Question

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

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

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

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

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.

Key concepts

Molar Mass

To understand the molar mass, we need to know that it's the sum of the atomic masses of all the atoms in a given molecule. Molar mass is expressed in grams per mole (g/mol). It's like the 'weight' of one mole of a chemical compound. For aspirin, with a molecular formula of \(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4\), we calculate it by adding up the contributions from each atom.

• Carbon (C): 12 g/mol
• Hydrogen (H): 1 g/mol
• Oxygen (O): 16 g/mol

For aspirin:

• 9 Carbon atoms: \(9 \times 12 = 108 \text{ g/mol}\)
• 8 Hydrogen atoms: \(8 \times 1 = 8 \text{ g/mol}\)
• 4 Oxygen atoms: \(4 \times 16 = 64 \text{ g/mol}\)

Adding these, the molar mass of aspirin is \(108 + 8 + 64 = 180 \text{ g/mol}\). This means one mole of aspirin weighs 180 grams.

Mass Percentage

Mass percentage shows us how much of a specific element is present in a compound, relative to the total mass. It's a useful way of expressing the composition of a compound. The mass percentage of an element is calculated by dividing the molar mass of the element by the molar mass of the entire compound, and then multiplying by 100 to get a percentage.In our aspirin sample, the calculations for hydrogen demonstrate this:The molar mass of hydrogen in aspirin is 8 g/mol and the molar mass of aspirin is 180 g/mol. Thus, the mass percentage is calculated as:\[\frac{8 \text{ g/mol}}{180 \text{ g/mol}} \times 100\% = 4.44\%\]This tells us that in a given sample of aspirin, 4.44% of the mass is due to hydrogen. This percentage is crucial for determining how much hydrogen is present in any given mass of aspirin.

Chemical Composition

Chemical composition refers to the identity and ratio of the different elements that make up a compound. It's important because it allows chemists to understand and predict the properties and behaviors of a compound.For aspirin, the chemical composition is detailed in its molecular formula \(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4\). This formula tells us that each molecule of aspirin consists of:

• 9 atoms of Carbon (C)
• 8 atoms of Hydrogen (H)
• 4 atoms of Oxygen (O)

This precise configuration of atoms defines aspirin as a compound, with specific properties and reactions. Understanding this allows chemists to manipulate and use aspirin effectively, whether it's in creating medicines or understanding its effects in the body.

Aspirin

Aspirin, known scientifically as acetylsalicylic acid, is a common medication used to reduce pain, fever, or inflammation. It was first discovered in the 19th century and has become one of the most widely used drugs globally.Chemically, aspirin is described by its molecular formula \(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4\). This informs about its makeup, indicating that a single aspirin molecule consists of nine carbon atoms, eight hydrogen atoms, and four oxygen atoms. These elements form a structure that contributes to aspirin's effectiveness as a medication.Because of its composition:

• Aspirin is soluble in water, which is why it can be ingested and absorbed quickly by the body.
• The specific arrangement of atoms allows it to block certain pathways that cause pain, making it an effective analgesic.
• Its efficacy and low cost have made it a staple in medical use around the world.

Aspirin's molecular understanding is crucial for healthcare providers, ensuring they know exactly what they are administering and how it will interact with the body.