Question

The oxidation number of carbon in ‘${{C}_{3}}{{O}_{2}}$’ and ‘$M{{g}_{2}}{{C}_{3}}$’ are respectively:
(a) $-\dfrac{4}{3},+\dfrac{4}{3}$
(b) $+\dfrac{4}{3},-\dfrac{4}{3}$
(c) $-\dfrac{2}{3},+\dfrac{2}{3}$
(d) $+\dfrac{2}{3},-\dfrac{2}{3}$

Answer 1

Hint: Both the molecules are neutral hence in ${{C}_{3}}{{O}_{2}}$ the sum of oxidation number of carbon and oxygen is taken zero and in $M{{g}_{2}}{{C}_{3}}$ the sum of oxidation number of carbon and magnesium is taken zero.

Complete step by step answer:
The oxidation number of an element is defined as the charge on an atom of the element that has in its ion or appears to have when present in the combined state with other atoms. We can call the oxidation number also as an oxidation state.
Some rules applied for the determination of oxidation number of an atom are:
The oxidation number of all the atoms of different elements in their respective elementary state and allotropic forms is always zero. For example, $He,{{N}_{2}},{{H}_{2}}$, etc.

In monatomic ions, the oxidation number is equal to the charge of the ion. For example, the oxidation number of $A{{l}^{3+}}$ ion is +3 and the oxidation number of ${{S}^{2-}}$ ion is -2.
In most of the compounds, the oxidation number of hydrogen is taken as +1. And in most of the compounds, the oxidation number of oxygen is taken as -2. The oxidation number of alkali metal ions is taken +1 and the oxidation number of halogen is taken -1.
In neutral molecules, the sum of the oxidation number of all atoms is zero.

In ${{C}_{3}}{{O}_{2}}$ the sum of the oxidation number of carbon and oxygen is taken zero.
$3x\text{ + 2(-2) = 0}$
$3x=+4$
$x=+\dfrac{4}{3}$

In ${{C}_{3}}{{O}_{2}}$, the oxidation number of carbon is $+\dfrac{4}{3}$
In $M{{g}_{2}}{{C}_{3}}$ the sum of the oxidation number of carbon and magnesium is taken zero.
$2(+2)\text{ + 3}x\text{ = 0}$
$3x=-4$
$x=-\dfrac{4}{3}$
In $M{{g}_{2}}{{C}_{3}}$, the oxidation number of carbon is $-\dfrac{4}{3}$
So, the correct answer is “Option B”.

Note: The oxidation number of magnesium is taken +2 because it belongs to group 2 of s-block. It mostly is in +2 with other atoms. If the molecule has some charge on the overall molecule, the sum of the oxidation numbers of all the atoms in the ion is always equal to the charge on the ion.