A patient is having an allergic reaction and takes a 12.5mg tablet of the over‑the‑counter antihistamine diphenhydramine hydroch

Question

1 year ago

9

loride, C17H22ClNO.How many molecules of diphenhydramine hydrochloride are in this tablet?

1 answer:

horsena [70] · Answer 1 · 2024-05-22T09:44:32+03:00

12.5 mg of the tablet contains 2.58×10¹⁹ molecules of diphenhydramine hydrochloride, C₁₇H₂₂ClNO

From Avogadro's hypothesis,

<h3>1 mole of any substance = 6.02×10²³ molecules </h3>

Therefore,

1 mole of C₁₇H₂₂ClNO = 6.02×10²³ molecules

Next, we shall determine the mass (in mg) of 1 mole of C₁₇H₂₂ClNO. This can be obtained as follow:

1 mole of C₁₇H₂₂ClNO = (17×12) + (22×1) + 35.5 + 14 + 16

= 204 + 22 + 35.5 + 14 + 16

= 291.5 g

Multiply by 1000 to express in mg

291.5 × 1000 = 291500 mg

Thus,

Therefore,

291500 mg of C₁₇H₂₂ClNO = 6.02×10²³ molecules

Finally, we shall determine the number molecules in 12.5 mg of C₁₇H₂₂ClNO. This can be obtained as follow:

291500 mg of C₁₇H₂₂ClNO = 6.02×10²³ molecules

Therefore

12.5 mg of C₁₇H₂₂ClNO = $\frac{12.5 * 6.02*10^{23}}{291500}\\$

<h3>12.5 mg of C₁₇H₂₂ClNO = 2.58×10¹⁹ molecules </h3>

Therefore, we can conclude that 12.5 mg of the tablet contains 2.58×10¹⁹ molecules of diphenhydramine hydrochloride, C₁₇H₂₂ClNO