Question

Loschmidt number is equal to:
$(a)$ Molecules present in 2ml of gas at STP
$(b)\text{ 2}\text{.69}\times \text{1}{\text{0}}^{19}$ Molecules of gas
$(c)\text{ 4}\text{.46}\times {10}^{-5}$Mole of gas
$(d)$ Both B and C

Answer 1

Hint – In this question use the concept that Loschmidt number is simply a constant that defines a unit of number density for substances mainly gases. Use the basic definition of Loschmidt distance to get the right option.

Complete answer:

Being a measure of number density, the Loschmidt constant is used to define the amagat, a practical unit of number density for gases and other substances:
Now the Loschmidt constant is exactly 1 amagat.
And 1 amagat = n0 = $$2.6867811\times {10}^{25}{m}^{-3}$$.
Which is approximately equal to $$2.69\times {10}^{25}{m}^{-3}$$
Loschmidt number: The number of molecules in one cubic centimeter of an ideal gas at standard temperature and pressure is equal to $2.69\times {10}^{19}$ molecules of gas or $4.46\times {10}^{-5}$ mole of gas.
As we know that Avogadro number = $6.023\times {10}^{23}$
So Loschmidt number = ${\displaystyle \frac{\text{molecules of gas}}{\text{Avagadro number}}}={\displaystyle \frac{2.69\times {10}^{19}}{6.023\times {10}^{23}}}=4.46\times {10}^{-5}\text{ mole of gas}$.
So this is the required answer.
Hence option (D) is the correct answer.

Note – It is required to have a good understanding of Avogadro's number, it is a proportion that relates molar mass on an atomic scale to physical mass on human scale or in other words it is the number of elementary particles that can be molecules, atoms or compounds per mole of a substance.