Calculate the oxidation number of `(i) C " in "CH_(4) ,(ii) Mn " in" KMnO_(4) , (iii)Cr" in " K_(2)Cr_(2)O_(7), (iv) P" in " H_(3)PO_(4) , (v) N " in " HNO_(3)`

Explanation

(i) `C` in `CH_(4)`
Let the oxidation number of `C` in `CH_(4)` be `x`
Write the oxidation number of each atom above its symbol
`overset(x)Coverset(+1)H_(4)`
Calculate the sum of the oxidation numbers of all the atoms
`x+4(+1)`
Since `CH_(4)` is a neutral molecule the sum of oxiation numbers must be zero.
`therefore " " x+4=0or x=-4`

(ii) `Mn` in ` KMnO_(4)`
Let the oxidation number of `Mn` in `KMnO_(4)` be `x`.
Write the oxidation number of each atom above its symbol
`overset(+1)K overset(x)Mn overset(-2)O_4`
Calculate the sum of the oxidation numbers of all the atoms
`+1+x+4(-2)=1+x-8=x-7`
Since `KMnO_(4)` is a neutral molecule, the sum of the oxidation numbers must be zero.
`x-7=0 or x=+7`

(iii) `Cr` in `K_(2)Cr_(2)O_(7)`
Let the oxidation number of `Cr` in `K_(2)Cr_(2)O_(7)` be `x`
Write the oxidation number of each atom above its symbol
`overset(+1)K_(2)overset(x)Cr_(2)overset(-2)O_(7)`
Calculate the sum of the oxidation memebers of the atoms
`2(+1)+2(x)+7(-2)=2+2x-14=2x-12`
Since `K_(2)Cr_(2)O_(7)` is a neutral molecule , the sum of the oxidation numbers must be zero.
`therefore " " 2x-12=0 " " or " " x=12//2=6`

(iv) `P` in `H_(3)PO_(4)`
Let the oxidation number of `P` in `H_(3)PO_(4)` be `x`
Write the oxidation numbers of each atom above its symbol
`overset(+1)H_(3) overset(x)P overset(-2)O_(4)`
Calculate the sum of the oxisdation numbers of all the atoms
`3(+1)+x+4(-2)=3+x-8=x-5`
Since `H_(3)PO_(4)` is a neutral molecule, the sum of the oxidation numbers must be zero.
`therefore` `x-5=0 or x=+5`

(v) `N` in `HNO_(3)`
Let the oxidation number of `N` in `HNO_(3)` be `x`
Write the oxidation numbers of each atom above its symbol.
`overset(+1)H overset(x)N overset(-2)O_(3)`
Calculate the oxidation numbers of all the atoms
`+1+x+3(-2)=1+x-6=x-5`
Since `HNO_(3)` is a neutral molecule, the sum of the oxidation numbers must be zero
`x-5=0 or x=+5`