Problem 138 - Chemistry The Molecular Nature of Matter

Question

Oxalic acid, a diprotic acid having the formula \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), is used to clean the rust out of radiators in cars. A sample of an oxalic acid mixture was analyzed by titrating a 0.1000 g sample dissolved in water with \(0.0200 M\) \(\mathrm{NaOH}\). A volume of \(15.20 \mathrm{~mL}\) of the base was required to completely neutralize the oxalic acid. What was the percentage by mass of oxalic acid in the sample?

Step-by-Step Solution

Answer

The percentage by mass of oxalic acid in the sample.

Step 1: Calculate the amount of substance (moles) of NaOH used in the titration

Use the concentration of NaOH and the volume used to find the moles. The number of moles of NaOH can be found using the formula: Moles of NaOH = concentration of NaOH * volume of NaOH in litersGiven that the concentration is 0.0200 M and the volume used was 15.20 mL, which is equivalent to 0.01520 liters, the calculation will be:Moles of NaOH = 0.0200 M * 0.01520 L

Step 2: Determine the moles of oxalic acid neutralized

Because oxalic acid is a diprotic acid, which means it can donate two protons per molecule, each mole of oxalic acid reacts with two moles of NaOH. Therefore, the moles of oxalic acid is half the number of moles of NaOH. If we found the moles of NaOH in step 1, we can find the moles of oxalic acid as follows:Moles of oxalic acid = (1/2) * Moles of NaOH

Step 3: Calculate the mass of oxalic acid

By using the molar mass of oxalic acid (which is 90.03 g/mol), the mass of oxalic acid in the sample can be calculated with the formula:Mass of oxalic acid = moles of oxalic acid * molar mass of oxalic acid

Step 4: Determine the percentage by mass of oxalic acid in the sample

The mass percentage of oxalic acid can be found using the total mass of the sample and the mass of oxalic acid obtained from the titration.Percentage by mass = (mass of oxalic acid / mass of sample) * 100%

Key Concepts

Diprotic Acid

Understanding what a diprotic acid is plays a crucial role in handling titration problems involving such substances. A diprotic acid, as the name suggests, is an acid that can donate two protons (hydrogen ions, H+) per molecule when it reacts in an aqueous solution. Oxalic acid, with its chemical formula \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\), is a perfect example of a diprotic acid. Each molecule of oxalic acid can undergo two successive ionization reactions to release two \(H^+\) ions.

This dual capacity is important in titration calculations, as it means that one mole of oxalic acid will react with two moles of a monoprotic base like sodium hydroxide (NaOH). It's critical to remember this 1:2 stoichiometry when doing calculations, or the results will be incorrect. Moreover, the ability to handle such an acid is also vital in certain industrial processes and laboratory settings where precise concentrations of chemical solutions are required.

Titration Calculations

Titration is a common laboratory technique used to determine the concentration of an unknown solution. It involves adding a titrant, in this case, a standard NaOH solution, to a solution containing the analyte, oxalic acid, until the reaction reaches an equivalence point, where the moles of acid equals the moles of base.

In the titration of a diprotic acid like oxalic acid, understanding the stoichiometry of the reaction is crucial. For oxalic acid, every mole of it requires two moles of NaOH to reach neutralization. The formula \(\text{Moles of oxalic acid} = \frac{1}{2} \times \text{Moles of NaOH}\) is derived from this stoichiometry and is pivotal in determining the amount of substance involved in the reaction. Such calculations allow chemists to determine the concentration and mass percentage of an analyte in a sample with precision.

Molar Mass

Knowing the molar mass of a substance is a fundamental aspect of chemical calculations. The molar mass is defined as the mass of one mole of a substance and has units of grams per mole (g/mol). It is particularly useful in converting between the mass of a substance and the amount in moles and vice versa.

The molar mass of oxalic acid is 90.03 g/mol, which is derived from the combined atomic weights of all atoms in its molecular formula (2 Hydrogens, 2 Carbons, and 4 Oxygens). Using molar mass, we can determine the mass of oxalic acid present in a solution through the equation \(\text{Mass of oxalic acid} = \text{moles of oxalic acid} \times \text{molar mass of oxalic acid}\). In titration, once the number of moles of the acid is known, this formula allows us to find out the actual mass of the acid that was present in the solution, thus aiding in various quantitative analyses.

Neutralization Reaction

Neutralization is a chemical reaction in which an acid and a base react to form water and a salt and often results in a significant change in pH. In the context of titrations involving a diprotic acid like oxalic acid, the neutralization reaction involves the double replacement of two hydroxide ions (OH-) from sodium hydroxide with two protons (H+) from the acid. The distinctive feature of this reaction is it proceeds in stages, as each proton is successively neutralized by a hydroxide ion.

The balanced chemical equation for oxalic acid reacting with sodium hydroxide can be written as: \(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4} + 2\mathrm{NaOH} \rightarrow \mathrm{Na}_{2}\mathrm{C}_{2}\mathrm{O}_{4} + 2\mathrm{H}_{2}\mathrm{O}\). The complete neutralization is reached when there are no more free protons in the solution, which is typically indicated by a color change in the presence of an indicator or by reaching a certain pH value. Understanding neutralization reactions is vital for performing and interpreting titrations accurately.