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
1
0
0
1
So pick an element and make sure you have the same
number of atoms of that element on both sides of the equation.
are there on each side of the equation?
One Fe both sides of the equations so it is already balanced!
That means the coefficients for FeCl3 and Fe(NO3)3 can be
set to 1.
1 FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = ? AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
Cl
1
3
0
0
0
1
1
0
Now let’s try the Cl
Cl. (Notice I will continue with the table
that I started on the last page)
3 Cl’s on the left, 1 Cl on the right.
So we need to multiply
p y the AgCl
g on the right
g hand side byy a
coefficient of 3 to get 3 Cl’s on this side.
1 FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = ? AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
Cl
1
3
0
0
0
3(1)
1
0
Now let’s try the Cl
Cl. (Notice I will continue with the table
that I started on the last page)
3 Cl’s on the left, 1 Cl on the right.
So we need to multiply
p y the AgCl
g on the right
g hand side byy a
coefficient of 3 to get 3 Cl’s on this side.
A d this
And
thi sets
t the
th coefficient
ffi i t off AgCl
A Cl to
t 3
1 FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = 3 AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
Cl
1
3
0
0
0
3(1)
1
0
Now let’s try the Cl
Cl. (Notice I will continue with the table
that I started on the last page)
3 Cl’s on the left, 1 Cl on the right.
So we need to multiply
p y the AgCl
g on the right
g hand side byy a
coefficient of 3 to get 3 Cl’s on this side.
A d this
And
thi sets
t the
th coefficient
ffi i t off AgCl
A Cl to
t 3
1 FeCl3((aq)
q) + ? AgNO
g 3((aq)
q) = 3 AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
Cl
Ag
1
3
0
0
0
1
0
3(1)
3(1)
1
0
0
Now let’s try the Ag’s
One on the left, three on the right, we will need to multiply
The AgNO3 by three to make it all balance.
balance
1 FeCl3((aq)
q) + 3 AgNO
g 3((aq)
q) = 3 AgCl(s)
g ( ) + 1 Fe(NO
( 3)3((aq)
q)
Fe
Cl
Ag
N
O
1
3
0
0
0
0
0
3(1)
3
9
0
3(1)
3(1)
0
0
1
0
0
3
9
Now let’s try the N’s…
The N’s look good, I didn’t have to mess with any coefficients,
so let’s
let s finish with the O
O’ss
The O’s are balanced as well, so we must be done. The final
balanced equation is:
1 FeCl3(aq) + 3 AgNO3(aq) = 3 AgCl(s) + 1 Fe(NO3)3(aq)
Balancing equations
As you balance a reactant and a product that both contain a
given element in an equation,
equation you try not to have to change
the coefficient on either of those two compounds again. If
you do, then you have to go back and start over. Notice how
thi worked
this
k d in
i the
th last
l t example.
l
Balancing equations
Step 1
Fe
FeCl3(aq) + AgNO3(aq) = AgCl(s) + Fe(NO3)3(aq)
1
0
0
1
Now you ttry nott tto mess with
N
ith either
ith F
FeCl
Cl3 or Fe(NO
F (NO3)3 from
f
this point onward. I will underline them remind myself to try
not to touch these coefficients again.
Balancing equations
Step 2
Fe
Cl
FeCl3(aq) + AgNO3(aq) = 3AgCl(s) + Fe(NO3)3(aq)
1
0
0
1
3
0
3(1)
0
Now with the Cl, the AgCl coefficient is fixed, so I will
underline that one as well.
Balancing equations
Step 3
Fe
Cl
A
Ag
FeCl3(aq) + 3AgNO3(aq) = 3AgCl(s) + Fe(NO3)3(aq)
1
0
0
1
3
0
3(1)
0
0
3(1)
3
0
Now with the Ag, the AgNO3 coefficient is fixed, so I will
underline that one as well.
Balancing equations
Steps 4 and 5
q) + 3AgNO
g 3((aq)
q) = 3AgCl(s)
g ( ) + Fe(NO
( 3)3((aq)
q)
FeCl3((aq)
Fe
1
0
0
1
Cl
3
0
3(1)
0
Ag
0
(3)1
0
3
N
0
3
0
3
O
0
9
0
9
And fixing the Ag fixes the coefficient of the last compound,
g
that the N and O will come into
so we cross our fingers
balance without and further changes.
Balancing Equations
Now try this one:
( ) + H2S(g)
(g)
Au2S3((s)) + H2(g) = Au(s)
? Au2S3(s) + ? H2(g) = ? Au(s) + ? H2S(g)
Au
2
0
1
0
Au first.
So you have 1 Au2S3 on the left for a total of 2 Au’s,
that means you need 2 Au(s) on the right.
1 Au2S3(s) + ? H2(g) = 2 Au(s) + ? H2S(g)
Au
1(2)
0
2(1)
0
S
3
0
0
1
S next.
So if you have 1 Au2S3 on the left, you’ll need 3 H2S
on the right.
1 Au2S3(s) + ? H2(g) = 2 Au(s) + 3 H2S(g)
Au
1(2)
0
2(1)
0
S
1(3)
0
0
H
0
2
0
3(1)
3(2)
H next.
So if you have 3 H2S on the left you’ll need 3 H2’s
on the right.
1 Au2S3(s) + 3 H2(g) = 2 Au(s) + 3 H2S(g)
Au
1(2)
0
2(1)
0
S
1(3)
H
0
0
3(2)
0
3(1)
0
3(2)