Question

Verify by calculating that $5\mathrm{moles}\mathrm{of}{\mathrm{CO}}_2$ and $5\mathrm{moles}\mathrm{of}{\mathrm{H}}_2\mathrm{O}$ do not have the same mass.

Answer 1

Step 1: Given information

• Moles of carbon dioxide, $\left({\mathrm{CO}}_2\right)=5\mathrm{mol}$
• Moles of water, $\left({\mathrm{H}}_2\mathrm{O}\right)=5\mathrm{mol}$

Step 2: Formula used to calculate the mass of a compound

$\mathrm{m}=\mathrm{n}\times \mathrm{M}$

• $\mathrm{m}$ is the mass.
• $\mathrm{n}$ is the number of moles.
• $\mathrm{M}$ is the molar mass.

Step 3: Determine the mass of carbon dioxide

• Molar mass of ${\mathrm{CO}}_2=44\mathrm{g}{\mathrm{mol}}^{-1}$
• The mass of carbon dioxides is as follows:

$\begin{array}{rcl}\mathrm{m}& =& \mathrm{n}\times \mathrm{M}\\ & =& 5\bcancel{\mathrm{mol}}\times 44\mathrm{g}\bcancel{{\mathrm{mol}}^{-1}}\\ & =& 220\mathrm{g}\end{array}$

Step 4: Determine the mass of water

• Molar mass of ${\mathrm{H}}_2\mathrm{O}=18\mathrm{g}{\mathrm{mol}}^{-1}$
• The mass of water is as follows:

$\begin{array}{rcl}\mathrm{m}& =& \mathrm{n}\times \mathrm{M}\\ & =& 5\bcancel{\mathrm{mol}}\times 18\mathrm{g}\bcancel{{\mathrm{mol}}^{-1}}\\ & =& 90\mathrm{g}\end{array}$

Therefore, the $\mathbf{5}\mathbf{}\mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{CO}}_{\mathbf{2}}$ and $\mathbf{5}\mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ do not have the same mass.