Problem 10 - Chemical Principles: The Quest for Insight

Question

A 15.00-mL. sample of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (with two acidic protons), was titrated to the stoichiometric point with \(17.02 \mathrm{~mL}\) of \(0.288 \mathrm{M} \mathrm{NaOH}(a q)\). (a) What is the molarity of the oxalic acid? (b) Dctermine the mass of oxalic acid in the solution.

Step-by-Step Solution

Answer

The molarity of the oxalic acid is approximately 0.163 M, and the mass of oxalic acid in the solution is approximately 0.2206 g.

Step 1 - Write down the balanced chemical equation

To determine the molarity of the oxalic acid, we must first establish the balanced chemical reaction between oxalic acid \( \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \) and sodium hydroxide \( \mathrm{NaOH} \) in a titration process. Oxalic acid has two acidic protons and will react with two hydroxide ions. The balanced chemical equation is: \[ \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4(aq) + 2\mathrm{H}_2\mathrm{O}(l) \]

Step 2 - Calculate the moles of NaOH used

To find the molarity of the oxalic acid, we first calculate the moles of \(\mathrm{NaOH}\) used in the titration. The moles of NaOH are found using the volume of the NaOH solution and its molarity: \[ \text{moles of }\mathrm{NaOH} = \text{Volume } (\text{in L}) \times \text{Molarity } (\text{in mol/L}) \] \[ \text{moles of }\mathrm{NaOH} = 0.01702 \text{ L } \times 0.288 \text{ mol/L } = 0.004902 \text{ mol} \]

Step 3 - Calculate the moles of oxalic acid

From the balanced equation, we see that 2 moles of \(\mathrm{NaOH}\) react with 1 mole of \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4\). Thus, using the stoichiometry of the reaction, we can determine the moles of oxalic acid: \[ \text{moles of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = \frac{\text{moles of }\mathrm{NaOH}}{2} = \frac{0.004902}{2} = 0.002451 \text{ mol} \]

Step 4 - Calculate the molarity of oxalic acid

The molarity (M) of the oxalic acid solution is the number of moles of oxalic acid divided by the volume of the oxalic acid solution in liters: \[ \text{Molarity of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = \frac{\text{moles of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4}{\text{Volume of solution in L}} \] \[ \text{Molarity of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = \frac{0.002451\text{ mol}}{0.01500\text{ L}} \approx 0.163 \text{ M} \]

Step 5 - Determine the molar mass of oxalic acid

To determine the mass of oxalic acid, we need to know its molar mass. The molar mass can be found by adding the atomic masses of the constituent atoms in oxalic acid (\(\mathrm{C_2H_2O_4}\)): \[ \text{Molar mass of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = 2(1.01) \text{ g/mol} + 2(12.01) \text{ g/mol} + 4(16.00) \text{ g/mol} \approx 90.04 \text{ g/mol} \]

Step 6 - Calculate the mass of oxalic acid

Now we can calculate the mass of oxalic acid by multiplying the moles of oxalic acid by its molar mass: \[ \text{Mass of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = \text{Moles of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \times \text{Molar mass of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \] \[ \text{Mass of }\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 = 0.002451\text{ mol} \times 90.04\text{ g/mol} \approx 0.2206\text{ g} \]

Key Concepts

Chemical Stoichiometry

Understanding chemical stoichiometry is essential for performing successful titrations, such as the one involving oxalic acid and sodium hydroxide. Stoichiometry refers to the calculation of the reactants and products in chemical reactions. It is based on the conservation of mass and the concept of the mole.

In the provided exercise, stoichiometry is used to determine the relationship between the reactants: oxalic acid, which has two acidic protons, and sodium hydroxide. Here, the balanced chemical equation is of paramount importance as it reveals the mole ratio between reactants and products. We observe that two moles of sodium hydroxide neutralize one mole of oxalic acid, showcasing a 2:1 ratio.

To successfully interpret or predict the outcomes of chemical reactions, mastering stoichiometry is indispensable. It enables us to accurately quantify how much reactant is needed to produce a certain amount of product, which is crucial for this titration.

Molarity Calculation

The concept of molarity is a cornerstone of quantitative analysis in chemistry, particularly in the context of titrations. Molarity, expressed as moles per liter (mol/L), is a measure of the concentration of a solution. In the problem at hand, after determining the moles of NaOH used in the titration, we need to calculate the molarity of the oxalic acid.

The molarity of a solution is found by dividing the number of moles of the solute by the volume of the solution in liters. It's imperative to ensure that the volume is converted to liters if it’s given in milliliters or any other unit to ensure uniformity in the calculation. In educational contexts, elucidating the process of molarity calculation fosters a deeper understanding of solution concentration and assists in the prediction of reactions' outcomes in various scenarios.

Acid-Base Titration

Acid-base titration is a powerful analytical technique used to determine the concentration of an acid or a base in a solution. This method involves a neutralization reaction, where an acid and a base react to produce a salt and water. Titrations are performed by gradually adding a solution of known concentration (the titrant) to a solution of unknown concentration (the analyte) until the reaction reaches the equivalence point, indicated by a color change with an indicator or via a pH meter.

The exercise requires performing a titration of oxalic acid with sodium hydroxide. By calculating the point at which the acidic protons of oxalic acid have completely reacted with the hydroxide ions from the sodium hydroxide, we can deduce the exact amount of acid in the original solution. Emphasizing the importance of precision and understanding the end-point readouts are vital in the learner’s competency in performing titrations.

Moles and Molar Mass

The mole is a fundamental unit in chemistry that represents a specific number of particles, be it atoms, molecules, ions, or electrons. This quantity, known as Avogadro's number, is approximately 6.022 x 10²³ entities per mole. The molar mass, expressed in grams per mole (g/mol), relates the mass of a substance to the number of moles, and is equivalent to the sum of the atomic masses of all atoms in a molecule.

In our oxalic acid exercise, determining the moles of the substance involved in the reaction is a crucial step. It is followed by calculating the mass of the oxalic acid using its molar mass, incorporating the atomic masses of carbon, hydrogen, and oxygen. These concepts are intertwined; understanding the relationship between moles, molar mass, and mass is fundamental for solving problems in stoichiometry and for conducting various other calculations in chemistry.