Balance the following equation by the oxidatoin number method.
`Cu+HNO_(3) to Cu(NO_(3))_(2)+NO_(2)+H_(2)O`

Explanation

Writing the oxidation number of all the atoms.
`overset(0)(Cu)+ overset(+1+5-2)(HNO_(3)) to overset(+2+5-2)(Cu(NO_(3))_(2))+overset(+4-2)(NO_(2))+overset(+1-2)(H_(2)O)`
Change in Ox. No. has occurred in copper and nitrogen,
`overset(0)(Cu) to overset(+2)(Cu)( NO_(3))_(2) ........(i)`
`Hoverset(+5)(NO_(3)) to overset(+4)(NO_(2)) .........(ii)`
Increase in Ox. no of copper =2 units per molecule Cu
Decrease in Ox. no. of nitrogen =1 unit per molecule `HNO_(3)`
To make increase and decrease equal, Eq. (ii) is multiplied by 2.
`Cu+2HNO_(3) to Cu(NO_(3))_(2)+2NO_(2)+H_(2)O`
Balancing nitrate ions, hydrogen and oxygen, the following equation is obtained
`Cu+4HNO_(3) to Cu(NO_(3))_(2)+2NO_(2)+2H_(2)O`
This is the balanced equation.