Question

A \(2.20-\mathrm{g}\) sample of an unknown acid (empirical formula = \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{3}\) ) is dissolved in \(1.0 \mathrm{~L}\) of water. A titration required \(25.0 \mathrm{~mL}\) of \(0.500 M \mathrm{NaOH}\) to react completely with all the acid present. Assuming the unknown acid has one acidic proton per molecule, what is the molecular formula of the unknown acid?

Short answer

The molecular formula of the unknown acid is C6H8O6, calculated by first finding the moles of NaOH used in the titration and then using this to determine the moles and molar mass of the acid. The ratio of the molar mass of the unknown acid to the molar mass of the empirical formula was found to be 2, thus the molecular formula is 2 times the empirical formula, resulting in C6H8O6.

Step-by-step solution

Calculate the moles of NaOH used in the titration

To find the moles of NaOH used in the titration, we will use the formula: moles = Molarity × Volume. We are given the volume of NaOH to be 25.0 mL (which has to be converted to Liters) and molarity of NaOH to be 0.500 M. Moles of NaOH = 0.500 M × 25.0 mL × (1 L / 1000 mL) = 0.0125 moles

Calculate the moles of unknown acid

As the unknown acid reacts with NaOH in a 1:1 ratio, the moles of acid will be equal to moles of NaOH. Moles of unknown acid = moles of NaOH = 0.0125 moles

Calculate molar mass of the empirical formula

We are given the empirical formula as C3H4O3. Now we can calculate the molar mass: Molar_mass_C3H4O3 = 3 × \( M_C \) + 4 × \( M_H \) + 3 × \( M_O \) = 3 × 12.01 g/mol + 4 × 1.01 g/mol + 3 × 16.00 g/mol = 88.05 g/mol

Calculate molar mass of the unknown acid

We have found the moles of the unknown acid and we are given the mass of the sample. We can now calculate the molar mass of the unknown acid using the formula: Molar mass = mass(moles) Molar mass of unknown acid = 2.20 g / 0.0125 moles = 176.00 g/mol

Determine molecular formula of the unknown acid

We will now find the ratio of molar mass of unknown acid to molar mass of empirical formula to find the molecular formula. Ratio = (Molar mass of unknown acid) / (Molar mass of empirical formula) = 176.00 g/mol / 88.05 g/mol = 2 Now, multiply the empirical formula by this ratio to obtain the molecular formula: Molecular formula = 2 × C3H4O3 = C6H8O6

Key concepts

Empirical and Molecular Formulas

Understanding the difference between empirical and molecular formulas is crucial for chemistry students. An empirical formula represents the simplest whole-number ratio of the atoms in a compound. In contrast, a molecular formula gives the actual number of atoms of each element in a molecule of the compound.

For example, the empirical formula of glucose is CH₂O; it shows the smallest ratio of carbon, hydrogen, and oxygen in the compound. However, the molecular formula of glucose is C₆H₁₂O₆, indicating that each molecule contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.

In the given exercise, we determined that the empirical formula of the unknown acid is C₃H₄O₃. To find the molecular formula, we compare the molar mass of the compound (calculated from the acid's mass and moles) to the molar mass of the empirical formula. Multiplying the empirical formula by the calculated ratio gives us the actual molecular formula.

Mole Concept

The mole concept is the bridge between the microscopic world of atoms and the macroscopic world we observe. One mole of any substance contains exactly Avogadro's number of particles (atoms, ions, molecules), which is approximately 6.022 x 10²³.

In titrations, the mole concept helps us quantify reactions between acids and bases. When we refer to moles of a substance, we're actually talking about how many Avogadro's numbers of particles are present. For instance, in our exercise, we calculated the moles of NaOH used in the titration to be 0.0125 moles, which implies that there are 0.0125 times Avogadro's number of NaOH molecules that reacted with the acid.

Molarity Calculation

Molarity is a measure of the concentration of a solution, expressed as moles of solute per liter of solution. It's a fundamental concept for understanding solution chemistry, especially in reactions like titrations.

To calculate molarity, you divide the number of moles of the solute by the volume of the solution in liters. In this exercise, the molarity of the NaOH solution was given as 0.500 M. With the volume of NaOH used in the titration at 25.0 mL, we converted this volume to liters (by dividing by 1000) and then calculated the moles of NaOH, effectively applying the concept of molarity to find out how much NaOH was present to neutralize the unknown acid.

Acid-Base Reactions

Acid-base reactions, also known as neutralization reactions, are processes where an acid reacts with a base to produce water and a salt. In a typical acid-base titration, a solution of known concentration (the titrant) is added to a measured amount of a solution with an unknown concentration until the reaction reaches its end point.

In our exercise, we dealt with the neutralization of an unknown acid by a sodium hydroxide (NaOH) solution. This reaction followed a 1:1 molar ratio, meaning that for every mole of acid present, one mole of NaOH was required to neutralize it. Understanding this stoichiometry is essential for calculating the molarity of the unknown acid and for many other quantitative aspects of chemistry.