Question

How many moles are there in $ 9.033 \times {10^{24}} $ atoms of Helium $ \left( {He} \right) $ $ ? $

Answer 1

Hint: One mole of a substance is equal to $ 6.022 \times {10^{23}} $ units of that substance (such as atoms, molecules, or ions). The number $ 6.022 \times {10^{23}} $ is known as Avogadro's number or Avogadro's constant. i.e., One mole $ = $ $ 6.022 \times {10^{23}} $ atoms, molecules, protons, etc.
To convert from moles to atoms, multiply the molar amount by Avogadro's number. To convert from atoms to moles, divide the atom amount (number of atoms of a substance) by Avogadro's number i.e., Number of moles $ = \dfrac{{number\;of\;atoms}}{{6.022 \times {{10}^{23}}}} $ .

Complete answer:
Helium $ \left( {He} \right) $ is a chemical element with the atomic number $ 2 $ . It is a colourless, odourless, tasteless, non-toxic, inert, monatomic gas, the first element in the noble gas group in the periodic table. Its boiling point is the lowest among all the elements.
Number of atoms in $ He $ $ = 9.033 \times {10^{24}} $ atoms
Number of moles in $ 6.022 \times {10^{23}} $ atoms $ = 1 $ mole.
Since we know that, Number of moles is the ratio of the number of atoms to the Avogadro number.
Hence, number of moles in $ 9.033 \times {10^{24}} $ atoms of Helium $ \left( {He} \right) $ $ = \dfrac{{number\;of\;atoms\;inHe}}{{6.022 \times {{10}^{23}}}} $
 $ = \dfrac{{9.033 \times {{10}^{24}}}}{{6.022 \times {{10}^{23}}}} $
 $ = \dfrac{{9.033 \times {{10}^{24 - 23}}}}{{6.022}} $
 $ = \dfrac{{9.033 \times 10}}{{6.022}} $
 $ = \dfrac{{90.33}}{{6.022}} $
 $ = \dfrac{{90330}}{{6022}} = 15 $ .
Hence the number of moles in $ 9.033 \times {10^{24}} $ atoms of Helium $ \left( {He} \right) $ is $ 15 $ .

Note:
Note that Avogadro number is used to measure the products obtained from the chemical reaction. The unit is denoted by $ mol $ .
The formula for the number of moles from grams is expressed as $ Number\;of\;Moles = \dfrac{{Mass\;of\;substance}}{{Mass\;of\;one\;mole}} $
Each element has a different molar mass depending on the weight of $ 6.022 \times {10^{23}} $ of its atoms. Example atoms in $ 12 $ grams are the same as $ 12 $ grams of carbon. Also note that, Helium is the second lightest and second most abundant element in the periodic table (Hydrogen is the lightest and most abundant element).