Question

\[4.4{\text{ g}}\]of \[C{O_2}\] ​ and \[{\text{2}}{\text{.24 litre}} \]of \[{H_2}\] ​ at STP are mixed in a container. The total number of molecules present in the container will be:

Answer 1

Hint: In this question, we have to calculate the number of moles of $C{O_2}$ and ${H_2}$. Then, we use Avogadro's number which represents the number of atoms/molecules present in one mole of the substance to find the molecules in the container.
Formula used: ${\text{No}}{\text{. of moles = }}\dfrac{{{\text{Mass of the Substance in grams}}}}{{{\text{Molar mass of a Substance}}}}$

Complete step by step answer:
Molar mass of \[C{O_{2}}\]\[ = 44{\text{g}}\]
No. of moles of \[C{O_2}\] in \[4.4{\text{ g}}\;\]\[C{O_{2}} = \dfrac{{4.4}}{{44}} = 0.1\;{\text{mole}}\].
No. of moles of \[{H_2}\] ​ gas in \[2.24{\text{L}}\]at STP=\[\dfrac{{2.24}}{{22.4}} = {\text{ }}0.1{\text{ mole}}\]
So total moles of \[{H_2}\]​ and \[C{O_2}\]gas are \[ = \left( {0.1 + 0.1} \right) = 0.2{\text{ moles}}{\text{.}}\]
$\therefore $Total number of Molecules in the container=\[0.2 \times 6.022 \times {10^{23}} = 1.2044 \times {10^{23}}\]

Note:
 The concept that a mole of any substance contains the same number of particles was formed out of research which was conducted by Italian physicist Amedeo Avogadro. Avogadro constant can be defined as the number of molecules, atoms, or ions in one mole of a substance: $6.022 \times {10^{23}}$ per mol. It is derived from the number of atoms of the pure isotope $^{{\text{12}}}{\text{C}}$in 12 grams of that substance and is the reciprocal of atomic mass in grams. Now the mole concept can be applied to ions and formula units.
 1 mole of \[{O_2}\]means Avogadro's number of oxygen molecules and it will be equal to 2 times Avogadro's number of oxygen atoms.
1 g-molecule of \[{O_2}\] is the same as one mole of the oxygen molecule and contains Avogadro's number of nitrogen molecules and twice this number of atoms.
1 g-atom of Nitrogen means 1 mole of nitrogen atoms and contains Avogadro's number of nitrogen atoms. The mass of 1 mole of any species is equal to its molar mass.