Question

There are$20$ drops in $2$ ml of a liquid. Number of molecules present in $1$ drops of the liquid is (Gram Molecular mass of liquid=$40$ and d =$1\,\,g\,m{L^{ - 1}}$, ${N_A}$= Avogadro number)
A.$\dfrac{{{N_A}}}{{{{(20)}^2}}}$
B.$\dfrac{{{{(20)}^2}}}{{{N_A}}}$
C.${(20)^2}\,{N_A}$
D.None of these

Answer 1

In this question, we have to find the number of molecules present in $1$ drop of the liquid. This can be calculated with the help of Avogadro numbers. The number of molecules present in one mole of substances is $6.023\, \times \,{10^{23}}$ particles i.e. it can be ion, atom or molecules. This number $6.023\, \times \,{10^{23}}$is known as Avogadro’s number denoted by ${N_A}$ .
Formula used –
Number of moles = $\,\dfrac{{Given\,\,mass\,(g)}}{{Molecular\,mass\,\,(g\,mo{l^{ - 1}})}}$

Complete answer:
We know that the number of moles of a substance is defined as the ratio of the given mass of the substance to the molecular mass of that particular substance.
Number of moles = $\,\dfrac{{Given\,\,mass\,(g)}}{{Molecular\,mass\,\,(g\,mo{l^{ - 1}})}}$
Also, the number of molecules present in one mole of a substance is $6.023\, \times \,{10^{23}}$ particles of that substance. In order to find the number of molecules present in $1$ drop of the liquid. First, we will calculate the number of moles of that liquid present in$2$ml of the liquid. And it is given that $2$ml of the liquid contains $20$ drops of the liquid.
Volume of $20$ drops of liquid =$2$ml
Volume of $1$ drop of liquid = ml
It is given that density is equal to $1\,\,g\,m{L^{ - 1}}$ which indicates that the volume of the liquid is equal to the mass of that liquid.
So, given mass of liquid =$\dfrac{1}{{10}}$ml
Gram Molecular mass of the liquid =$40$g
We know that,
Number of moles = $\,\dfrac{{Given\,\,mass\,(g)}}{{Molecular\,mass\,\,(g\,mo{l^{ - 1}})}}$
Number of moles of the liquid = $\dfrac{1}{{10\, \times \,40}}$
Number of moles of the liquid = $\dfrac{1}{{\,400}}$
Number of moles of the liquid = $\dfrac{1}{{\,{{(20)}^2}}}$
We know that, Number of molecules of liquid =number of moles of liquid $\times$Avogadro number (${N_A}$)
Number of molecules of liquid =$\dfrac{1}{{\,{{(20)}^2}}}\, \times \,{N_A}$
Number of molecules of liquid = $\dfrac{{{N_A}}}{{\,{{(20)}^2}}}$
Hence, the correct answer is option (A).

Note:
The Avogadro number can be used to indicate the number of molecules, ions or atoms depending upon the nature of substances. It is a dimensionless quantity. The Avogadro’s number of particles i.e. ion, molecules or atoms are present in one mole of substances.