Question

What is the number of molecules present in $0.5$ mole of hydrogen?
A) $3.011 \times {10^{22}}\;{\rm{molecules}}$
B) $3.011 \times {10^{23}}\;{\rm{molecules}}$
C) $3.011 \times {10^{20}}\;{\rm{molecules}}$
D) $6.022 \times {10^{23}}\;{\rm{molecules}}$

Answer 1

Hint: The number of molecules of any given species can be calculated or evaluated with the help of the Avogadro’s number that is $6.022 \times {10^{23}}\;{\rm{atom/mol}}$. The Avogadro’s number can be represented by using the symbol which is depicted as ${{\rm{N}}_{\rm{A}}}$.

Complete answer:
We know that, ${\rm{1}}\;{\rm{mol}}$ of any known compound is usually equivalent to the Avogadro’s number that is $6.022 \times {10^{23}}\;{\rm{molecules}}$. The number of molecules of the given species can be identified via respective moles of that species and the Avogadro’s constant. The Avogadro constant can be proposed by the renowned scientist named Josef Loschmidt in 1865. The unit of Avogadro constant is usually represented as atom/mol.
So, for calculating the molecules present in ${\rm{0}}{\rm{.5}}\;{\rm{mol}}$ of hydrogen is shown below.
${\rm{Number}}\;{\rm{of}}\;{\rm{molecules}} = {\rm{Number}}\;{\rm{of}}\;{\rm{moles}} \times {\rm{Avogadro's}}\;{\rm{Number}}$
Substitute the respective values in the above equation.
$1\;{\rm{mol}} = 6.022 \times {10^{23}}\;{\rm{molecules}}\\
{\rm{0}}{\rm{.5}}\;{\rm{mol}} = 0.5 \times 6.022 \times {10^{23}}\;{\rm{molecules}}\\
{\rm{ = 3}}{\rm{.011}} \times {\rm{1}}{{\rm{0}}^{23}}\;{\rm{molecules}}$

Hence, the correct choice for ${\rm{0}}{\rm{.5}}\;{\rm{mol}}$ of hydrogen is B that is $3.011 \times {10^{23}}\;{\rm{molecules}}$.

Note: The number of molecules can be determined through the mole of that species and the Avogadro’s number. The multiplication of both the quantity will be resultant in the molecules of species.