Question

Calculate the mass of $N{a_2}S{O_4}.7{H_2}O$ that contains $6.02 \times {10^{22}}$ atoms of oxygen?

Answer 1

Hint: To know the mass of the given compound, $N{a_2}S{O_4}.7{H_2}O$ that contains $6.02 \times {10^{22}}$ atoms of oxygen, first we will find the number of moles then we will find the molar mass of the given compound.

Complete step by step answer:
Given Molecular Formula = $N{a_2}S{O_4}.7{H_2}O$
$\therefore (4 + 7)$ 0 atoms in each molecule.
Given that-
Number of 0 atoms $(N)$ = $6.02 \times {10^{22}}$
Number of moles of 0 atoms $({n_1})$ $ = \dfrac{N}{{{N_A}}} = \dfrac{{6.02 \times {{10}^{22}}}}{{6.02 \times {{10}^{23}}}} = 0.1mole$
Now, Moles of $N{a_2}S{O_4}.7{H_2}O$ , $(n) = \dfrac{{{n_1}}}{{11}} = \dfrac{{0.1}}{{11}} = \dfrac{1}{{110}}mole$
So, Molar mass of $N{a_2}S{O_4}.7{H_2}O$ $(M) = 268g/mol$
$\therefore $ Mass of $\dfrac{1}{{110}}mole$
$ = n \times M \\
   = \dfrac{1}{{110}} \times 268 \\
   = 2.436g \\
$

Hence, the mass of $N{a_2}S{O_4}.7{H_2}O$ that contains $6.02 \times {10^{22}}$ atoms of oxygen is $2.436g$ .

Note: The mass of a given substance (chemical element or chemical compound in g) divided by its amount of substance. Chemists can measure a quantity of matter using mass, but in chemical reactions it is often important to consider the number of atoms of each element present in each sample.