Question

Calculate the number of atoms in each of the following.
(I) 52 moles of Ar
(II) 52u of He
(III) 52g of He

Answer 1

Hint- Before calculating the numbers of atoms in the given amount of element, we will first see how the numbers of atoms are related with the mass in amu, grams, moles etc. to get the required relation. Also one mole of any atom contains Avogadro numbers of atoms.

Complete step by step answer:
(I) Now 52 moles of Ar
As we know
1 mole of Ar = $6.022 \times {10^{23}}$ atoms
We have to find for 52 moles, therefore
52 moles of Ar = $52 \times 6.022 \times {10^{23}}$ atoms
$= 313.144 \times {10^{23}}$ atoms
Hence 52 moles of Ar contains $313.144 \times {10^{23}}$ atoms

(II) For 52u of He
As we know that
Mass of 1 atom of He = 4u
4u of He = 1 He atom
Therefore 1u of He = $\dfrac{1}{4}$ He atom
$52u$ of He = $\dfrac{{52}}{4}$ He atoms = 13 atoms
Hence, 52u of He contains 13 atoms

(III) Now for 52g of He
1 mole of He = 4g
Therefore 52g of He = $\dfrac{{52}}{4} = 13$ moles
1 mole of any substance contains $6.022 \times {10^{23}}$ atoms
Therefore 13 moles contains
= $13 \times 6.022 \times {10^{23}}$
= $78.286 \times {10^{23}}\,{\text{atoms}}$
Hence 52g of He contains $78.286 \times {10^{23}}\,{\text{atoms}}$

Note- To solve this type of question remember the value of Avogadro’s constant and atomic mass of the elements. The above questions we solved are using unitary method i.e. find the quantity for one unit and then for the asked unit. In chemistry, atomic mass is highly important because it is a connection between the mass that can be measured in the laboratory and the moles, which are the number of atoms.