Question

You take \(1.00 \mathrm{~g}\) of an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen), burn it in air, and collect \(2.20\) \(\mathrm{g} \mathrm{CO}_{2}\) and \(0.400 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). You know that the molar mass of aspirin is between 170 and \(190 \mathrm{~g} / \mathrm{mol}\). Reacting 1 mole of salicylic acid with 1 mole of acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) gives you 1 mole of aspirin and 1 mole of acetic acid \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right)\). Use this information to determine the molecular formula of salicylic acid.

Short answer

The molecular formula of salicylic acid is C4H4O2.

Step-by-step solution

Calculate moles of carbon and hydrogen in aspirin

Given that 1.00 g of aspirin was burned and generated 2.20 g of CO2 and 0.400 g of H2O, we will calculate the moles of carbon and hydrogen in aspirin. Moles of Carbon: Moles of CO2 = \( \frac{2.20}{44.01} \) (1 mol of CO2 contains 1 mol of carbon) Moles of Hydrogen: Moles of H2O = \( \frac{0.400}{18.02} \) (1 mol of H2O contains 2 mol of hydrogen) Now calculate the moles: Moles of C = 0.050 mol Moles of H = 0.044 mol

Determine the moles of oxygen in aspirin

Since aspirin contains only carbon, hydrogen, and oxygen, compute the mass of oxygen in aspirin using the difference between the mass of aspirin and the sum of the masses of carbon and hydrogen. Mass of C = 0.050 mol × 12.01 g/mol = 0.600 g Mass of H = 0.044 mol × 1.01 g/mol = 0.044 g Thus, the mass of oxygen in aspirin = 1.00 g - 0.600 g - 0.044 g = 0.356 g Calculate the moles of oxygen using its molar mass: Moles of O = \( \frac{0.356}{16.00} \) = 0.022 mol

Find the empirical formula of aspirin

Now that we have the moles of each element, divide each by the smallest value (0.022 mol in this case) to get the empirical formula: C: \( \frac{0.050}{0.022} \) ≈ 2 H: \( \frac{0.044}{0.022} \) ≈ 2 O: \( \frac{0.022}{0.022} \) = 1 So, the empirical formula of aspirin is C2H2O.

Determine the molecular formula of aspirin

To find the molecular formula of aspirin, consider its molar mass between 170 and 190 g/mol and its empirical formula. Using the empirical formula, we have: Empirical formula molar mass: Molar mass of C2H2O = (2 × 12.01 g/mol) + (2 × 1.01 g/mol) + (1 × 16.00 g/mol) = 42.04 g/mol Now calculate the ratio between the molar mass of aspirin and the molar mass of its empirical formula \( \frac{170 - 190}{42.04} \) = 4 (rounded to the nearest whole number) So, the molecular formula of aspirin is 4 times the empirical formula: C6H8O4.

Determine the molecular formula of salicylic acid

The balanced equation for the reaction between salicylic acid and acetic anhydride is: Salicylic acid + C4H6O3 → Aspirin + Acetic acid Salicylic acid + C4H6O3 → C6H8O4 + C2H4O2 Using this equation, we can deduce the molecular formula of salicylic acid: C6H8O4 - C2H4O2 = C4H4O2 Hence, the molecular formula of salicylic acid is C4H4O2.

Key concepts

Empirical Formula

Grasping the concept of an empirical formula is essential in chemistry. Think of the empirical formula as the simplest ratio of elements in a compound, showing the relative numbers of atoms of each element. It doesn't tell you about the actual number of atoms in the molecule, but rather the simplest whole number ratio between them.

For instance, in our aspirin example, after burning the aspirin and conducting careful measurements, we determined the moles of carbon, hydrogen, and oxygen. These measurements were critical because they allowed us to compute the ratio of atoms of each element. By dividing the moles of each element by the smallest number of moles obtained, we found that aspirin has a 2:2:1 ratio of carbon to hydrogen to oxygen, which simplifies to the empirical formula C2H2O.

This process, often part of a chemical composition analysis, enables us to simplify complex information to its most basic form, an essential step before proceeding to determine the true molecular formula of a compound.

Stoichiometry

Stoichiometry is the method of calculating the relative quantities of reactants and products in chemical reactions. We use this quantitative relationship between reactants and products to predict the outcomes of reactions and understand the proportions in which chemicals combine.

In our exercise, stoichiometry comes into play when deriving the empirical formula and eventually the molecular formula of salicylic acid. It's essential to understand that stoichiometry is not just about balancing equations, but also about the quantitative analysis of the compounds involved. For example, by knowing the mass of aspirin and its combustion products, we were able to calculate the moles of carbon, hydrogen, and oxygen, which is essential for establishing the empirical formula, and eventually the molecular weight of the compound, which is a stoichiometric calculation itself.

Remember, stoichiometry can only work with balanced equations. Thus, knowing the reaction between salicylic acid and acetic anhydride was pivotal in determining the molecular formula of salicylic acid, as it allowed us to use stoichiometry to subtract the moles of acetic acid produced from aspirin, yielding the molecular formula of salicylic acid.

Chemical Composition Analysis

Chemical composition analysis is a broad term that encompasses various methods used to determine the composition of a substance. In the context of our example, the chemical composition analysis involved burning aspirin to discover the amounts of carbon dioxide and water produced. By applying the principles of stoichiometry, we were able to back-calculate the amount of carbon and hydrogen in the original aspirin tablet.

This analysis is a practical application of the conservation of mass; the elements in the reactants (aspirin and oxygen from the air) are conserved in the products (carbon dioxide and water). From the masses of the products, we used the known molar masses of carbon dioxide and water to determine the moles of the constituent elements. This is a direct and quantitative chemical composition analysis, pivotal in finding the empirical formula.

Understanding chemical composition is not just about the 'what' but also the 'how much'. By meticulously quantifying the substances produced from chemical reactions, we can infer the amount of each element present in the original compound, which is the cornerstone for deducing its molecular structure.