Question

a patient is having an allergic reaction and takes a 25.0 mg tablet of the over - the - counter antihistamine diphenhydramine hydrochloride, c₁₇h₂₂clno. how many molecules of diphenhydramine hydrochloride are in this tablet?

Explanation:

Step1: Calculate molar mass of $C_{17}H_{22}ClNO$

The molar mass of carbon ($C$) is approximately $12.01\ g/mol$, hydrogen ($H$) is $1.01\ g/mol$, chlorine ($Cl$) is $35.45\ g/mol$, nitrogen ($N$) is $14.01\ g/mol$ and oxygen ($O$) is $16.00\ g/mol$.
$M=(17\times12.01 + 22\times1.01+35.45 + 14.01+16.00)\ g/mol$
$M=(204.17+22.22 + 35.45+14.01 + 16.00)\ g/mol=291.85\ g/mol$

Step2: Convert mass to moles

The mass of the tablet is $m = 25.0\ mg=0.025\ g$.
The number of moles $n=\frac{m}{M}=\frac{0.025\ g}{291.85\ g/mol}=8.57\times 10^{-5}\ mol$

Step3: Calculate number of molecules

Using Avogadro's number $N_A = 6.022\times 10^{23}\ molecules/mol$.
The number of molecules $N=n\times N_A=(8.57\times 10^{-5}\ mol)\times(6.022\times 10^{23}\ molecules/mol)=6.45\times 10^{19}$ molecules

Answer:

$6.45\times 10^{19}$ molecules