Question

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

Answer 1

Hint:In this question, we will be learning about how to calculate the number of moles of an individual molecule using the given ratio of the mixture. We will learn to find out the molecules ratio in the mixture.

Complete step by step answer:
As given in the question, let us find out the number of moles of the gas. This can be done using the formula we know; that is:
Number of moles of given gas(n) = $\dfrac{mass\ of\ the\ given\ gas(m)}{Molecular\ Mass(M)}$
Now, let us calculate the number of moles of the molecule that is given to us- ${O_2}$ and ${N_2}$separately
That is:
The number of moles of Oxygen Molecule is ${n_{{O_2}}}$ = $\dfrac{{{m_{{O_2}}}}}{{{M_{{O_2}}}}}$ .
And
The number of moles of Nitrogen Molecule is ${n_{{N_2}}}$ = $\dfrac{{{m_{{N_2}}}}}{{{M_{{N_2}}}}}$.
To find the ratio of their number of molecules we use:
\[ \Rightarrow \] $\dfrac{{{n_{{O_2}}}}}{{{n_{{N_2}}}}}$ = $\dfrac{{{m_{{O_2}}}}}{{{M_{{O_2}}}}}$$ \times $ $\dfrac{{{m_{{N_2}}}}}{{{M_{{N_2}}}}}$
Let us re-arrange the above values as follows:
$ \Rightarrow $ $\dfrac{{{m_{{O_2}}}}}{{{m_{{N_2}}}}}$$ \times $ $\dfrac{{{M_{{N_2}}}}}{{{M_{{O_2}}}}}$
= $\dfrac{1}{4}$$ \times $$\dfrac{{28}}{{32}}$
$ \Rightarrow $ $\dfrac{{{n_{{O_2}}}}}{{{n_{{N_2}}}}}$ = $\dfrac{7}{{32}}$

Hence, option B is correct.

Note:
The atomic mass (m) is the mass of a given particle: it is estimated in Daltons. Various atoms of a similar compound may have diverse sub-atomic masses since they contain various isotopes of a component. The related quantity relative sub-atomic mass, as characterized by IUPAC, is the proportion of the mass of a particle to the bound together atomic mass unit (otherwise called the Dalton) and is unit less.
The molar mass is characterized as the mass per unit measure of substance of a given chemical element. With regards to the meaning of the mole, the chemical element being referred to ought to consistently be determined. Generally this will be a perceived atom, molecule or ion, but any collection, or indeed fragment, of such species might be determined.