Question

question 10 of 15 > 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

The molar mass of $C_{17}H_{22}ClNO$:
$M=(17\times12.01 + 22\times1.01+35.45 + 14.01+16.00)\text{ g/mol}=291.82\text{ g/mol}$

Step2: Convert mass to moles

The mass of the tablet is $m = 25.0\text{ mg}=0.0250\text{ g}$.
The number of moles $n=\frac{m}{M}=\frac{0.0250\text{ g}}{291.82\text{ g/mol}}=8.57\times 10^{-5}\text{ mol}$

Step3: Calculate number of molecules

Using Avogadro's number $N_A = 6.022\times 10^{23}\text{ molecules/mol}$.
The number of molecules $N=n\times N_A=(8.57\times 10^{-5}\text{ mol})\times(6.022\times 10^{23}\text{ molecules/mol}) = 6.11\times 10^{19}$ molecules

Answer:

$6.11\times 10^{19}$ molecules