Balance the following equations by oxidation number method.
`K_(2) Cr_(2) O_(7) +FeSO_(4) + H_(2)SO_(4) rarrK_(2) SO_(4) +Cr_(2) (SO_(4))_(3) + Fe_(2) (SO_(4))_(3) + H_(2)O`

Explanation

Step-1`:` To find out atoms undergoing change in oxidation.
`overset(+1)(K_(2))overset( + 6) ( Cr_(2)) overset( -2) ( o_(7)) + overset( +1)(H_(2)) overset(+6)(S) overset(-2)(O_(4)) +overset( +2) ( Fe)overset( + 6) ( S) overset( -2)(O_(4)) rarr overset( + 1) ( K_(2)) overset( + 6) ( S) overset( -2) ( O_(4))+overset( +3)(Cr_(2))overset(+6-2)((SO_(4))_(3))O+overset( +1-2)(H_(2)O)`
Step-2`:` To find out total increase and decrease in oxidation.
`K_(2) overset( +6)(Cr_(2)) O_(7) rarr overset( + 3) ( Cr_(2)) ( SO_(4))_(3)` ( Decrease of 3 unit `//` atom , 6 unit `//` 2 atoms )
Total decrease = 6 units
`overset(+2)(Fe_(2) SO_(4)) rarr overset( +3)( Fe_(2))(SO_(4))_(3)`( increase of 1 unit `//` atom )
Total increase `1 xx 6 = 6`
Step-3`:` To balance the total increase and total decrease, multiply `FeSO_(4)` by 6.
`K_(2)Cr_(2) O_(7) + 6FeSO_(4) + H_(2) SO_(4) rarr K_(2) SO_(4) + Fe_(2) ( SO_(4))_(2) + Cr_(2) ( SO_(4))_(3) + H_(2) O`
Step-4 `:` Balance all atoms other than .H. and .O.
Since Fe is oxidised (LHS) to `Fe^(+3)` ( RHS) balance `Fe_(2) (SO_(4))_(3)` balance Fe is oxidised ( LHS) to `Fe^(+3)` ( RHS) balance `Fe_(2) ( SO_(4))_(3)` by multiplying by 3.
Now the equation becomes,
`K_(2)Cr_(2) O_(7) + 6FeSO_(4) + H_(2) SO_(4) rarr K_(2) SO_(4) + Cr_(2) ( SO_(4))_(3) + 3Fe_(2) ( SO_(4))_(3) + H_(2) O`
The sulphur atoms in `SO_(4)^(-2)` radical does not undergo any change in O.N. There are 7,`SO_(4)^(-2)` radicals in LHS and 13, `SO_(4)^(_3)` radicals in RHS. To balance them, multiply `H_(2)SO_(4)` in LHS by 7. The equation now becomes
`K_(2)Cr_(2) O_(7) + 6FeSO_(4) + 7 H_(2) SO_(4) rarr K_(2) SO_(4) + Cr_(2) ( SO_(4))_(3) + 3Fe_(2) ( SO_(4))_(3) + H_(2) O`
To balance, .H. atoms multiply `H_(2) O` molecules in RHS by 7.
`K_(2)Cr_(2) O_(7) + 6FeSO_(4) + 7 H_(2) SO_(4) rarr K_(2) SO_(4) + Cr_(2) ( SO_(4))_(3) + 3Fe_(2) ( SO_(4))_(3) + 7H_(2) O`
This is the balanced equation.