Question

5.6 L of oxygen gas at STP contains :
A. $6.02 \times {10^{23}}$ atoms
B. $3.01 \times {10^{23}}$ atoms
C. $1.505 \times {10^{23}}$ atoms
D. $0.7525 \times {10^{23}}$ atoms

Answer 1

Hint : The molar volume, symbol ${V_m}$ , of a material is the occupied volume divided by the amount of material at a certain temperature and pressure in chemistry and related sciences. It's calculated by dividing the molar mass (M) by the mass density ( $\rho$ ):
${V_{\text{m}}} = \dfrac{M}{\rho }$ .

Complete Step By Step Answer:
We know that the
Even one gram of a pure element is known to have a large number of atoms when dealing with particles at the atomic (or molecular) level. The mole notion is commonly employed in this context. It is primarily concerned with the mole,' which is a count of a vast number of particles.
The sum of the atomic masses of a compound's component atoms in g/mol is the compound's molar mass. Although there is no physical means to measure the number of moles in a chemical, we may use its molar mass as a direct conversion factor to connect its mass to the number of moles. The molar mass of a material can be used to convert between mass and number of moles. The number of moles may then be converted to atoms using Avogadro's number.
${\text{Number of moles = }}\dfrac{{{\text{Given Molar Volume}}}}{{{\text{STP Molar Volume}}}}$
Given Molar volume = 5.6 l
STP Molar volume = 22.4 L
Hence
${\text{Number of moles = }}\dfrac{{{\text{Given Molar Volume}}}}{{{\text{STP Molar Volume}}}} = \dfrac{{5.6}}{{22.4}} = \dfrac{1}{4}$
$\Rightarrow {\text{Number of moles = }}\dfrac{1}{4} = 0.25$
One oxygen gas element has two atoms of oxygen
So
${\text{Number of moles of Oxygen molecule = }}\dfrac{1}{4} = 0.25$
${\text{Number of moles of Oxygen atom = 2}} \times \dfrac{1}{4} = 0.5$
We also know that
${\text{Number of moles = }}\dfrac{{{\text{Given Number of Molecules}}}}{{{N_A}}}$
Hence
${\text{Number of moles }} \times {{\text{N}}_A}{\text{ = Given Number of Molecules}}$
${\text{Given Number of Molecules = 0}}{\text{.5 }} \times {\text{6}}{\text{.023 }} \times {\text{1}}{{\text{0}}^{23}}$
$\Rightarrow {\text{Given Number of Molecules = }}3.015{\text{ }} \times {\text{1}}{{\text{0}}^{23}}$ molecules
Hence option B is correct.

Note :
The physicist Jean Perrin invented the moniker Avogadro's number in 1909, defining it as the number of molecules in exactly 32 gram of oxygen. The purpose of this definition was to make the mass of a mole of a material, in gram, be numerically equivalent to the mass of one molecule relative to the mass of the hydrogen atom, which was supposed to be 1/16 of the atomic mass of oxygen due to the law of definite proportions.