Balancing Redox Equations Using the Oxidation Number Method
Key Questions

You follow a series of steps in order.
For example, balance the equation
HNO₃ + H₃AsO₃(aq) → NO(g) + H₃AsO₄(aq) + H₂O(l)

Identify the oxidation number of every atom.
Left hand side: H= +1; N= +5; O = 2; As = +3
Right hand side: N = +2; O = 2; H = +1; As = +5 
Determine the change in oxidation number for each atom that changes.
N: +5 → +2; Change = 3
As: +3 → +5; Change = +2 
Make the total increase in oxidation number equal to the total decrease in oxidation number.
We need 2 atoms of N for every 3 atoms of As. This gives us total changes of 6 and +6. 
Place these numbers as coefficients in front of the formulas containing those atoms.
2HNO₃ + 3H₃AsO₃(aq) → 2NO(g) + 3H₃AsO₄(aq) + H₂O(l) 
Balance all remaining atoms other than H and O.
Done. 
Balance O.
Done. 
Balance H.
Done.
Now try to balance the equations in the link below (answers included).


There's no real difference between the oxidation number method and the halfreaction method.
They are just different ways of keeping track of the electrons transferred during the reaction.
The only surefire way to balance a redox equation is to recognize the oxidation part and the reduction part. Then you balance by making the electron loss equal the electron gain.
In the oxidation number method, you determine the oxidation numbers of all atoms. Then you multiply the atoms that have changed by small whole numbers.
You are making the total loss of electrons equal to the total gain of electrons. Then you balance the rest of the atoms.
In the halfreaction method, you determine the oxidation numbers and write two halfreactions. Then you multiply them by small whole numbers to make the loss and gain of electrons equal. Then you add the two half reactions together and balance the rest of the atoms.
In both methods, you must know what the oxidation numbers are and what they become during the reaction.
Sometimes one method is more convenient than the other method.
It's just one process and one method with variations. None of it will happen if you don't get the oxidation number of every player in the reaction.

The oxidation number method is a way of keeping track of electrons when balancing redox equations.
The general idea is that electrons are transferred between charged atoms.
Here's how the oxidation number method works for a very simple equation that you could probably balance in your head.
#"Zn" + "HCl" → "ZnCl"_2 + "H"_2# Step 1. Identify the atoms that change oxidation number
Left hand side:
#"Zn"# = 0;#"H"# = +1;#"Cl"# = 1
Right hand side:#"Zn"# = +2;#"Cl"# = 1;#"H"# = +1The changes in oxidation number are:
#"Zn"# : 0 → +2; Change = +2
#"H"# : +1 → 0; Change = 1Step 2. Equalize the changes in oxidation number
Each
#"Zn"# atom has lost two electrons, and each#"H"# atom has gained one electron.You need 2 atoms of
#"H"# for every 1 atom of#"Zn"# . This gives us total changes of +2 and 2.Step 3. Insert coefficients to get these numbers
#color(red)(1)"Zn" + color(red)(2)"HCl" → color(red)(1)"ZnCl"_2 + color(red)(1)"H"_2# The balanced equation is
#color(red)("Zn" + 2"HCl" → "ZnCl"_2 + "H"_2)#