Question

Calculate the moles, molecules, and total number of atoms in $1.1 \times {10^{ - 4}}$ kg of carbon dioxide ( $C{O_2}$ )
(Given $C = 12$ , $O = 16$ , $N = 14$ , $H = 1,He = 4$ )

Answer 1

The mole is represented by Avogadro’s number, which is $6.022 \times {10^{23}}$ atoms or molecules per mol.
-To convert from moles to molecules, multiply the molar amount by Avogadro’s number.
-To convert from molecules to atoms, multiply the number of molecules by the atomicity of the atom.

Complete answer:
Given ,
Mass of $C{O_2} = 1.1 \times {10^{ - 4}}Kg$
Molar mass of $C{O_2} = 12 + 32$
$= 44g/mol$
$= 44 \times {10^{ - 3}}kg/mol$
(i) Number of moles (n) $= \dfrac{given\,\,mass\,\,of\,\,C{O_2}}{molar\,\,mass\,\,of\,\,C{O_2}}$ ​​
$= 1.1 \times {10^{ - 4}}Kg/44 \times {10^{ - 4}}Kg$
$n = 2.5 \times {10^{ - 3}}mol$
(ii) Number of molecules of ​ $C{O_2}\, =$ n $\times$ Avogadro's number
$= 2.5 \times {10^{ - 3}} \times 6.022 \times {10^{23}}$
$= 1.5 \times {10^{21}}$ molecules
(iii) Number of atoms present $=$ no. of molecules $\times$ atomicity
$= 1.5 \times {10^{21}} \times 3$
$= 4.5 \times {10^{21}}$ atoms
$C{O_2}$ is triatomic, hence multiplied by $3$ .

Note:
Avogadro’s number is typically dimensionless, but when it defines the mole, it can be expressed as $6.022 \times {10^{23}}$ elementary entities/mol. This form shows the role of Avogadro’s number as a conversion factor between the number of entities and the number of moles. Therefore, given the relationship 1 mol $=$ $6.022 \times {10^{23}}$ atoms, converting between moles and atoms of a substance becomes a simple dimensional analysis problem.