Question

What are the equivalent volumes of hydrogen, oxygen and nitrogen ?

Answer 1

Hint: In order to answer this question, it is necessary to know what is the condition of NTP and what is the actual meaning when we use the term equivalent volume and equivalent mass. The valency and the N-factor also play an important role here in order to calculate the amount of equivalent volumes of the given species.

Complete answer:
Equivalent volume is defined as the volume occupied by the one equivalent of the gas at NTP. Now, in order to answer the following, we need to understand what is meant by the equivalent of gas. Mathematically, it is defined as:
$equivalent = \dfrac{{number{\text{ }}of{\text{ }}moles}}{{n - factor}}$
Here, n-factor means the valency factor, i.e. the number of moles of electrons a particular element will gain or lose in any redox reaction.
For the gaseous atoms given:
$H \to {H^ + } + {e^ - }{\text{ n - factor = 1}}$
$O + 2{e^ - } \to {O^{ - 2}}{\text{ n - factor = 2}}$
$N + 3{e^ - } \to {N^{ - 3}}{\text{ n - factor = 3}}$
Now, after understanding the concept and relation between the n-factor, equivalent and number of moles; we can find out the equivalent volume.
At NTP, the volume of one mole of any gas is $22.4l$
Since in equivalent volume, we take the volume of one mole of atom. Hence, the volume of one mole of any diatomic gas$ = \dfrac{{22.4}}{2} = 11.2l$
Hence, using the equation : $equivalent{\text{ }}volume = \dfrac{{volume{\text{ }}of{\text{ 1mole }}of{\text{ }}gas}}{{n - factor}}$
Hence, for hydrogen$ = \dfrac{{11.2}}{1} = 11.2l$
For oxygen$ = \dfrac{{11.2}}{2} = 5.6l$
For nitrogen$ = \dfrac{{11.2}}{3} = 3.73l$

Note:
There are certain areas where students tend to make mistakes if the conditions and requirements of certain definitions like n-factor, equivalent mass, equivalent volume, etc are not known. Pertaining to this question, one should keep in mind that the volume occupied by the one mole of atoms of a diatomic gas is equal to $11.2l$.