# Balancing Chemical Equations

Balancing Chemical Equations Using The Algebraic Method

## Balancing chemical equations, step by step - Example

Problem 1 :  Example balancing equations:

Balance the chemical equation for combustion of penthane

Balance, step by step Problem 1: Balance the equation for the combustion of pentane

Step 1. Insert 1 in front of the most complicated looking compound.
1C5H12 + O2 --> CO2 + H2O

Step 2. To balance C's, 5 must be inserted in front of CO2.
1C5H12 + O2 --> 5CO2 + H2O

Step 3. To balance H's, 6 must be inserted in front of H2O .
1C5H12 + O2 --> 5CO2 + 6H2O

Step 4. To balance O's, 8 must be inserted in front of O2 .
1C5H12 + 8O2 = 5CO2 + 6H2O

Erase 1 from the equation:

C5H12 + 8O2 = 5CO2 + 6H2O

The equation is now balanced!
Note: If any fractions should occur, simply multiply the equation by a suitable number. This will be demonstrated in the next problem.

The algebraic solution to Problem 1: How to balance the equation for the combustion of pentane   ( C5H12 )

Step 1. Insert coefficients in front of the all compounds.

aC5H12 + bO2 --> cCO2 + dH2O

C:      5a =  c                    let a = 1                                    ->     c = 5*1                                    = 5
H:     12a =  2d          we know that a=1                            ->    d = (12*1)/2                            = 6
O:      2b =  2c + d     we know that a = 1 and d = 6         ->    b = (2c + d)/2   =  (2*5+6)/2   = 8

C5H12 + 8O2 --> 5CO2 + 6H2O

Figure:  How to balance the combustion of ethane.  Note: Picture from an older CHEMIX School version

Figure: The Formation Of Water - Balancing Chemical Equation Example - CHEMIX School

Problem 2: Balance the equation for the combustion of ethane

Step 1. Insert 1 in front of the most complicated looking compound.
1C2H6 + O2 --> CO2 + H2O

Step 2. To balance C's, 2 must be inserted in front of CO2.
1C2H6 + O2 --> 2CO2 + H2O

Step 3. To balance H's, 3 must be inserted in front of H2O .
1C2H6 + O2 --> 2CO2 + 3H2O

Step 4. To balance O's, 7/2 must be inserted in front of O2 .
1C2H6 + 7/2O2 = 2CO2 + 3H2O

Step 5. Eliminate the fraction 7/2. This can be done by multiplying the equation by 2.
2C2H6 + 7O2 = 4CO2 + 6H2O

The equation is now balanced!

The algebraic solution
to Problem 2: How to balance the equation for the combustion of ethane   ( C2H6 )

Step 1. Insert coefficients in front of the all compounds.

aC2H6 + bO2 --> cCO2 + dH2O

C:   2a = c                              let a = 1                                    ->     c = 2*1                                     = 2
H:  6a = 2d                    we know that a=1                             ->     d = (6*1)/2                               = 3
O: 2b = 2c + d              we know that c = 2 and d = 3            ->    b = (2c + d)/2   =  (2*2+3)/2     =7/2

1C2H6 + 7/2O2 = 2CO2 + 3H2O

The equation is now in balance but we have to eliminate the fraction 7/2. This can be done by multiplying the equation by 2.

2C2H6 + 7O2 = 4CO2 + 6H2O

Figure:  How to balance the combustion of ethane.

### Balancing equations - Signs and Symbols

Tab. Guidelines for balancing equations using the CHEMIX School program

Sign/symbol Example Interpretation
+ H2 + O2 .... Separates compounds in equations
> H2 + O2 > H2O Separates left and right side (normally an arrow)
e- Cu + H2O > Cu2O + H+ + e- Electron

CHEMIX School - Balancing chemical equations

Balancing Chemical Equations - Examples from CHEMIX School program

1) FeS2+O2>Fe3O4+SO2

2) C3H8+O2>CO2+H2O and calculate the amount of CO2 and H2O formed if 2 grams of C3H8 (propane) reacts with O2.

3) C3H8+O2>CO2+H2O and calculate the amount of CO2 and H2O formed if 2 moles of C3H8 (propane) reacts with O2.

4) C3H8+O2>CO2+H2O and calculate the amount of CO2 and H2O formed if 5 grams of C3H8 (propane) reacts with 3 grams of O2.

5) C3H8+O2>CO2+H2O and calculate the amount of CO2 and H2O formed if C3H8 (propane) containing 2 grams of H reacts with 3 grams of O2.

6) As2S3+NaNO3+Na2CO3>Na3AsO4+Na2SO4+NaNO2+CO2 and calculate the amount of As2S3 used forming CO2 containing 10 grams of carbon.