12.5 mg of the tablet contains 2.58×10¹⁹ molecules of diphenhydramine hydrochloride, C₁₇H₂₂ClNO
From Avogadro's hypothesis,
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 = [tex]\frac{12.5 * 6.02*10^{23}}{291500}\\[/tex]
Therefore, we can conclude that 12.5 mg of the tablet contains 2.58×10¹⁹ molecules of diphenhydramine hydrochloride, C₁₇H₂₂ClNO
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