Question

How many silver atoms are there in ${\text{4}}{\text{.01}}$ g of silver?

Answer 1

In the above question, we are asked to find out the number of silver atoms present in the given amount of silver. For this, we have to first find out the number of moles of silver atoms present. We know that 1 mole of silver contains ${{\text{N}}_{\text{A}}}$ atoms and hence, after comparing we will get the number of silver atoms present.

Formula used:
${\text{n = }}\dfrac{{\text{m}}}{{\text{M}}}$ , where
n= number of moles
m= given mass
M= molar mass .

Complete step by step solution:
Let us first find out the number of moles of silver present.
Molar mass of silver is 108.
So, ${\text{n = }}\dfrac{{\text{m}}}{{\text{M}}}{\text{ = }}\dfrac{{{\text{4}}{\text{.01}}}}{{{\text{108}}}}{\text{ = 0}}{\text{.037}}$
$1$ mole of the Ag $=$ ${{\text{N}}_{\text{A}}}$ atoms
Now, to find out the number of atoms present in ${\text{0}}{\text{.037}}$ mole of the silver, we will multiply $0.037$ to both sides of the equations.
So, ${\text{0}}{\text{.037}}$ of the silver $=$ ${\text{0}}{\text{.25 }}{{\text{N}}_{\text{A}}}{\text{ = 0}}{\text{.037 6}}{\text{.022 1}}{{\text{0}}^{{\text{23}}}}{\text{ = 2}}{\text{.22 1}}{{\text{0}}^{{\text{22}}}}$ atoms
$\therefore$ There are ${\text{2}}{\text{.22 1}}{{\text{0}}^{{\text{22}}}}$ silver atoms in ${\text{4}}{\text{.01}}$ g of silver.

Additional Information
Avogadro’s number is used in chemistry to deal with large numbers. It is the basis of the mole unit of measurement. It is a simple way of conversion between mole, mass and number of molecules. Suppose, to get the number of particles present in a substance, first, we have to find the number of moles present in it and then by using Avogadro’s number we can find the number of particles present inside it.
Note:
Avogadro’s number is kind of generalized number, hence, we can write:
${\text{1 mole}}$ = $6.022 {10^{23}}$ atoms, or molecules, or protons, or electrons etc.
In short, it is the number of particles in a mole.
Hence, in order to solve these types of questions, we have to first decide which quantity (electron, proton, atom) is equivalent to Avogadro’s number.