Question

A gaseous mixture contains oxygen and nitrogen in the ratio $1:4$ by weight. Therefore, the ratio of number of molecules is:
A.$1:4$
B.$1:8$
C.$7:32$
D.$3:16$

Answer 1

Hint:
Number of moles is equal to the ratio of mass and molar mass of the substance. The number of molecules is the product of the number of moles and Avogadro’s number.

Complete step by step answer:
Atomic mass of nitrogen $ = 14$
Since nitrogen is diatomic molecule in gaseous form
Therefore, the mass of ${N_2}$ molecule will be
$ = 14 \times 2$
$ = 28$
Atomic mass of oxygen$ = 16$
Since oxygen is diatomic molecule in gaseous form
Therefore, the mass of ${O_2}$ molecule will be
$ = 16 \times 2$
$ = 32$
Thus the mass of nitrogen and oxygen are $28$ and $32$ respectively.
In the gaseous mixture oxygen and nitrogen are present in the ratio $1:4$
From this we will find out the number of molecules of oxygen and nitrogen with the help of molar ratio.
Molar ratio helps to determine the number of moles of product that has been formed from a particular reactant and how much more number of moles are required to compete with other reactants.

Ratio of oxygen and nitrogen: $1:4$
Ratio of the atomic masses of oxygen and nitrogen will be $\dfrac{1}{{32}}:\dfrac{4}{{28}}$
Now ratio in terms of number of molecules will be: $\dfrac{{{N_A}}}{{32}}:\dfrac{{4{N_A}}}{{28}}$
As we know number of molecules given by the product of number of moles and Avogadro’s number,
Number of molecules $ = n \times {N_A}$
Where, $n = $ number of moles, ${N_A} = $ Avogadro's Number
Now number of molecules in the form of ratio will be: $\dfrac{{{N_A}}}{{32}}:\dfrac{{4{N_A}}}{{28}}$
Cross multiplying the ratios we get: $\dfrac{{28 \times {N_A}}}{{32 \times 4 \times {N_A}}}$
$ = \dfrac{7}{{32}}$
Therefore, the number of molecules of oxygen and nitrogen present in the gaseous mixture are in the ratio $7:32$ respectively.
So, the correct answer is option C) $7:32$ .

Note:In this Avogadro’s number is one mole of the substance which is equal to $6.023 \times {10^{23}}$ particles. Its unit depends on the nature of the substance and the character of the reaction. The molecular weight of the compound contains one mole of the molecule or one mole of atoms of that element.