Question

The largest number of molecules are in?

• A. $28\mathrm{g}\mathrm{CO}$
• B. $54\mathrm{g}{\mathrm{N}}_2{\mathrm{O}}_5$
• C. $36\mathrm{g}{\mathrm{H}}_2\mathrm{O}$
• D. $46\mathrm{g}{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}$

Answer 1

The correct option is C

$36\mathrm{g}{\mathrm{H}}_2\mathrm{O}$

Explanation for correct options

(C) $\mathbf{36}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

Step 1: Formula used to calculate the number of molecules

• $\mathrm{N}=\frac{\mathrm{m}}{\mathrm{M}}\times {\mathrm{N}}_{\mathrm{A}}$
• $\mathrm{N}$ is the number of molecules.
• $\mathrm{m}$ is the mass.
• $\mathrm{M}$ is the molecular mass.
• ${\mathrm{N}}_{\mathrm{A}}$ is the Avogadro's number.

Step 2: Determine the number of molecules in $36\mathrm{g}{\mathrm{H}}_2\mathrm{O}$

• Mass of water, $\left({\mathrm{H}}_2\mathrm{O}\right),\mathrm{m}=36\mathrm{g}$
• Molecular mass of water, $\mathrm{M}=18\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of molecules is as follows:

$\begin{array}{rcl}\mathrm{N}& =& \frac{\mathrm{m}}{\mathrm{M}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{36\bcancel{\mathrm{g}}}{18\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& 2\mathrm{mol}{\mathrm{N}}_{\mathrm{A}}\end{array}$

Explanation for incorrect options

(A) $\mathbf{28}\mathbf{}\mathbf{g}\mathbf{}\mathbf{CO}$

• Mass of carbon monoxide, $\left(\mathrm{CO}\right),\mathrm{m}=28\mathrm{g}$
• Molecular mass of carbon monoxide, $\mathrm{M}=28\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of molecules is as follows:

$\begin{array}{rcl}\mathrm{N}& =& \frac{\mathrm{m}}{\mathrm{M}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{28\bcancel{\mathrm{g}}}{28\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& 1\mathrm{mol}{\mathrm{N}}_{\mathrm{A}}\end{array}$

(B) $\mathbf{54}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{5}}$

• Mass of nitrogen pentoxide, $\left({\mathrm{N}}_2{\mathrm{O}}_5\right),\mathrm{m}=54\mathrm{g}$
• Molecular mass of ${\mathrm{N}}_2{\mathrm{O}}_5,\mathrm{M}=108\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of molecules is as follows:

$\begin{array}{rcl}\mathrm{N}& =& \frac{\mathrm{m}}{\mathrm{M}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{54\bcancel{\mathrm{g}}}{108\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& 0.5143\mathrm{mol}{\mathrm{N}}_{\mathrm{A}}\end{array}$

(D) $\mathbf{46}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}$

• Mass of ethanol, $\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\right),\mathrm{m}=46\mathrm{g}$
• Molecular mass of ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH},\mathrm{M}=46\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of molecules is as follows:

$\begin{array}{rcl}\mathrm{N}& =& \frac{\mathrm{m}}{\mathrm{M}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& \frac{46\bcancel{\mathrm{g}}}{46\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\times {\mathrm{N}}_{\mathrm{A}}\\ & =& 1\mathrm{mol}{\mathrm{N}}_{\mathrm{A}}\end{array}$

Therefore, the correct option is (C) $\mathbf{36}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$.