Question

How many molecules are there in $122$ grams of $N{{O}_{2}}$ ?

Answer 1

Hint:‌Before talking about the answer, you should know the basic formula to calculate the number of moles, which is equal to weight per molar mass of the compound. So, to calculate the mass of the compound, you will need to multiply weight with the number of moles.


Complete answer:
Here, it is given that the weight of $N{{O}_{2}}$ is $122\,g$
As we know, the atomic mass of nitrogen is $14\,g$
And, atomic mass of oxygen is $16\,g$
So, we will calculate the molecular mass of $N{{O}_{2}}$ , in which we add atomic masses of each element present in the compound.
Molecular mass $(m)=14+2\times 16=46\,g$
Now, by using the moles formula, we will calculate the number of moles present in $122$ grams of $N{{O}_{2}}$
$n=\dfrac{W}{m}$
where, $n$ is the number of moles, $W$ is the weight of the compound and $m$ is the molar mass of the compound.
Now, we will substitute the value of molar mass and weight of $N{{O}_{2}}$
$n=\dfrac{122}{46}$
$\Rightarrow n=2.65\,mol$
The number of molecules is equal to the product of the number of moles and Avogadro’s number.
Avogadro’s number $({{N}_{A}})$ is equal to $6.022\times {{10}^{23}}$
$M=n\times {{N}_{A}}$
where, $M$ is the number of molecules, $n$ is the number of moles and ${{N}_{A}}$ is the Avogadro’s number.
Now, substituting the value in the above formula, we get,
$M=2.65\times 6.022\times {{10}^{23}}$
$\Rightarrow M=15.97\times {{10}^{23}}$ or $1.59\times {{10}^{24}}$

Therefore, the number of molecules present in $122$ grams of $N{{O}_{2}}$ is $1.59\times {{10}^{24}}$.

Additional information:Moles is defined as a scientific unit which is used to measure large quantities of atoms and molecules. It is defined as the amount of substance present in a sample.
$1\,mole=6.022\times {{10}^{23}}particles$
This is also called Avogadro's number $({{N}_{A}})$ .
Molar mass is defined as the addition of atomic mass of atoms, combined in a molecule. Here, the molar mass of $N{{O}_{2}}$ is $46g$ .Moles are defined as the weight if the compound per molar mass of the compound.Formula mass is different from molecular mass. In formula mass, there is an addition of atomic masses of ions present in an ionic compound, whereas molecular mass is the addition of atomic masses of the atoms in a molecule.

Note:The molar mass is calculated in $g\,mo{{l}^{-1}}$ .We should know how to calculate molar mass of a compound and then substitute the values in the mole concept formula.