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Chapter 3: Problem 72

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .$ a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains 500 . mg $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\( . What amount (moles) of \)\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$ molecules and what number of molecules of acetylsalicylic acid are in a 500 -mg tablet?

Short Answer

Expert verified
The molar mass of aspirin (acetylsalicylic acid) is 180.17 g/mol. In a 500-mg tablet, there are 0.002774 moles and \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

Step by step solution

01

a. Calculate the molar mass of aspirin

To calculate the molar mass, we first need to find the molar mass of each element in the molecular formula, which we can find from the periodic table. Then, we will multiply each element's molar mass by its number of atoms in the molecule and sum all values. Molar mass of C: 12.01 g/mol Molar mass of H: 1.01 g/mol Molar mass of O: 16.00 g/mol Molar mass of aspirin = (9 × 12.01) + (8 × 1.01) + (4 × 16.00) = \(108.09 + 8.08 + 64\) g/mol = 180.17 g/mol Molar mass of acetylsalicylic acid is 180.17 g/mol.
02

b. Calculate moles and number of molecules of acetylsalicylic acid in the 500-mg tablet

Firstly, to calculate the moles of C9H8O4 in the 500-mg tablet, we need to convert the mass of the tablet from mg to g (500 mg = 0.500 g) and divide it by the molar mass of aspirin. Moles of acetylsalicylic acid = mass of tablet (in g) / molar mass Moles = \(0.500 \div 180.17\) Moles = 0.002774 mol Now, we need to find the number of molecules of acetylsalicylic acid in the tablet. We will use Avogadro's number (6.022 × 10^23) for this calculation. Number of molecules = moles × Avogadro's number Number of molecules = 0.002774 × \(6.022 \times 10^{23}\) Number of molecules = \(1.67 \times 10^{21}\) In a 500-mg tablet, there are 0.002774 moles and \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

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