Which has the maximum number of molecules?

The correct option is A

$2\mathrm{g}{\mathrm{H}}_2$

Explanation for correct option

(A) $\mathbf{2}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{H}}_{\mathbf{2}}$

Mole

• A mole is the amount of substance that has the same number of elementary particles as there are atoms in $12\mathrm{g}$ of carbon $\left(\mathrm{C}12\right)$.
• Formula to calculate number of moles is as follows:

$\mathrm{Number}\mathrm{of}\mathrm{mole}=\frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}$

Determine number of moles in ${\mathbf{H}}_{\mathbf{2}}$

• Mass of hydrogen gas $\left({\mathrm{H}}_2\right)=2\mathrm{g}$
• Molecular mass ${\mathrm{H}}_2=2\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{2\bcancel{\mathrm{g}}}{2\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\\ & =& 1\mathrm{mol}\end{array}$

Explanation for incorrect options

(B) $\mathbf{7}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{N}}_{\mathbf{2}}$

• Mass of nitrogen gas $\left({\mathrm{N}}_2\right)=7\mathrm{g}$
• Molecular mass ${\mathrm{N}}_2=28\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{7\bcancel{\mathrm{g}}}{28\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\\ & =& 0.25\mathrm{mol}\end{array}$

(C) $\mathbf{16}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{O}}_{\mathbf{2}}$

• Mass of oxygen gas $\left({\mathrm{O}}_2\right)=16\mathrm{g}$
• Molecular mass ${\mathrm{O}}_2=32\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{16\bcancel{\mathrm{g}}}{32\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\\ & =& 0.5\mathrm{mol}\end{array}$

(D) $\mathbf{16}\mathbf{}\mathbf{g}\mathbf{}{\mathbf{NO}}_{\mathbf{2}}$

• Mass of nitrogen dioxide $\left({\mathrm{NO}}_2\right)=16\mathrm{g}$
• Molecular mass ${\mathrm{NO}}_2=46\mathrm{g}{\mathrm{mol}}^{-1}$
• The number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{16\bcancel{\mathrm{g}}}{46\bcancel{\mathrm{g}}{\mathrm{mol}}^{-1}}\\ & =& 0.347\mathrm{mol}\end{array}$

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