Question

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1:4.The ratio of number of their molecules is:
A.1:8
B. 3:16
C. 1:4
D. 7:32

Answer 1

Hint: The molar mass is calculated by the sum of individual atomic masses of each atom present in the molecule and further mole concept can be used for solving the problem. Number of moles can be determined by dividing given mass with the molar mass of molecules. Then, the number of molecules can be determined by multiplying the number of moles obtained with Avogadro’s Number which is equal to $6.022\times{ 1}{{\text{0}}^{23}}$.

Complete step by step answer:
Now in the given question, we have been given the ratio of masses of two gases which are oxygen and nitrogen respectively.
So the ratio is 1:4, so to find the number of molecules:
We should also remember here that the moles ratio= molecular ratio.
The mass of nitrogen in the mixture=4w
The mass of oxygen in the mixture= w
Now, we need to calculate the number if moles, which is given by the formula:$\dfrac{\text{Given Weight}}{\text{Molecular Weight}}$

So, molar mass of nitrogen is : 28g/mol
And molar mass of oxygen is : 32g/mol
Now the number of moles of nitrogen is : 4w/28 moles
And the number of moles of oxygen is : w/32 moles
So in order to find the number of molecules, we need to multiply the number of moles by the avogadro's number.
But first let's learn the definition of avogadro's number:
It is defined as one mole of any substance equal to $\text{6}\text{.023 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{23}}}$
${{\text{N}}_{\text{A}}}$ = $\text{6}\text{.023 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{23}}}$ /mol

So, Molecules of ${{N}_{2}}=\dfrac{4w}{28}\text{x }{{\text{N}}_{\text{A}}}$

Molecules of ${{O}_{2}}=\dfrac{w}{32}\text{x }{{\text{N}}_{\text{A}}}$
Now, taking the ratio of oxygen to nitrogen molecules=$\dfrac{\dfrac{w}{32}\text{x }{{\text{N}}_{a}}}{\dfrac{4w}{28}\text{x }{{\text{N}}_{a}}}=7:32$
Hence the ratio we get is 7:32

Therefore the correct answer is option D.

Note: It's very important here to clarify our doubt of why we are not taking 16 gm/mol and 14 gm/mol as the molar masses of oxygen and nitrogen respectively. This is so because one molecule of both these gases has two atoms each and both individual masses must be considered to calculate their molar mass, so we should be careful while carrying out this calculation.