Question

Which has more number of atoms ?

100 g of ${\mathrm{N}}_2$or 100 g of ${\mathrm{NH}}_3$

Answer 1

We know that

Moles =$\frac{givenmass}{molarmass}$

Explanation of part 1:

• Moles of ${\mathrm{N}}_2$=$\frac{100}{28}=3.57moles$
• Number of atoms =Atomicity $\times$Moles $\times$Avagadro number
• So, Number of atoms of ${\mathrm{N}}_2$molecule=$$\begin{gathered} =2\times 3.57\times 6.022\times {10}^{23} \\ =42.99\times {10}^{23}atoms \end{gathered}$$

Explanation of part 2:

• Moles of ${\mathrm{NH}}_3$=$\frac{100}{17}=5.88moles$
• Number of atoms =Atomicity $\times$Moles $\times$Avagadro number
• So, Number of atoms of ${\mathrm{NH}}_3$ molecule= $$\begin{gathered} =4\times 5.88\times 6.022\times {10}^{23} \\ =141.63\times {10}^{23}atoms \end{gathered}$$

Thus, the ${\mathrm{NH}}_3$ molecule has a greater number of atoms as compared to the ${\mathrm{N}}_2$ molecule.