Question

Which has the maximum number of molecules among the following?
A) $44gC{O}_2$
B) $48g{O}_3$
C) $8g{H}_2$
D) $64gS{O}_2$

Answer 1

Hint:As we know that one mole of a substance is defined as the amount of a substance that contains as many particles or entities as there are atoms in exactly $12g$ of the carbon atoms and it is also equivalent to the ratio of number of atoms or molecules to the Avogadro’s number.

Complete answer:
As we know that the number of moles is the ratio of the given mass to the molecular mass of the substance which in turn is equivalent to the ratio of number of molecules to the Avogadro’s number. Therefore, we can write it as:
$moles={\displaystyle \frac{givenmass}{molecularmass}}={\displaystyle \frac{no.ofmolecules}{N_A}}$
So, using the above formula we can easily calculate the number of molecules of every given substance.
The first one is $44gC{O}_2$, so we are given a mass of carbon dioxide as $44g$ and we know that the molecular mass of carbon dioxide is also $44g$. Therefore the number of molecules will be calculated as:
$$\begin{gathered} \Rightarrow {\displaystyle \frac{44}{44}}={\displaystyle \frac{no.ofmolecules}{N_A}} \\ \Rightarrow 1\times N_A=no.ofmolecules \end{gathered}$$
Similarly, we can calculate the number of molecules in $48g{O}_3$ and we know that molecular mass of three atoms of oxygen is also $48g$, so:
$$\begin{gathered} \Rightarrow {\displaystyle \frac{48}{48}}={\displaystyle \frac{no.ofmolecules}{N_A}} \\ \Rightarrow 1\times N_A=no.ofmolecules \end{gathered}$$
Then we have $8g{H}_2$, we know that the molecular mass of two hydrogen atoms is $2g$ and the given mass is $8g$, hence the number of molecules will be equivalent to:
$$\begin{gathered} \Rightarrow {\displaystyle \frac{8}{2}}={\displaystyle \frac{no.ofmolecules}{N_A}} \\ \Rightarrow 4\times N_A=no.ofmolecules \end{gathered}$$
Lastly we have $64gS{O}_2$ and the molecular mass of sulphur dioxide is again $64g$, so the number of molecules will be:
$$\begin{gathered} \Rightarrow {\displaystyle \frac{64}{64}}={\displaystyle \frac{no.ofmolecules}{N_A}} \\ \Rightarrow 1\times N_A=no.ofmolecules \end{gathered}$$
Therefore, hydrogen contains the maximum number of molecules.

Hence from the above calculation and explanation we can say that the correct answer is (C).

Note:As we know that hydrogen is the simplest molecule in the periodic table containing only two protons and two electrons. It is a colourless, odourless and flammable gaseous substance and it burns with oxygen to form water molecules.