A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: 50 mL.

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Identify the initial moles of pyridine (C5H5N) using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).

Calculate the moles of HCl added using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).

Determine the limiting reactant by comparing the initial moles of pyridine and the moles of HCl added.

Calculate the moles of pyridine and pyridinium ion (C5H5NH^+) after the reaction, considering the stoichiometry of the reaction: \( \text{C5H5N} + \text{HCl} \rightarrow \text{C5H5NH}^+ + \text{Cl}^- \).

Use the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{C5H5N}]}{[\text{C5H5NH}^+]} \right) \), where \( \text{pK}_a \) is derived from the \( \text{K}_b \) of pyridine.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Acid-Base Titration

An acid-base titration is a quantitative analytical method used to determine the concentration of an acid or base in a solution. In this process, a solution of known concentration (the titrant) is added to a solution of unknown concentration until the reaction reaches its equivalence point, where the amount of acid equals the amount of base. The pH changes during the titration, and understanding this change is crucial for calculating the pH at various points.

Buffer Solutions

Buffer solutions are mixtures that can resist changes in pH upon the addition of small amounts of acid or base. In the case of pyridine, a weak base, when titrated with HCl, it forms a buffer system that can maintain a relatively stable pH until a significant amount of acid is added. Understanding how buffers work is essential for predicting the pH at different stages of the titration.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It relates the pH of the solution to the pKa of the acid and the ratio of the concentrations of the conjugate base and the acid. This equation is particularly useful in titration problems involving weak acids and bases, as it allows for the determination of pH at various points in the titration process.

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Henderson-Hasselbalch Equation

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Textbook Question

A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: equivalence point.

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Textbook Question

A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: one-half equivalence.

Textbook Question

A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: 40 mL.

Textbook Question

A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: 0 mL, 10 mL, 20 mL, equivalence point, one-half equivalence point, 40 mL, 50 mL. Sketch the titration curve.

Textbook Question

Consider the titration curves (labeled a and b) for two weak acids, both titrated with 0.100 M NaOH.

(i) Which acid solution is more concentrated?

Textbook Question

Consider the titration curves (labeled a and b) for two weak acids, both titrated with 0.100 M NaOH.

(ii) Which acid has the larger Ka?