Question

A sample of ${{N}_{2}}$ weighs 42.8g. How many molecules of ${{N}_{2}}$are present in this sample? How many atoms of $N$ do these represent?

Answer 1

Hint: The answer to this question is dependent on the concept of Avogadro number of molecules where one mole of a compound contains$6.023\times {{10}^{23}}$ number of atoms. Multiply this value to the number of moles which is being calculated.

Complete answer:
The concept of Avogadro law and Avogadro number of molecules and also about the related concepts are familiar to us.
We shall see the required answer by first calculating the number of moles of the atom given and then multiply this value with the Avogadro number of molecules.
- Avogadro number of molecules states that one mole of a compound contains$6.023\times {{10}^{23}}$ number of atoms.
- Now, we know that the atomic number of nitrogen is 7 and mass number is 14. We have two atoms of nitrogen that is diatomic nitrogen and thus the molar mass of nitrogen will be$2\times 14=28$g.
- We shall now divide this given mass by this number to get the total number of moles. This will be,$\dfrac{42.8}{28}=1.53$ moles.
Now, let us multiply the Avogadro number of molecules to this above value of the number of moles. This will be,
\[1.53\times 6.023\times {{10}^{23}}=9.20\times {{10}^{23}}\]
Thus, there are $9.20\times {{10}^{23}}$ molecules of${{N}_{2}}$
Since, each molecule of ${{N}_{2}}$ contains two atoms of nitrogen, the total number of atoms will be twice the above value which is found and that is $1.80\times {{10}^{24}}$ atoms of $N$

Note:
Note that the Avogadro value per mole is obtained by dividing the charge on a mole of electrons by the charge on a single electron and this value is obtained by scientist Avogadro by his experiment.