# Which has more number of atoms?

Question:

Which has more number of atoms?

$100 \mathrm{~g}$ of $\mathrm{N}_{2}$ or $100 \mathrm{~g}$ of $\mathrm{NH}_{3}$

Solution:

(a) Gram molar mass of $\mathrm{N}_{2}=2 \times 14=28 \mathrm{~g}$

$28 \mathrm{~g}$ of $\mathrm{N}_{2}$ have nitrogen atoms $=2 \times \mathrm{N}_{\mathrm{A}}$

$100 \mathrm{~g}$ of $\mathrm{N}_{2}$ have nitrogen atoms $=2 \times \mathrm{N}_{\mathrm{A}} \times \frac{(100 \mathrm{~g})}{(28 \mathrm{~g})}=7 \cdot 143 \times \mathrm{N}_{\mathrm{A}}$

$=7.143 \times 6.022 \times 10^{23}=4.3 \times 10^{24}$ atoms

(b) Gram molar mass of $\mathrm{NH}_{3}=14+3 \times 1=17 \mathrm{~g}$

$17 \mathrm{~g}$ of $\mathrm{NH}_{3}$ have atoms $=4 \times \mathrm{N}_{\mathrm{A}}$

$100 \mathrm{~g}$ of $\mathrm{NH}_{3}$ have atoms $=4 \times \mathrm{N}_{\mathrm{A}} \times \frac{(100 \mathrm{~g})}{(17 \mathrm{~g})}=2.53 \times \mathrm{N}_{\mathrm{A}}$

$=23.53 \times 6.022 \times 10^{23}=1.42 \times 10^{25}$ atoms.

$100 \mathrm{~g}$ of $\mathrm{NH}_{3}$ have more number of atoms.