Question

A 0.125-g sample of a monoprotic acid of unknown molar mass is dissolved in water and titrated with \(0.1003 \mathrm{M}\) \(\mathrm{NaOH}\). The equivalence point is reached after adding \(20.77\) \(\mathrm{mL}\) of base. What is the molar mass of the unknown acid?

Short answer

The molar mass of the unknown acid is approximately 61.10 g/mol.

Step-by-step solution

Calculate moles of NaOH used

To find the moles of NaOH used in the reaction, multiply the concentration of the NaOH solution by the volume used to reach the equivalence point, converting milliliters to liters.

Determine moles of monoprotic acid

Because the acid is monoprotic and we've reached the equivalence point, the moles of NaOH will equal the moles of the acid. Therefore, the moles of acid is the same as the moles of NaOH found in Step 1.

Calculate molar mass of the unknown acid

Divide the mass of the acid sample by the moles of acid to find the molar mass. The mass of the acid sample is given, and the moles of acid were calculated in Step 2.

Key concepts

Monoprotic Acid

In chemistry, a monoprotic acid is a type of acid that has the ability to donate one proton or hydrogen ion (H⁺) per molecule during the process of dissociation. This is crucial to understand when performing calculations in acid-base reactions. Common examples of monoprotic acids include hydrochloric acid (HCl) and acetic acid (CH₃COOH). They are simpler to work with in titration problems because the stoichiometry, which is the calculation of reactants and products in chemical reactions, involves a one-to-one ratio. This means for every mole of monoprotic acid, one mole of hydroxide ions (OH^-) is required to neutralize it, which directly leads to the concept of equivalence point in titrations.

To calculate the molar mass of a monoprotic acid, as in the original exercise, the assumption is that for each mole of base added, one mole of the acid reacts, facilitating a straightforward determination of the acid's moles, provided the moles of base are known.

Titration

Titration is a common laboratory method of quantitative chemical analysis used to determine the concentration of an identified analyte. It involves a slow addition of one solution of a known concentration (the titrant) to a known volume of another solution of unknown concentration (the analyte) until the reaction reaches neutralization, which is indicated by a color change or an electrical measurement. Titration is an essential tool in chemistry because it allows scientists and students alike to calculate concentrations with high precision.

During the titration process, the solution's pH changes gradually until it rapidly swings at the equivalence point, where moles of acid equal moles of base. A pH indicator or a pH meter can determine this turning point. Improving one's understanding of titration helps not only in the laboratory but also in understanding reactions in a wider environmental and biological context.

Equivalence Point

The equivalence point is a term specific to the process of titration and refers to the point at which the amount of titrant added equals the amount of substance present in the sample. In the context of an acid-base reaction, it's the point at which the number of moles of hydrogen ions equals the number of moles of hydroxide ions added to the solution. This is the moment when the reaction is complete and the analyte is fully neutralized.

To enhance a student's grasp of this concept: at the equivalence point, the reaction has reached its stoichiometrically exact proportions—neither the acid nor the base is in excess. This is the key point for the calculation in the exercise, as it means the moles of NaOH used will be exactly the same as the moles of monoprotic acid in the solution. By knowing the total moles and having the mass of the sample, one can directly calculate the molar mass, which is a fundamental aspect of understanding a substance's chemical properties.