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

Hint: 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.