Question

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

Answer 1

Mole concept gives the relationship between the number of moles, weight and molar mass of the compound.
-It is the most convenient method to express the amount of a substance
-Molar mass is calculated by adding up the atomic masses of the element combined to form a molecule.
Formula used:
$n=\dfrac{W}{M}$
where, $n$ is the number of moles, $W$ is the weight of the compound and $M$ is the molar mass of the compound.
Number of molecules $=6.023\times {{10}^{23}}\times$ moles

Complete step by step solution:
The number of moles is defined as the weight per molar mass. It is a unit of measurement which is used to express the amount of reactants and products in a chemical reaction.
In this question, a gaseous mixture of oxygen and nitrogen is in the ratio of $1:4$ by weight.
Molar mass of oxygen $({{O}_{2}})$ is $32$ and that of nitrogen $({{N}_{2}})$ is $28$ .
The molar ratio of oxygen $({{O}_{2}})$ : nitrogen $({{N}_{2}})$ will be:
$\dfrac{{{W}_{{{O}_{2}}}}}{{{M}_{{{O}_{2}}}}}:\dfrac{{{W}_{{{N}_{2}}}}}{{{M}_{{{N}_{2}}}}}$
Now, substituting the values in the above formula, we get,
The molar ratio of oxygen $({{O}_{2}})$ : nitrogen $({{N}_{2}})$ will be:
$\dfrac{1}{32}:\dfrac{4}{28}$
On further solving, we get,
$\Rightarrow \dfrac{1}{32}:\dfrac{1}{7}$
This is equation $(1)$
To calculate the number of moles, formula used is:
$n=\dfrac{W}{M}$
where, $n$ is the number of moles, $W$ is the weight of the compound and $M$ is the molar mass of the compound.
Now, applying this formula in equation $(1)$ , we get,
Ratio of their molecules:
$\Rightarrow \dfrac{6.023\times {{10}^{23}}}{32}:\dfrac{6.023\times {{10}^{23}}}{7}$
On further solving, the final ratio would be,
$\Rightarrow 7:32$
Therefore, the correct option is (C) $7:32$ .

Note:
-Avogadro’s number is defined as the proportionality factor that tells the relationship between the number of constituent particles with the amount of substance in a sample. Its SI unit is $mo{{l}^{-1}}$ . It is denoted with a symbol, ${{N}_{A}}$ .
${{N}_{A}}=6.023\times {{10}^{23}}mo{{l}^{-1}}$
-It is the number of units in a mole of any substance.