Question

Calculate the number of molecules of sulphur (${\mathrm{S}}_8$) present in $16\mathrm{g}$ of solid sulphur.

Answer 1

Step 1: Calculate the number of moles.

• The number of moles can be calculated by using the formula:

$\mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}$

• According to the question, the given mass is $16\mathrm{g}$ and the molecular mass can be calculated as:

$\mathrm{Molecular}\mathrm{mass}\mathrm{of}{\mathrm{S}}_8=32\times 8=256\mathrm{g}{\mathrm{mol}}^{-1}$

• Thus, the number of moles of ${\mathrm{S}}_8$ are $\frac{16\mathrm{g}}{256\mathrm{g}{\mathrm{mol}}^{-1}}=0.0625\mathrm{moles}$

Step 2: Calculate the number of molecules.

• We know that one mole of any substance contains $6.023\times {10}^{23}$ molecules
  Thus, the number of molecules in any material may be calculated by multiplying the number of moles by Avogadro's number, which is $6.023\times {10}^{23}$.
• We can state:
  $\mathrm{Number}\mathrm{of}\mathrm{molecules}=\mathrm{number}\mathrm{of}\mathrm{moles}\times 6.023\times {10}^{23}$
• Thus, the number of molecules in $16\mathrm{g}$ of $S_8$ are $=0.0625\times 6.023\times {10}^{23}=3.764\times {10}^{22}$

So, the number of molecules in $16\mathrm{g}$ of $S_8$ are $3.764\times {10}^{22}$