Question

Which has more number of atoms? $100\mathrm{g}\mathrm{of}{\mathrm{N}}_2\mathrm{or}100\mathrm{g}\mathrm{of}{\mathrm{NH}}_3$

Answer 1

Step 1: Determine number of moles in $\mathbf{100}\mathbf{}\mathbf{g}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{N}}_{\mathbf{2}}$

• Mass of Nitrogen gas $\left({\mathrm{N}}_2\right)=100\mathrm{g}$
• Molecular mass of ${\mathrm{N}}_2=28\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{100\mathrm{g}}{28\mathrm{g}{\mathrm{mol}}^{-1}}\\ & =& 3.57\mathrm{mol}\end{array}$

Step 2: Determine number of atoms in $\mathbf{100}\mathbf{}\mathbf{g}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{N}}_{\mathbf{2}}$

• Calculate the number of atoms is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{atoms}& =& 3.57\times 6.022\times {10}^{23}\times 2\mathrm{atom}\\ & =& 43\mathrm{atom}\end{array}$

Step 3: Determine number of moles in $\mathbf{100}\mathbf{}\mathbf{g}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{NH}}_{\mathbf{3}}$

• Mass of Ammonia gas $\left({\mathrm{NH}}_3\right)=100\mathrm{g}$
• Molecular mass of ${\mathrm{NH}}_3=17\mathrm{g}{\mathrm{mol}}^{-1}$
• Calculate the number of moles is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{mole}& =& \frac{\mathrm{Mass}}{\mathrm{Molecular}\mathrm{mass}}\\ & =& \frac{100\mathrm{g}}{17\mathrm{g}{\mathrm{mol}}^{-1}}\\ & =& 5.88\mathrm{mol}\end{array}$

Step 4: Determine number of atoms in $\mathbf{100}\mathbf{}\mathbf{g}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{NH}}_{\mathbf{3}}$

• Calculate the number of atoms is as follows:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{atoms}& =& 5.88\times 6.022\times {10}^{23}\times 4\mathrm{atom}\\ & =& 141.64\mathrm{atom}\end{array}$

Therefore, $100\mathrm{g}\mathrm{of}{\mathrm{NH}}_3$ has more number of atoms then $100\mathrm{g}\mathrm{of}{\mathrm{N}}_2$.