Question

What would be the number of atoms in $20g$ of $S{O_3}$ approximately?
A) $1 \times {10^{23}}$
B) $1.5 \times {10^{23}}$
C) $2 \times {10^{23}}$
D) $6 \times {10^{23}}$

Answer 1

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.

Formula used:
$moles = \dfrac{{mass}}{{molecular\;mass}} = \dfrac{{no.\;of atoms}}{{{N_A}}}$

Complete solution:
As we know that the sulphur trioxide is a chemical compound which is produced on the reaction between the sulphur trioxide and oxygen. Sulphur trioxide is the primary agent found in the acid rain and is a significant pollutant. We also 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 the number of molecules or atoms to the Avogadro’s number. Therefore, we can write it as:
$moles = \dfrac{{mass}}{{molecular\;mass}} = \dfrac{{no.\;of atoms}}{{{N_A}}}$
So, using the above formula we can easily calculate the number of atoms of every given substance. For that we can either calculate the number of moles of sulphur trioxide first or we can directly use the mass and molecular mass ratio of the sulphur trioxide to calculate the number of atoms present.
Now, we are given a mass of sulphur trioxide which is $20g$and we know that the molecular mass of sulphur trioxide which is $80g$. Therefore, the number of atoms will be calculated as:
$\dfrac{{mass}}{{molecular\;mass}} = \dfrac{{no.\;of atoms}}{{{N_A}}}$
$\Rightarrow no.\;of atoms = \dfrac{{20 \times 6.022 \times {{10}^{23}}}}{{80}}$
$\Rightarrow no.\;of\;atoms = 1.5055 \times {10^{23}}$

Therefore, from the above explanation we can say that the correct answer is (B).

Note: Always remember and learn the below given formula $moles = \dfrac{{mass}}{{molecular\;mass}} = \dfrac{{no.\;of atoms}}{{{N_A}}} = \dfrac{{no.\;of\;molecules}}{{{N_A}}} = \dfrac{{volume\;at\;STP}}{{22.4\;l}}$
We can calculate the unknown parameter when some of the parameters are given. We can first calculate the moles of the given substance and then calculate the mass, volume or number of atoms as well as number of molecules present in that substance.