Question

How many molecules are there in $35.5g$ of $C{l_2}$?

Answer 1

Hint: In order to solve this problem we must do the following steps. Firstly, we use the molar mass of chlorine gas in order to calculate the number of moles present in that sample. Then we use Avogadro's number to convert the number of moles which is calculated from the previous step to find the number of molecules.

Complete step-by-step answer:
$C{l_2}$ is a diatomic gas hence the molar mass is calculated by,
$2 \times 35.45 = 70.9g/mol$
Therefore we can say that one mole of chlorine gas has a mass of $70.9g$
Now we can use molar mass as a conversion factor to convert grams of chlorine gas to moles.
$35.5g \times \dfrac{{1molC{l_2}}}{{70.9}} = 0.5007molesC{l_2}$
One mole of a molecular compound contains $6.022 \times {10^{23}}$ molecules of said compound, this is known as Avogadro's number.
Hence the number of molecules present in $35.5g$ of $C{l_2}$ is calculated by,
$0.5007molesC{l_2} \times \dfrac{{6.022 \times {{10}^{23}}moleculesC{l_2}}}{{1moleC{l_2}}} = 3.02 \times {10^{23}}molesC{l_2}$

Additional information:
The molar mass of a substance is defined as the total mass of one mole of a substance. It is represented in terms of grams per mole. Molar mass can be represented by the following formula:
The atomic mass of an element is the mass of one atom of the element expressed in atomic mass units. It accounts for the abundance of the various isotopes of the element and assigns an average value to the mass of one atom of the element.

Note: Make sure to multiply $2 \times 35.45$ to find out the molar mass of chlorine gas because it is diatomic. Mole concept is the most convenient method of expressing the amount of a substance. While we are dealing with particles at an atomic or at a molecular level, even one gram of a pure element will contain a huge number of atoms. This is where we use the mole concept. It mainly focuses on the unit known as a ‘mole’, which is a count of a very large number of particles.