Question

Which has more number of atoms: $100$ g of $N_2$ or $100$ g of $N{H}_3$?

• A. $N{H}_3$
• B. $N_2$
• C. Both have same number of atoms
• D. Cannot be determined

Answer 1

The correct option is A $N{H}_3$

Atomic mass of N = 14 u

Atomic mass of H = 1 u

Number of moles = $\frac{Mass}{MolarMass}$

$\left(i\right)100g{N}_2$ $=\frac{100}{(14\times 2)}$ moles $=\frac{100}{28}$ moles

Number of $N_2$ molecules $=\frac{100}{28}\times 6.022\times {10}^{23}$

1 molecule of $N_2$ has 2 atoms. So, number of $N$ atoms $=\frac{100}{28}\times 6.022\times {10}^{23}\times 2=43.01\times {10}^{23}$ atoms

$\left(ii\right)100gN{H}_3=\frac{100}{14+(3\times 1)}=\frac{100}{17}$ moles

$=\frac{100}{17}\times 6.022\times {10}^{23}$ molecules

$=\frac{100}{17}\times 6.022\times {10}^{23}\times 4$ atoms (since one molecule of $N{H}_3$ has 4 atoms.)

$=141.69\times {10}^{23}$ atoms

$\therefore$ $N{H}_3$ would have more atoms