Question

How many moles of magnesium are in $3.011\times {{10}^{22}}$ atoms of magnesium?

Answer 1

Hint: To solve this question, one must know about Avogadro's constant. The proportionality factor that is used to find the relation between the number of particles like ions, atoms or molecules constituted in a sample and the amount of substance in the sample is known as the Avogadro's constant.

Complete answer:
Since the Avogadro's constant gives the relation between the number of constituent particles and the amount of substance, its SI unit is the reciprocal of mole and has the value ${{N}_{A}}=6.022\times {{10}^{22}}mo{{l}^{-1}}$.
When the Avogadro's constant's numerical value is expressed without its dimensions (that is without the SI unit- reciprocal of mole), it gives the exact number of particles present in one mole of any substance. This is called the Avogadro's number and it has a value of $N=6.022\times {{10}^{23}}$.
When Avogadro's (N) number of particles of any chemical compound or molecule are present together, their sum of mass will be equal to the mass of one mole of that compound or molecule.
The vice-versa for this is also true. That is when a mass of one mole of any chemical compound or molecule is present, the number of particles in it will be equal to the Avogadro's number.
So, from this definition, we can interpret that one mole of magnesium has number of atoms equal to the Avogadro's number $N=6.022\times {{10}^{23}}$.
Now, to find out the moles of magnesium present in $3.011\times {{10}^{22}}$ atoms, we simply have to divide this number with the Avogadro's constant.
\[\begin{align}
  & Number\text{ }of\text{ }moles=\dfrac{3.011\times {{10}^{22}}}{6.022\times {{10}^{23}}mo{{l}^{-1}}} \\
 & Number\text{ }of\text{ }moles\text{ = }0.05\text{ }mol \\
\end{align}\]
So, there are 0.05 moles of magnesium present in $3.011\times {{10}^{22}}$ atoms of magnesium.

Note:
When a particular number of particles are given, the number of moles can be determined by dividing by the Avogadro's constant regardless of the nature or type of the substance.