Question

Find the number of oxygen molecules in $8\,g$ oxygen.

Answer 1

Hint: We know that Avogadro’s number is the number of atoms in one mole of any substance. The units of Avogadro’s number are electrons, atoms, ions, or molecules depending on the nature of the substance.
${\text{1}}\,{\text{mole = 6}}{\text{.022 X 1}}{{\text{0}}^{{\text{23}}}}\,{\text{unit}}$

Complete step by step answer:We know that the molecular weight of oxygen molecules is $32\,g/mol$.
Given,
The mass of oxygen is $8\,g$.
To find the number of molecules first, find the number of moles in the oxygen molecule.
The mole can be given by,
${\text{Mole = }}\dfrac{{{\text{weight}}}}{{{\text{Molecular}}\,{\text{weight}}}}$
\[{\text{Mole = }}\dfrac{{8\,\not g}}{{32\,\not g/mol}} = 0.25\,moles\]
The number of moles in the oxygen molecule is $0.25\,moles$.
Oxygen is molecule; the number of molecules in $0.25\,mol$ of oxygen is,
$Molecules\,of{\text{ }}\,{O_2} = \dfrac{{6.022 \times {{10}^{23}}\,molecules}}{{1\,mole\,{O_2}}} \times 0.25\,mol\,{O_2}$
\[Molecules\,of{\text{ }}\,{O_2} = 1.5 \times {10^{23}}\,molecules\]
$\therefore $ The number of molecules in $0.25\,mol$ of oxygen is ${\text{1}}{\text{.5 X 1}}{{\text{0}}^{{\text{23}}}}\,molecules{\text{.}}$

Additional note:
Concepts related to moles:
Molar Mass:
The atomic mass of an element in grams contains Avogadro’s number of atoms and is defined as the molar mass of that element. To find the molar mass, we have to change the units of atomic mass from the atomic mass unit to grams.
For example, sulfur has an atomic mass of $32\,amu$ so one mole of sulfur has a molar mass of $32\,g$ and contains Avogadro’s number of atoms.
Molar concentration:
Molar concentration is also called the molarity of the solution. The molarity of the solution is the number of moles per unit volume of the solution. The unit of molarity is $mol/Lit$.


Note:
We know that the oxygen molecule has two atoms. Thus, the number of moles in the oxygen atoms is $2 \times 0.25 = 0.5\,mole$
The number of atoms in an oxygen molecule can be calculated as,
${\text{Atoms }}\,{O_2} = \dfrac{{6.022 \times {{10}^{23}}\,atoms}}{{1\,mole\,{O_2}}} \times 0.5\,mol\,{O_2}$
${\text{Atoms }}\,{O_2} = 3.01 \times {10^{23}}\,atoms$
The number of atoms in an oxygen molecule is $3.01 \times {10^{23}}\,atoms$.