Question

A sample of Ammonia has a mass of 45.5g. How many molecules are in this sample?

Answer 1

Ammonia has the chemical formula $N{H_3}$ and it's molar mass can be found as (atomic weights can be found in the periodic table)

$${M_{N{H_3}}} = {M_N} + 3{M_H}$$ $${M_{N{H_3}}} \approx 14.007[{{\rm{g}} \over {{\rm{mol}}}}] + 3 \cdot 1.008[{{\rm{g}} \over {{\rm{mol}}}}] = 17.031[{{\rm{g}} \over {{\rm{mol}}}}]$$

The number of moles can be found as

$${\nu _{N{H_3}}} = {{{m_{N{H_3}}}} \over {{M_{N{H_3}}}}}$$

and in each mole there are ${N_A} \approx 6.022 \cdot {10^{23}}[{{\rm{1}} \over {{\rm{mol}}}}]$ molecules. Thus the number of molecules in our sample

$$N = {N_A}{{{m_{N{H_3}}}} \over {{M_{N{H_3}}}}} \approx 6.022 \cdot {10^{23}}[{{\rm{1}} \over {{\rm{mol}}}}]{{45.5[{\rm{g}}]} \over {17.031[{{\rm{g}} \over {{\rm{mol}}}}]}} \approx 1.61 \cdot {10^{24}}$$