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Chapter 8: Problem 61

The commonly used pain reliever, aspirin, has the molecular formula \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) If a sample of aspirin contains \(0.968 \mathrm{~g}\) of carbon, what is the mass of hydrogen in the sample? (a) \(0.717 \mathrm{~g}\) (b) \(0.0717 \mathrm{~g}\) (c) \(8.000 \mathrm{~g}\) (d) \(0.645 \mathrm{~g}\)

Short Answer

Expert verified
a) 0.0642 g b) 0.0717 g c) 0.0810 g d) 0.0938 g Answer: b) 0.0717 g

Step by step solution

01

Calculate the molar mass of aspirin

To find the molar mass of aspirin, multiply the number of atoms of each element by its atomic mass and then add up all the values. The atomic masses of C, H, and O are approximately 12 g/mol, 1 g/mol, and 16 g/mol, respectively. Molar mass of aspirin = (9 × 12 g/mol) + (8 × 1 g/mol) + (4 × 16 g/mol) = 108 + 8 + 64 = 180 g/mol
02

Determine the mass of aspirin

Now we need to find the mass of aspirin in the sample. We know that there are 0.968 g of carbon in the sample and that the molecular formula of aspirin has 9 carbon atoms. First, find the molar mass of carbon in the formula: Molar mass of carbon in aspirin = 9 × 12 g/mol = 108 g/mol Then, calculate the mass of aspirin in the sample by multiplying the mass of carbon by the ratio of the molar mass of aspirin to the molar mass of carbon in the formula: Mass of aspirin = 0.968 g × (180 g/mol ÷ 108 g/mol) = 0.968 g × (180 ÷ 108) = 1.6 g
03

Calculate the mass of hydrogen

Now, we will find the mass percentage of hydrogen in aspirin. The molar mass of hydrogen in the molecular formula is 8 g/mol, and the molar mass of aspirin is 180 g/mol. So, the mass percentage of hydrogen is: Mass percentage of hydrogen = (8 g/mol ÷ 180 g/mol) × 100% = (8 ÷ 180) × 100% = 4.44% Finally, we can find the mass of hydrogen in the sample by multiplying the mass of aspirin by the mass percentage of hydrogen in aspirin: Mass of hydrogen = Mass of aspirin × Mass percentage of hydrogen = 1.6 g × 4.44% = 0.071 g So the correct answer is (b) 0.0717 g.

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