Question

A 0.105-g sample of a diprotic acid of unknown molar mass is dissolved in water and titrated with \(0.1288 \mathrm{M}\) \(\mathrm{NaOH}\). The equivalence point is reached after adding \(15.2\) \(\mathrm{mL}\) of base. What is the molar mass of the unknown acid?

Short answer

The molar mass of the unknown acid is 123.81 g/mol.

Step-by-step solution

Calculate the amount of NaOH used in moles

Use the concentration of NaOH and the volume of NaOH added to determine the moles of NaOH that reacted with the acid. The number of moles () can be calculated using the equation: n = concentration (M) * volume (L).

Determine the moles of the unknown acid

Since the unknown acid is diprotic, each mole of the acid can react with 2 moles of NaOH. Therefore, the moles of acid will be half the moles of NaOH.

Calculate the molar mass of the unknown acid

Divide the mass of the acid sample by the moles of the acid to obtain its molar mass. The molar mass (M) can be calculated using the equation: M = mass (g) / moles.

Key concepts

Diprotic Acid

Understanding what a diprotic acid is can be crucial when analyzing acid-base reactions, especially during titration. A diprotic acid is an acid that can donate two protons (hydrogen ions, H+) when it dissociates in solution. This characteristic defines its specific behavior in chemical reactions like titration, where it requires two hydroxide ions (OH-) to neutralize each molecule of acid. A common example of a diprotic acid is sulfuric acid (H₂SO₄).

When performing a titration with a diprotic acid, it is essential to remember that the acid will react with the base in a 1:2 molar ratio, where each mole of acid reacts with two moles of a monobasic (single proton) base like NaOH. This stoichiometric relationship is central to calculating the mass or concentration of the acid involved in the reaction.

Molar Mass

Molar mass is another fundamental concept in chemistry, acting as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. It is defined as the mass of one mole of a substance and is expressed in grams per mole (g/mol).

The molar mass of an element is simply the atomic mass listed on the periodic table, while the molar mass of a compound is calculated by adding up the atomic masses of all the atoms in a molecule of that compound. In practice, knowing the molar mass allows us to convert between the mass of a substance and the number of moles, laying the foundation for all stoichiometric calculations. For the diprotic acid in the titration example, calculating the molar mass from the mass of the sample and the moles of acid involved reveals the identity of the unknown acid.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. These relationships are derived from the balanced chemical equation for the reaction, which shows the ratio in which substances react and are produced—a concept known as the stoichiometric ratio.

In the context of a titration involving a diprotic acid and a base like NaOH, stoichiometry guides us to understand the mole-to-mole relationships. With diprotic acids, the stoichiometry becomes slightly more complex as you need two moles of a monoprotic base to neutralize one mole of the acid. This 1:2 stoichiometric ratio is essential in calculating the correct amounts of substances involved in the reaction.

Equivalence Point

The equivalence point in a titration is a significant moment in the process—it's where the number of moles of the titrant (the substance in the burette, typically a base like NaOH) equals the number of moles of the substance being titrated (in this case, the diprotic acid). This point represents the complete neutralization of the acid by the base.

For a diprotic acid, the equivalence point is reached once two moles of the base are added for every mole of the acid. By carefully measuring the volume of the titrant added to reach this point, we can determine the concentration or moles of the acid using stoichiometric calculations. In our example, finding the equivalence point allows us to work backwards to find the molar mass of the unknown diprotic acid, given the sample's mass and the molarity of the titrant.