Question

Calculate the number of molecules in $11\mathrm{g}$ of ${\mathrm{CO}}_2$.

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 $11\mathrm{g}$ and the molecular mass can be calculated as:

$\mathrm{Molecular}\mathrm{mass}\mathrm{of}{\mathrm{CO}}_2=(1\times \mathrm{C})+(2\times \mathrm{O})=(1\times 12)+(2\times 16)=44\mathrm{g}{\mathrm{mol}}^{-1}$

• Thus, the number of moles of ${\mathrm{CO}}_2$ are $\frac{11\mathrm{g}}{44\mathrm{g}{\mathrm{mol}}^{-1}}=0.25\mathrm{moles}$

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 $11\mathrm{g}$ of ${\mathrm{CO}}_2$ are $=0.25\times 6.023\times {10}^{23}=1.505\times {10}^{23}$

So, the number of molecules in $11\mathrm{g}$ of ${\mathrm{CO}}_2$ are $1.505\times {10}^{23}$.