Question

The chemical formula for aspirin is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). What is the mass percent for each element in 1 mole of aspirin? (Give your answer to four significant figures.) carbon hydrogen oxygen

Short answer

The mass percent of carbon, hydrogen, and oxygen in aspirin is approximately 60.00%, 4.478%, and 35.52%, respectively.

Step-by-step solution

Calculate the molar mass of aspirin

To calculate the molar mass of aspirin, we first need to find the molar mass of each element and then multiply it by the number of atoms of that element in the formula. Then we will add up these masses to find the total molar mass. Molar mass of Carbon (C) = 12.01 g/mol Molar mass of Hydrogen (H) = 1.008 g/mol Molar mass of Oxygen (O) = 16.00 g/mol The molar mass of aspirin = (9 * 12.01 g/mol) + (8 * 1.008 g/mol) + (4 * 16.00 g/mol)

Determine the mass contribution of each element

Now, let's find out the mass contribution of each element in aspirin by multiplying the molar mass of each element by the corresponding number of atoms present in the formula. Mass contribution of Carbon = 9 * 12.01 g/mol = 108.09 g/mol Mass contribution of Hydrogen = 8 * 1.008 g/mol = 8.064 g/mol Mass contribution of Oxygen = 4 * 16.00 g/mol = 64.00 g/mol

Calculate the total molar mass of aspirin

Add up the mass contributions of carbon, hydrogen, and oxygen to find the total molar mass of aspirin. Total molar mass of aspirin = 108.09 g/mol + 8.064 g/mol + 64.00 g/mol ≈ 180.15 g/mol

Calculate the mass percent for each element

Now, we can find the mass percent of each element by dividing its mass contribution by the total molar mass of aspirin and multiplying by 100. Mass percent of Carbon = (108.09 g/mol) / (180.15 g/mol) * 100 ≈ 60.00% Mass percent of Hydrogen = (8.064 g/mol) / (180.15 g/mol) * 100 ≈ 4.478% Mass percent of Oxygen = (64.00 g/mol) / (180.15 g/mol) * 100 ≈ 35.52% The mass percent of carbon, hydrogen, and oxygen in aspirin is approximately 60.00%, 4.478%, and 35.52%, respectively.

Key concepts

Molar Mass Calculation

The concept of molar mass is crucial for understanding the composition of substances in chemistry. Molar mass is defined as the mass of one mole of a substance, and it is typically expressed in grams per mole (g/mol). One mole contains Avogadro's number of entities, which is approximately 6.022 x 10^23, of the substance in question.

For a compound such as aspirin with the chemical formula \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\), we calculate its molar mass by summing the molar masses of each constituent element multiplied by their respective number of atoms in the molecule. The molar mass serves as a bridge between the microscopic scale of atoms and molecules and the macroscopic world we can measure and observe.

Understanding the calculation of molar mass enables students to determine the amount of substance required in a reaction, the yield of a product, or, as in our exercise, the mass percent composition of each element within a compound.

Chemical Formula

A chemical formula represents the types and quantities of atoms that constitute a particular chemical compound. In the case of aspirin, the chemical formula is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\), indicating that a single molecule consists of 9 carbon atoms, 8 hydrogen atoms, and 4 oxygen atoms. The subscripts in the formula tell us the exact stoichiometry, or atom ratio, within a molecule.

Chemical formulas are not only critical for representing the composition of compounds but also serve as the foundation for balancing chemical equations, understanding molecular geometry, and exploring the chemical properties of substances. When working with chemical formulas, one must be careful to account for each atom, as this will affect all subsequent calculations involving the compound.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships of the elements and compounds as they undergo chemical reactions. It arises from the law of conservation of mass and the concept of the mole. Stoichiometry allows chemists to predict the amounts of products formed in a reaction from a given amount of reactants and vice versa.

When calculating mass percent composition, stoichiometry helps us link the mass of each element to the total mass of the compound. By knowing the stoichiometric coefficients (the numbers before the formulas in a balanced chemical equation) and the molar masses, we can perform calculations that reveal important details about the makeup of a compound, which is exactly what we applied in finding the mass percent composition for each element in aspirin.