Question

A sample of chlorine gas has a mass of 39.2 grams. How many $C{{l}_{2}}$ molecules are there in the sample?

Answer 1

Hint: The answer here is dependent on the calculation of total number of molecules present which takes into account of the Avogadro number of molecules and the value of Avogadro constant is $6.023\times {{10}^{23}}$

Complete step by step answer:
In the classes of general chemistry, we have come across the very basic concept which deals with the calculation of number of molecules present in the compound and also about the Avogadro constant.
Let us now calculate the total number of $C{{l}_{2}}$ molecules which is present in the sample based on the data given.
- According to Avogadro's hypothesis, one mole of any substance contains $6.023\times {{10}^{23}}$ in it.
- Chlorine has the atomic number 17 and mass number of 35.45 atomic mass units (amu) and therefore the atomic mass for two atoms of chlorine should be calculated.
- Now to find the number of moles of $C{{l}_{2}}$ present in the sample, we have to convert the mass of given $C{{l}_{2}}$ into moles and then followed by the conversion into the molecules.
Let us do this stepwise which is as follows,
Now, according to the data given, mass of $C{{l}_{2}}$ is = 39.2 g
Since there are two chlorine atoms, Molar mass of the compound is $2\times 35.45=70.9g/mol$
Now, the total number of moles of $C{{l}_{2}}$ is
\[39.2gC{{l}_{2}}\times \dfrac{1molC{{l}_{2}}}{7.9gC{{l}_{2}}}\times \dfrac{6.022\times {{10}^{23}}}{1molC{{l}_{2}}}\]
\[=3.33\times {{10}^{23}}\] molecules of$C{{l}_{2}}$
Thus, the correct answer is 39.2 g of $C{{l}_{2}}$ has \[3.33\times {{10}^{23}}\] molecules.

Note: Note that moles and molecules are two different quantities where mole is the measure of atoms, ions and the molecule is nothing but the Avogadro number multiplied by the number of moles of a substance.