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

Explanation

(i) The probable partial equations for the above reaction are :
`{:(HNO_(3)rarrH_(2)O+NO+[O]....("equation 1")),(Cu+OrarrCuO....("equation 2")),(Cu+HNO_(3)rarrCu(NO_(3))_(2)+H_(2)O....("equation 3")):}`
(ii) After balancing by hit and trial method, the balanced partial equations may be written as :
`{:(2HNO_(3)rarrH_(2)O+2NO+3O....("equation 1")),(Cu+OrarrCuO....("equation 2")),(CuO+2HNO_(3)rarrCu(NO_(3))_(2)+H_(2)O....("equation 3")):}`
(iii) Multiply equation 2 as well as equation 3 by 3 in order to cancel out O and CuO which donot appear in the final equation. Finally add the three partial equations to get the final equation
`{:(" "2HNO_(3)rarrH_(2)O+2NO+3O....("equation 1")),(" "Cu+OrarrCuO"]"xx3....("equation 2")),(" "Cu+2HNO_(3)rarrCu(NO_(3))_(2)+H_(2)O"]"xx3.....("equation 3")),(bar(3Cu+8HNO_(3)rarrCu(NO_(3))_(2)+2NO+4H_(2)O)):}`.