Question 4.10: The Mole Concept—Converting between Mass and Number of Molec...
The Mole Concept—Converting between Mass and Number of Molecules
An aspirin tablet contains 325 mg of acetylsalicylic acid (C_9H_8O_4). How many acetylsalicylic acid molecules does it contain?
SORT You are given the mass of acetylsalicylic acid and asked to find the number of molecules.
GIVEN: 325 mg C_9H_8O_4
FIND: number of C_9H_8O_4 molecules
STRATEGIZE First convert to grams and then to moles (using the molar mass of the compound) and then to number of molecules (using Avogadro’s number). You need both the molar mass of acetylsalicylic acid and Avogadro’s number as conversion factors. You also need the conversion factor between g and mg.
CONCEPTUAL PLAN
RELATIONSHIPS USED
C_9H_8O_4 molar mass = 9(12.01) + 8(1.008) + 4(16.00)
= 180.15 g/mol
6.022 \times 10^{23} = 1 mol
1 \ mg = 10^{-3} g
SOLVE Follow the conceptual plan to solve the problem.
325 \ \cancel{mg} \ \cancel{C_9H_8O_4}\times \frac{10^{-3} \cancel{g}}{1 \ \cancel{mg}} \times \frac{1 \ \cancel{mol} \ \cancel{C_9H_8O_4}}{180.15 \ \cancel{g} \cancel{C_9H_8O_4} }\times \frac{6.022\times 10^{23}C_9H_8O_4 molecules}{1 \ \cancel{mol \ C_9H_8O_4}}
= 1.09 \times 10^{21} C_9H_8O_4 molecules
CHECK The units of the answer, C_9H_8O_4 molecules, are correct. The magnitude is smaller than Avogadro’s number, as expected, since you have less than one molar mass of acetylsalicylic acid.