Question

Aspirin is a monoprotic acid called acetylsalicylic acid Its formula is \(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\). A certain pain reliever was analyzed for aspirin by dissolving \(0.118 \mathrm{~g}\) of it in water and titrating it with \(0.0300 \mathrm{M} \mathrm{KOH}\) solution. The titration required \(14.76 \mathrm{~mL}\) of base. What is the percentage by weight of aspirin in the drug?

Short answer

The weight percentage of aspirin in the drug is calculated using the steps above.

Step-by-step solution

Calculate the amount (in moles) of KOH used in the titration

Use the molarity of KOH and the volume of KOH solution used to find the moles of KOH. The formula to calculate moles is: \( n = M \times V \), where \( n \) is the number of moles, \( M \) is the molarity, and \( V \) is the volume in liters. Convert the volume from milliliters to liters before calculating.

Determine the moles of aspirin

Since aspirin is a monoprotic acid, one mole of aspirin reacts with one mole of KOH. Hence, the moles of KOH used are equal to the moles of aspirin.

Calculate the molar mass of aspirin

The molar mass of aspirin (acetylsalicylic acid, \( \mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4} \)) is calculated by adding the atomic masses of its constituent atoms. For acetylsalicylic acid: C (12.01 g/mol) \( \times 9 \), H (1.008 g/mol) \( \times 8 \), and O (16.00 g/mol) \( \times 4 \).

Calculate the mass of aspirin

Use the number of moles of aspirin and its molar mass to calculate the mass of aspirin that was in the sample.

Calculate the percentage by weight of aspirin in the drug

Divide the mass of aspirin (from Step 4) by the total mass of the sample and multiply by 100 to get the percentage by weight of aspirin.

Key concepts

Acid-Base Titration

Acid-base titration is a quantitative chemical analysis method used to determine the concentration of an unknown acid or base by reacting it with a known volume and concentration of base or acid respectively. In the case of aspirin, which is acetylsalicylic acid, titration involves adding a strong base like potassium hydroxide (KOH) to the solution containing the aspirin until the reaction is complete—signified by a change in pH or an indicator's color change.

This process is based on a stoichiometric reaction, where one mole of the acid reacts with one mole of the base. By measuring the amount of base needed to neutralize the acid, you can calculate the amount of the acid present in the solution. It's a classic technique used in chemistry to determine molar concentrations and to gauge the purity of substances, such as aspirin in a pharmaceutical preparation.

Molarity Calculation

Molarity is one of the most common units of concentration in chemistry, representing the number of moles of a solute per liter of solution (\textbf{mol/L}). To find the molarity, you use the formula:
\( M = \frac{n}{V} \),
where \( M \) is the molarity, \( n \) is the number of moles, and \( V \) is the volume in liters. It's essential to convert the volume to liters if it's given in milliliters. This concept is crucial when performing a titration as you need the molarity of the titrant (in this case, KOH) to calculate the number of moles that reacted, which in turn helps determine the concentration of the unknown substance. Molarity calculations form the foundation for further analysis in stoichiometry and deriving other vital data such as the percentage purity of substances.

Molar Mass

Molar mass, often referred to in units of grams per mole (\textbf{g/mol}), is a substance's mass per unit mole and is calculated by adding the atomic masses of all atoms in a molecule. It's a fundamental constant that converts between grams and moles, making it essential in stoichiometry. For acetylsalicylic acid (\textbf{C\(_9\)H\(_8\)O\(_4\)}), the molar mass is the sum of the masses of 9 carbon atoms, 8 hydrogen atoms, and 4 oxygen atoms. The precise molar mass is necessary for accurate stoichiometric calculations, as it allows us to convert between the mass of a substance and the number of moles present. Knowing the molar mass of aspirin is critical for determining the exact amount of the substance in a given sample, especially when analyzing the substance's percentage purity or concentration.

Stoichiometry

Stoichiometry is essentially the math behind chemistry. It deals with the calculations of the quantities of reactants and products involved in a chemical reaction. It is grounded in the law of conservation of mass, where the total mass of the reactants equals the total mass of the products.

In stoichiometric calculations, understanding the mole ratio of reactants and products, as dictated by a balanced chemical equation, is crucial. For the aspirin titration, the reaction between acetylsalicylic acid and KOH is one-to-one; thus, the moles of KOH used gives us the moles of aspirin originally present in the solution. These moles can then be converted into grams using the molar mass and subsequently used to calculate the percentage by weight of aspirin in the pain reliever. Mastery of stoichiometry is vital for any aspiring chemist, as it enables the prediction of outcomes of chemical reactions and quantification of the purity and concentrations of substances.