Question

A particular oral contraceptive contains 0.038 mg of ethinyl estradiol in each pill. The formula of this compound is C20H24O2. How many molecules of ethinyl estradiol are there in one pill?

Answer 1

Answer: The number of molecules of ethinyl estradiol present in one pill are $7.71\times 10^{16}$

Explanation:

To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Given mass of ethinyl estradiol = 0.038 mg = $3.8\times 10^-5}g$    (Conversion factor: 1 g = 1000 mg)

Molar mass of ethinyl estradiol $(C_{20}H_{24}O_2)=[(20\times 12)+(24\times 1)+(2\times 16)]=296g/mol$

Putting values in above equation, we get:

$\text{Moles of ethinyl estradiol}=\frac{3.8\times 10^{-5}g}{296g/mol}=1.28\times 10^{-7}mol$

According to mole concept:

1 mole of a compound contains $6.022\times 10^{23}$ number of molecules

So, $1.28\times 10^{-7}mol$ of ethinyl estradiol will contain = $(1.28\times 10^{-7}\times 6.022\times 10^{23})=7.71\times 10^{16}$ number of molecules

Hence, the number of molecules of ethinyl estradiol present in one pill are $7.71\times 10^{16}$