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In GENERAL before one attempts to balance the masses in a chemical reaction is necessary to determine first if there is a change of OXIDATION state  (* ) from the reactants to the product of the reaction..If there is a change the total units of oxidation-reduction must be first balanced before balancing the mass.

In this case :   N2 + H2 = NH3   N2 is in the 0 oxidation state ( uncombined) and as a product in NH3

is in the -3 oxidation state ( because it is combined with 3H+) this means  there is a reduction of 3 units per N atom  and a total of 6 for the 2 atoms reacting.. now H is in the 0 oxidation state also and is oxidized to the +1 state in the product NH3 and since there are 2 of them the total oxidation units are2.

  A reaction requires the number of oxidation units to be equal to the reduction units. We can obtain this by using 3 molecules of H . If we use 3H2,the equation will be balanced in redox units.

 

 

              N2+ 3H2  = NH3

 

Now the mass balance.

There are 2 N on the left and only one on the right. a coefficient of 2 for NH3 will satisfy the mass requirements  ( 2N,left; 2N right; 6H left; 6H right )

 

                                    N2 + 3H2  = 2 NH3