Question

A 0.5224-g sample of an unknown monoprotic acid was titrated with 0.0998 M \(\mathrm{NaOH}\). The equivalence point of the titration occurred at \(23.82 \mathrm{~mL}\). Determine the molar mass of the unknown acid.

Short answer

The molar mass of the unknown acid is calculated to be \frac{0.5224\text{ g}}{0.02382\text{ L} \times 0.0998\text{ M}} \frac{0.5224\text{ g}}{0.002376\text{ mol}} = 219.79\text{ g/mol}.

Step-by-step solution

Calculate moles of NaOH used

Use the concentration of the NaOH solution and the volume at the equivalence point to calculate the moles of NaOH used in the titration. The formula is: moles of NaOH = concentration of NaOH (in mol/L) * volume of NaOH (in L).

Determine moles of unknown acid neutralized

Since the acid is monoprotic, one mole of NaOH reacts with one mole of the acid. Therefore, the moles of NaOH used is equal to the moles of the unknown acid neutralized.

Calculate the molar mass of the unknown acid

Using the mass of the unknown acid sample and the moles of acid determined in Step 2, calculate the molar mass. The formula is: molar mass of acid = mass of acid sample (in g) / moles of acid.

Key concepts

Acid-Base Titration

Understanding acid-base titration is fundamental when studying chemistry. This process involves reacting a solution of known concentration, typically a base, with an acid of unknown concentration to determine its molar concentration.
The procedure is done by slowly adding the base to the acid until the reaction is complete, which is indicated by a change in color thanks to an indicator substance added to the acid. This moment is important—it's when stoichiometry comes into play. Stoichiometry is the calculation of reactants and products in chemical reactions, and in a titration, it helps us deduce the exact amount of substance in the unknown solution. For instance, in the given problem, we use stoichiometry to find out the molar mass of the unknown monoprotic acid using the known concentration and the volume of sodium hydroxide (NaOH).

Monoprotic Acid

A monoprotic acid is a type of acid that can donate only one proton or hydrogen atom per molecule to a base during the reaction. This means that the acid has only one ionizable hydrogen.
In the context of the given problem, knowing that the acid is monoprotic simplifies our calculations, as we establish a 1:1 molar ratio between the acid and the base—sodium hydroxide (NaOH). This directly leads us to the understanding that the moles of NaOH used in the titration are equal to the moles of the unknown monoprotic acid. Thus, when the solution of NaOH of known concentration reacts with the unknown monoprotic acid, they neutralize each other on a one-to-one basis.

Equivalence Point

The equivalence point is a term specific to titration that refers to the moment when the acid and base have reacted with each other in exactly the right proportions to neutralize one another. It is the point at which the number of moles of hydrogen ions from the acid equals the number of moles of hydroxide ions supplied by the base.
In the case of our monoprotic acid example, since the unknown acid donates one hydrogen ion per molecule, the equivalence point is reached when the number of moles of acid equals the number of moles of NaOH added. This was found to be at a volume of 23.82 mL of the NaOH solution. Indicators or pH meters are often used to identify the equivalence point with precision during a titration.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the calculation of the quantities of substances involved in chemical reactions. It is based on the laws of conservation of mass and the concept that in a chemical reaction, atoms are neither created nor destroyed but transformed.
For the molar mass determination of our unknown monoprotic acid, stoichiometry is used to calculate the molar mass after understanding the one-to-one mole relationship at the equivalence point between NaOH and the unknown acid. From the stoichiometry of the balanced chemical equation, and knowing the molar concentration and volume of NaOH used, we can calculate the moles of the unknown acid neutralized and from there, by considering the initial mass of the acid sample, we can determine its molar mass. This is a powerful application of stoichiometry to find out important information about a substance's identity.