Problem 97 - Chemistry An Atoms First Approach

Question

A student intends to titrate a solution of a weak monoprotic acid with a sodium hydroxide solution but reverses the two solutions and places the weak acid solution in the buret. After \(23.75 \mathrm{mL}\) of the weak acid solution has been added to \(50.0 \mathrm{mL}\) of the \(0.100 \mathrm{M} \mathrm{NaOH}\) solution, the \(\mathrm{pH}\) of the resulting solution is \(10.50 .\) Calculate the original concentration of the solution of weak acid.

Step-by-Step Solution

Answer

The original concentration of the weak acid solution is approximately \(0.2105 \: \mathrm{M}\).

Step 1: Calculate moles of NaOH

First, we need to calculate the moles of sodium hydroxide (NaOH). To do this, we will use the formula: Moles of NaOH = Molarity × Volume Given that the molarity of NaOH is 0.100 M and the volume of NaOH is 50.0 mL, Moles of NaOH = 0.100 M × 50.0 mL × \(\frac{1 L}{1000 mL}\) = \(5.0 \times 10^{-3} \: \mathrm{moles}\)

Step 2: Calculate moles of the weak acid added

Next, we need to find the moles of the weak acid that have been added to the solution. Since the volumes of acid and base are equal and the pH of the resulting solution is 10.50, all of the sodium hydroxide reacted with the weak acid, meaning the moles of the weak acid and base are equal: Moles of the weak acid = Moles of NaOH

Step 3: Calculate the concentration of the weak acid

The moles of the weak acid are now known, so the concentration of the weak acid solution can be determined by dividing the moles by the volume of the acid solution: Concentration of weak acid = \(\frac{\text{Moles of weak acid}}{\text{Volume of weak acid solution}}\) Given that the volume of the weak acid solution is 23.75 mL, Concentration of weak acid = \(\frac{5.0 \times 10^{-3} \: \mathrm{moles}}{23.75 \: \mathrm{mL} \times \frac{1 \: \mathrm{L}}{1000 \: \mathrm{mL}}}\) = \(0.2105 \: \mathrm{M}\) Therefore, the original concentration of the weak acid solution is approximately 0.2105 M.

Key Concepts

Weak Monoprotic Acid

A weak monoprotic acid is an acid that has only one hydrogen atom that can be donated (or dissociated) in a chemical reaction. Unlike strong acids, which completely dissociate in water, weak acids only partially dissociate. Therefore, in an aqueous solution, a mixture of the acid and its conjugate base will be present. This balance between the acid and its conjugate base is what determines the pH of the solution.

When titrating such an acid with a strong base, like sodium hydroxide (NaOH), it is essential to remember that the reaction will reach its equivalence point when the moles of hydrogen ions from the weak acid equal the moles of hydroxide ions from the base.

Understanding the behavior of weak acids is crucial for laboratory work and numerous applications across biochemistry, environmental science, and pharmaceuticals.

pH Calculation

pH and pOH Relationship

The pH calculation is a critical part of understanding acid-base reactions. The pH is a scale used to specify the acidity or basicity of an aqueous solution. For weak bases, the pOH can be used in a similar manner, which represents the concentration of hydroxide ions. At 25°C (298 K), the sum of pH and pOH is always 14, which is derived from the ion product of water.

Using the pH to Find Concentration

If you know the pH (or pOH) of a solution, you can calculate the concentration of hydrogen (H+) or hydroxide (OH-) ions, which is crucial for finding the unknown concentration in a titration, as in our example problem.

Molarity

Molarity, symbolized by the capital letter M, is a measure of concentration for a chemical solution, expressing the number of moles of solute per liter of solution. It is vital to express the volume in liters (L) when calculating molarity to maintain consistency and accuracy in the scientific community.

When performing a titration, understanding molarity is key to finding accurate stoichiometric relationships between the reactants. Correctly using molarity is also essential for predicting the outcomes of reactions, adjusting concentrations for proper reaction rates, and ensuring safety in handling chemicals.

Stoichiometry

Stoichiometry refers to the quantitative relationships between the reactants and products in chemical reactions. It is based on the conservation of mass and the concept that matter is neither created nor destroyed during a chemical reaction, so the mass of the reactants equals the mass of the products.

In the context of a titration, stoichiometry helps us understand the proportions of acid and base that will react with each other. By using the known molarity and volume of one solution, and the stoichiometric ratio provided by the chemical equation, we can find the concentration of an unknown solution after the reaction has reached the equivalence point – as done in our step-by-step example.