Download Balancing Chemical Equations Using Algebra

Balancing Chemical Equations Using Algebra
Given this equation:
___C2H7N + ___O2  ___CO2 + ___H2O + ___NO2
Step 1. Assign a variable to each unknown coefficient.
_a_C2H7N + _b_O2  _c_CO2 + _d_H2O + _e_NO2
Step 2. Write an MASS BALANCE equation for each element in the overall reaction using subscripts and
coefficients to represent the number of atoms of each element in reactants and in products. The arrow () is the
equals sign of the equation. These are the mass balance equations.
Carbon
Hydrogen
Nitrogen
Oxygen
C
H
N
O
2a
7a
a
2b
=
=
=
=
c
2d
e
2c + d + 2e
Note: You have just created a set of simultaneous algebraic equations the solution of which is the set of whole
number coefficients that satisfy this chemical equation.
Step 3. Examine the mass balance equations. Which variable is the most common, that is, the variable that appears
in the most equations? “a” Right! Well, you will substitute 1 into all of the equations for “a” and solve the
equations.
C
H
N
O
2a
7a
a
2b
Now we know that:
a
b
c
d
e
=
=
=
=
c
2d
e
2c + d + 2e
=
=
=
=
=
1
?
2
7/2
1
If
then
a
2(1)
7(1)
(1)
2b
=
=
=
=
=
1
c
2d
e
2c + d + 2e
Step 4. Make secondary substitutions into the Oxygen equation to solve for “b” using the values you now have for
“c”, “d”, and “e”.
2b
2b
b
=
=
=
2(2) + 7/2 + 2(1)
19/2
19/4
Step 5. Multiply the set of coefficients by the largest denominator of any fractional solutions to generate a set of
whole numbers as the coefficients for the balanced equation.
a
b
c
d
e
=
=
=
=
=
1
19/4
2
7/2
1
x4
a
b
c
d
e
=
=
=
=
=
4
19
8
14
4
Step 6. Substitute the solution into the chemical equation:
_4_C2H7N + _19_O2  _8_CO2 + _14_H2O + _4_NO2