Question

Calculate the number of molecules in $4\mathrm{g}$ of oxygen.

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 $4\mathrm{g}$ and the molecular mass can be calculated as:

$\mathrm{Molecular}\mathrm{mass}\mathrm{of}{\mathrm{O}}_2=(2\times \mathrm{O})=(2\times 16)=32\mathrm{g}{\mathrm{mol}}^{-1}$

• Thus, the number of moles of ${\mathrm{O}}_2$ are $\frac{4\mathrm{g}}{32\mathrm{g}{\mathrm{mol}}^{-1}}=0.125\mathrm{moles}$

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 $4\mathrm{g}$ of ${\mathrm{O}}_2$ are $=0.125\times 6.023\times {10}^{23}=7.52\times {10}^{22}$

So, the number of molecules in $4\mathrm{g}$ of ${\mathrm{O}}_2$ are $7.52\times {10}^{22}$