Question

(a) By titration, 15.0 \(\mathrm{mL}\) of 0.1008 \(\mathrm{M}\) sodium hydroxide is needed to neutralize a \(0.2053-\mathrm{g}\) sample of a weak acid. What is the molar mass of the acid if it is monoprotic? (b) An elemental analysis of the acid indicates that it is composed of \(5.89 \% \mathrm{H}, 70.6 \% \mathrm{C},\) and 23.5\(\% \mathrm{O}\) by mass. What is composed of \(5.89 \% \mathrm{H}, 70.6 \% \mathrm{C},\) and 23.5\(\% \mathrm{O}\) by mass. What is its molecular formula?

Short answer

The molar mass of the acid is found to be 122.09 g/mol, and its molecular formula is C₇H₆O₂.

Step-by-step solution

Calculate the moles of sodium hydroxide

We are given the volume and molarity of sodium hydroxide, which is needed to neutralize the acid. We can use this information to find the moles of sodium hydroxide. Moles of sodium hydroxide = Volume (in liters) × Molarity \(Moles\,of\,NaOH = 15.0 \times 10^{-3} \,L\,× 0.1008\,M\]

Calculate the moles of the weak acid

Since the acid is monoprotic, it means that one mole of sodium hydroxide reacts with exactly one mole of the acid in a 1:1 ratio. Therefore, the moles of sodium hydroxide will also be equal to the moles of the acid. So, the moles of acid = moles of sodium hydroxide.

Calculate the molar mass of the acid

Now that we have the moles of the acid and its mass, we can calculate its molar mass. Divide the given mass of the acid by the moles of the acid. Molar mass of the acid = \( \frac{Mass\,of\,acid}{Moles\,of\,acid}\)

Calculate the empirical formula of the acid using percent composition

First, convert each percentage to grams, assuming a 100 g sample. This will give us the number of grams of each element present. Then, divide the grams of each element by their respective atomic masses to obtain the number of moles. Finally, divide the moles of each element by the smallest number of moles to get the empirical formula ratios.

Determine the molecular formula of the acid

Now that we have the empirical formula and the molar mass of the acid, we can find its molecular formula. Divide the molar mass of the acid by the molar mass of the empirical formula to find the multiplier. Multiply the empirical formula by this multiplier to determine the molecular formula.

Key concepts

Titration

Titration is an essential technique in chemistry used to determine the concentration of an unknown solution by reacting it with a solution of a known concentration. This process involves a titrant (known solution) which is gradually added to the analyte (unknown solution) until the reaction reaches the endpoint, which can be indicated by a color change due to a pH indicator. The point at which the reaction is complete is known as the equivalence point.

In the context of the exercise, titration is used to find the amount of sodium hydroxide (the titrant) needed to neutralize a specific mass of a weak monoprotic acid (the analyte). Knowing the volume and molarity of the sodium hydroxide solution allows us to calculate the moles of the acid present, which is a crucial step in determining the molar mass of the acid.

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements within the compound. It reflects the relative number of atoms of each element, but not the actual number of atoms found in a single molecule of the compound.

In the problem, once the percent composition by mass of the elements in the acid has been determined, these percentages are then assumed to represent parts per hundred in a 100-gram sample. This simplification allows us to directly convert percentages to grams, thereby facilitating the calculation of the empirical formula. After finding the moles of each element by dividing by their atomic masses, the ratios of atoms are deduced by dividing each by the smallest number of moles.

Molecular Formula

The molecular formula differs from the empirical formula as it indicates the actual number of atoms of each element in a molecule of the compound. It might be the same as the empirical formula or it could be a whole-number multiple of the empirical formula.

In our exercise, once the empirical formula is found, the molecular formula is determined by comparing the molar mass of the empirical formula with the molar mass derived from the titration. By dividing the molar mass of the compound by the molar mass of the empirical formula, the number of empirical units in the molecule is obtained. Multiplying the subscripts in the empirical formula by this number will give the molecular formula of the compound.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a balanced chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

In this exercise, stoichiometry is used to relate the moles of sodium hydroxide needed to neutralize the weak acid. Since the acid is monoprotic, meaning it donates one proton per molecule, the stoichiometry is 1:1. Knowing the amount of sodium hydroxide allows us to directly calculate the number of moles of the acid, which is crucial for finding the molar mass of the acid.

Percent Composition

Percent composition refers to the percent by mass of each element present in a compound. It is a measure of the relative quantities of elements in a substance and can be determined from the compound’s molecular or empirical formula.

For the analysis in our problem, the percent composition is used to establish the base ratios of elements in the empirical formula calculation. First, each element’s mass percentage is converted to grams as if we had a 100-gram sample of the compound. Then, these masses are converted to moles, subsequently allowing us to establish the lowest whole-number ratio of atoms in the compound, leading us to the empirical formula.