Question

Calculate the number of molecules of sulphur $\left( {{S}_{8}} \right)$ present in 16g of solid sulphur. (Atomic mass of sulphur = 32)

Answer 1

Hint: To solve this, firstly find out the molar mass of the molecule of sulphur. Use that to find the number of moles of sulphur in 16g of solid sulphur. To convert the moles into molecules you can multiply it by the Avogadro’s number.

Complete Step by Step Solution: In the question, the atomic mass of sulphur is given to us and we have to find the number of molecules of sulphur present in 16g of solid sulphur. So for that, firstly let us calculate the mass of solid sulphur.
We know that the atomic mass of sulphur is 32.
 Therefore, the molecular mass of a molecule of sulphur that is ${{S}_{8}}$ will be $32\times 8g$ = 256g.
Therefore, we can write that the molar mass of solid sulphur is 256 g/mol.
Now, we can write that-
Number of moles of sulphur in 256g is 1 mol.
Therefore, the number of moles of sulphur in 1 g will be $\dfrac{1}{256}$ mol.
Now, we have to find the number of moles in 16g of sulphur.
Therefore, the number of moles in 16g of sulphur is $\dfrac{1}{256}\times 16$mol = 0.0625moles.
Therefore, in 16g of solid sulphur we have 0.0625 moles of sulphur.
Now, we have to calculate the number of molecules of sulphur in 16g of solid sulphur. We can easily find this by multiplying the number of moles by the Avogadro’s number.
So the number of molecules that we will get is $0.0625\times {{N}_{A}}$
We know that Avogadro’s number is denoted as ${{N}_{A}}$.The value of Avogadro’s number is $6.022\times {{10}^{23}}mo{{l}^{-1}}$ .
Multiplying it by the number of moles of sulphur we will get $0.0625mol\times 6.022\times {{10}^{23}}mo{{l}^{-1}}=3.764\times {{10}^{22}}$
We can see from the above discussion that it contains $3.764\times {{10}^{22}}$ molecules.
Therefore, the answer is will be – the number of molecules of sulphur $\left( {{S}_{8}} \right)$ present in 16g of solid sulphur is $3.764\times {{10}^{22}}$.

Note: The Avogadro’s number is the number of units of one mole of any substance. Therefore, we multiplied the moles here to get the required answer. To get moles from molecules, we can divide the molecules by Avogadro’s number and to get molecules from moles, we can multiply (as we did here).
We can also solve this question simply by dividing the mass of the substance (16g) by its molar mass (256g/mol) and then multiplying it by Avogadro's number.