Balancing Chemical Equations

Balancing Chemical Equations Using The Algebraic Method



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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
How to balance the combustion of pentane.



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

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.

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



 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.

How to download CHEMIX School for balancing equations

For downloading CHEMIX School - simply click the download link at the top of this page. There is more to CHEMIX School than balancing chemical equations. Examples of other tools integrated in CHEMIX School chemistry program are: Molecular weight calculator, periodic table, solubility product calculator, balancing redox equations and much more. Try it.

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