Question

How many moles are in $1.56\times {{10}^{23}}$ atoms of silver (Ag)?

Answer 1

Hint: To solve this question, we first need to understand what is a mole. Mole is the SI unit of measurement and is used to determine the amount of a substance. A mole of any substance has exactly $6.022\times {{10}^{23}}$ particles which can be ions, atoms, electrons, or molecules.

Complete step-by-step answer:
Avogadro's constant is used to find the relation between the amount of substance in a sample and the number of particles (which can be ions, atoms, electrons, or molecules) constituted in a sample. Its SI unit is $mo{{l}^{-1}}$ and has value ${{N}_{A}}=6.022\times {{10}^{23}}mo{{l}^{-1}}$.
Now, the exact number of particles present in one mole of a substance can be expressed by the numerical value of Avogadro's constant without its dimension. This is called the Avogadro's number.
So, one mole of a substance contains exactly the Avogadro number $(N)$ of particles.
$N=6.022\times {{10}^{23}}$
We can also say that when the number of particles equivalent to the Avogadro's number ($N=6.022\times {{10}^{23}}$) are present, it means that one mole of that substance is present.
Now, it is given to us that there are $1.56\times {{10}^{23}}$ atoms of silver (Ag). So, to find out the number of moles present, we just need to divide it with the Avogadro's constant.
\[\begin{align}
  & n=\dfrac{1.56\times {{10}^{23}}}{6.022\times {{10}^{23}}mo{{l}^{-1}}} \\
 & n\cong 0.259mol \\
\end{align}\]
Where n is the number of moles.
So, there are approximately 0.259 moles of silver present in $1.56\times {{10}^{23}}$ atoms of silver (Ag).

Additional Information:
The mass of a sample can be given by the sum of the mass of all the particles in it.
So, we can say that the mass of one mole of a compound is equivalent to the mass of all the particles contained in one mole of a substance i.e., $6.022\times {{10}^{23}}$ particles.
The molar mass of a substance is the mass of one mole of the substance. Its SI base unit is kg/mol but it is usually expressed in g/mol. It is a bulk property of a substance, not a molecular property.

Note: The number of particles in a mole of a given substance does not depend on the type or nature of a substance. So, the number of moles of any substance can be determined by dividing the number of particles in the sample by Avogadro's constant.