Question

A gas mixture contains ${O_2}$ and ${N_2}$ in the ratio of 1:4 by weight. The ratio of their number of molecules is
(A) 1:8
(B) 1:4
(C) 3:16
(D) 7:32

Answer 1

Hint : One of the four basic states of matter is gas (the others being solid, liquid, and plasma). A pure gas can be made up of individual atoms (such as a noble gas like neon), elemental molecules (such as oxygen), or complex molecules (composed of a variety of atoms) (e.g. carbon dioxide). A gas mixture, such as air, consists of a number of different pure gases.

Complete Step By Step Answer:
Between the liquid and plasma phases, the gaseous state of matter exists, with the latter serving as the upper temperature barrier for gases. Degenerate quantum gases, which exist at the lower end of the temperature scale, are rising in popularity. High-density atomic gases that have been supercooled to extremely low temperatures are categorised as either Bose gases or Fermi gases based on their statistical behaviour. See the list of states of matter for a complete list of these unusual states of matter.
The chemical element oxygen has the symbol O, a mass number of 16, and an atomic number of 8. It is a highly reactive nonmetal and an oxidising agent that quickly produces oxides with most elements and other compounds. It belongs to the chalcogen group in the periodic table. By mass, oxygen is the third most plentiful element in the universe, behind hydrogen and helium. Two atoms of the element bond together at normal temperature and pressure to create dioxygen, a colourless and odourless diatomic gas with the formula ${O_2}$ .
Given the ratio according to the question is 1 : 4
As given, the ratio of moles of ${{\text{O}}_2}:{{\text{N}}_2} = \dfrac{1}{{32}}:\dfrac{4}{{28}} = \dfrac{1}{{32}}:\dfrac{1}{7}$
(As we know, mole $= \dfrac{{\text{w}}}{{\text{M}}}$ )
The ratio of number of molecules $= \dfrac{{{{\mathbf{N}}_{\text{A}}}}}{{32}}:\dfrac{{{{\mathbf{N}}_{\text{A}}}}}{7} = \dfrac{7}{{32}}:1 = 7:32$
Hence option D is correct.

Note :
Nitrogen is the lightest element in Periodic Group 15, often known as the pnictogens. It is a common element in the cosmos, with a total abundance estimated to be around eighth in the Milky Way and Solar System. Two atoms of the element bond together at ordinary temperature and pressure to create dinitrogen, a colourless and odourless diatomic gas with the formula ${N_2}$ .