Question

How many atoms are present in $1\,mole$ of $N{a_3}P{O_4}\,?$
(i) $4.72 \times {10^{24}}\,atoms$
(ii) $4.82 \times {10^{24}}\,atoms$
(iii) $4.82 \times {10^{23}}\,atoms$
(iv) $4.72 \times {10^{23}}\,atoms$

Answer 1

Hint:For calculating the number of atoms present in $1\,mole$ of $N{a_3}P{O_4}$ you must use the fact that $1\,mole$ of any substance contains $6.022 \times {10^{23}}$atoms, molecules or formula units of the substance. Since $N{a_3}P{O_4}$ is an ionic compound $1\,mole$ of $N{a_3}P{O_4}$ will contain $6.022 \times {10^{23}}$ formula units of $N{a_3}P{O_4}$. Calculate the number of atoms present per formula unit of $N{a_3}P{O_4}$ and hence calculate the number of atoms present in one mole.

Complete solution:
We know, per mole of any substance contains Avogadro's number $\left( {6.022 \times {{10}^{23}}} \right)$ of atoms, molecules or formula units of the substance.
Since $N{a_3}P{O_4}$ is an ionic compound, $1\,mole$ of $N{a_3}P{O_4}$ will contain $6.022 \times {10^{23}}$ formula units of $N{a_3}P{O_4}$.
Now we need to calculate the number of atoms present in one formula unit of $N{a_3}P{O_4}$.
The chemical formula is $N{a_3}P{O_4}$ hence one formula unit contains $3$ atoms of $Na$, $1$ atom of $P$ and $4$atoms of $O$.
Therefore the total number of atoms in one formula unit of $N{a_3}P{O_4}$ $ = \,\,(\,$Number of atoms of $Na\,) + \,(\,$Number of atoms of $P\,) + \,(\,$Number of atoms of $O\,)$
$ = \,\left( {3 + 1 + 4} \right)\,\, = \,\,8$
Hence one formula unit of $N{a_3}P{O_4}$ contains $8$ atoms.
Now, one mole of $N{a_3}P{O_4}$ contains $6.022 \times {10^{23}}$ formula units of $N{a_3}P{O_4}$.
$ \Rightarrow $ One mole of $N{a_3}P{O_4}$ will contain $6.022 \times {10^{23}}\,formula\,\,units\, \times \,\dfrac{{8\,atoms}}{{1\,formula\,\,unit}}$ of $N{a_3}P{O_4}$.
$ \Rightarrow $ One mole of $N{a_3}P{O_4}$ will contain $4.8176 \times {10^{24\,}}\,atoms$ of $N{a_3}P{O_4}$.
So one mole of $N{a_3}P{O_4}$ will contain $4.82 \times {10^{24}}\,atoms$of $N{a_3}P{O_4}$.

Hence the correct answer is (ii) $4.82 \times {10^{24}}\,atoms$.

Note:We must remember a mole of a substance always contains $6.022 \times {10^{23}}$ particles called the Avogadro’s number. Also do not forget that the given molecule is ionic hence we used the concept of formula units. Make sure to calculate the number of atoms present in one formula unit only.