Balance the following chemical equation by partial equation method.
`Cu+HNO_(3)rarrCu(NO_(3))_(2)+NO+H_(2)O`

Explanation

Write the oxidation number of all the atoms.
`{:(0,,+1+5+2,,+2+5-2,,+4-2,,+1-2),(Cu,+,HNO_(3),rarr,Cu(NO_(3))_(2),+,NO_(2),+,H_(2)O):}`
There is change in oxidation number of Cu and N.
`{:(overset(0)Curarroverset(+2+5-2)(Cu(NO_(3))_(2))," .........................(1) (Oxidation number of Cu is increased by 2)"),(overset(+5)(HNO_(3))rarroverset(+4)(NO_(2))," .........................(2) (Oxidation number of N is decreased by 1)"):}`
To make increase and decrease equal, eq. (2) is multipled by 2.
`Cu+2HNO_(3)rarrCu(NO_(3))_(2)+2NO_(2)+H_(2)O`
Balancing nitrates ions, hydrogen and oxygen, the following equation is obtained.
`Cu+4HNO_(3)rarrCu(NO_(3))_(2)+2NO_(2)+2H_(2)O`
This is balanced equation.