Question

Repeat the procedure in Exercise \(67,\) but for the titration of 25.0 \(\mathrm{mL}\) of 0.100\(M\) pyridine with 0.100\(M\) hydrochloric acid \(\left(K_{\mathrm{b}} \text { for pyridine is } 1.7 \times 10^{-9}\right) .\) Do not calculate the points at 24.9 and 25.1 \(\mathrm{mL}\)

Short answer

The pH at various stages of the titration can be calculated as follows: 1. Initial pH: Using the given Kb value, calculate the [OH⁻] concentration, determine the pOH, and then find the pH as \(pH = 14 - pOH\). 2. Equivalence point: Find the Ka value for the conjugate acid, C₅H₅NH⁺, using the relationship \(K_aK_b = K_w\). Calculate the [H⁺] concentration, and then determine the pH as \(pH = -\log{[H^+]}\). 3. Final pH: Calculate the moles of remaining pyridine (C₅H₅N) after the addition of hydrochloric acid, determine the final concentration of pyridine, use the Kb expression to find the [OH⁻] concentration, calculate the pOH, and then determine the pH as \(pH = 14 - pOH\).

Step-by-step solution

Calculate the initial pH of the pyridine solution

First, we need to calculate the initial concentration of pyridine in the solution before the addition of hydrochloric acid. This is given by the equilibrium expression: \(K_{\mathrm{b}} = \frac{[\mathrm{C_5H_5N}^+][\mathrm{OH^-}]}{[\mathrm{C_5H_5N}]}\) Rearranging to solve for [OH⁻]: \([\mathrm{OH^-}] = \frac{K_{\mathrm{b}}[\mathrm{C_5H_5N}]}{[\mathrm{C_5H_5N}^+]}\) Now we can find the pOH of the solution: \(pOH = -\log{[\mathrm{OH^-}]}\) Finally, the pH of the solution can be found using the relationship: \(pH = 14 - pOH\)

Calculate the pH at the equivalence point

At the equivalence point, the amount of pyridine is equal to the amount of hydrochloric acid added. Given the volumes and concentrations of the two solutions, we can calculate the moles of pyridine and hydrochloric acid: moles of pyridine = (25.0 mL)(0.100 M) = 2.5 mmol moles of hydrochloric acid = (25.0 mL)(0.100 M) = 2.5 mmol As the moles are equal at the equivalence point, we can use the Kb value for the conjugate acid, C5H5NH+, to find the pH. To find the conjugate acid's Ka value, we use the following relationship: \(K_{\mathrm{a}}K_{\mathrm{b}} = K_{\mathrm{w}}\) where Kw is the ion product constant of water, which is equal to 1.0 x 10^-14 at 25°C. First, find the Ka value for the conjugate acid: \(K_{\mathrm{a}} = \frac{K_{\mathrm{w}}}{K_{\mathrm{b}}} = \frac{1.0 \times 10^{-14}}{1.7 \times 10^{-9}}\) Calculate the [H⁺] using the Ka expression: \([\mathrm{H^+}] = \sqrt{K_{\mathrm{a}} [\mathrm{C_5H_5NH^+}]}\) Then, calculate the pH: \(pH = -\log{[\mathrm{H^+}]}\)

Calculate the final pH after addition of hydrochloric acid

After the addition of hydrochloric acid, we can assume that the H⁺ ions from the titrant will combine with the pyridine ions in the solution (C5H5N), forming the conjugate acid (C5H5NH⁺) and increasing the pH. To find the final pH, assume that the reaction is complete and that the amount of remaining pyridine (C5H5N) is equal to the amount of H⁺ ions introduced through the addition of hydrochloric acid: moles of remaining pyridine = moles of added H⁺ - initial moles of pyridine Calculate the final concentration of pyridine, C5H5N: \([\mathrm{C_5H_5N}] = \frac{\text{moles of remaining pyridine}}{\text{total volume}}\) Now we can use the Kb expression to calculate the [OH⁻] concentration: \([\mathrm{OH^-}] = \frac{K_{\mathrm{b}} [\mathrm{C_5H_5N}]}{[\mathrm{C_5H_5N}^+]}\) Find the pOH: \(pOH = -\log{[\mathrm{OH^-}]}\) Finally, calculate the pH: \(pH = 14 - pOH\)

Key concepts

Equivalence Point

Understanding the equivalence point is crucial in acid-base titrations. It represents the stage in the titration when the amount of titrant added is stoichiometrically equivalent to the amount of substance initially present in the solution. In simpler terms, it is the point where the acid exactly neutralizes the base or vice versa.
The equivalence point is identified by an observable change, often in pH. It is essential to know that the pH at the equivalence point depends on the nature of the acid and base involved in the reaction.
For the titration of pyridine (a weak base) with hydrochloric acid (a strong acid), at the equivalence point, you will have equal moles of pyridine and hydrochloric acid. This balance indicates that all pyridine has been used to form its conjugate acid, pyridinium ion (m{C_5H_5NH^+}). Therefore, understanding the equivalence point is key to determining the pH of the resulting solution after neutralization.

pH Calculation

Calculating the pH at different stages of a titration helps us understand how the concentration of hydrogen ions (m{[H^+]}) changes. Initially, before adding the titrant, the pH is determined by the dissociation of the base (pyridine) in water using its m{K_b} value.
When pyridine undergoes titration with hydrochloric acid, pH calculations are necessary at each stage:

• Initial pH: Evaluate the m{pOH} using the hydroxide ion concentration, then convert to pH using m{pH = 14 - pOH}.
• Equivalence Point pH: Here, use the solution of the conjugate acid (m{C_5H_5NH^+}) to find the m{[H^+]} concentration and calculate pH.
• Final pH: After adding the acid, assume completion of the reaction to find any shifts in pH based on displacement of hydrogen and hydroxide ions.

These calculations help reveal the titration curve and highlight the completeness of the reaction between pyridine and hydrochloric acid.

Conjugate Acid-Base Pair

A conjugate acid-base pair consists of two species in a chemical reaction that transform into each other by gain or loss of a proton (m{H^+}). In the context of pyridine titration, pyridine (m{C_5H_5N}, a weak base) forms a conjugate acid, pyridinium ion (m{C_5H_5NH^+}), upon accepting a proton from hydrochloric acid.
This pairing demonstrates the concept of equilibrium in acid-base reactions. Here’s how it works:

• Weak Base to Conjugate Acid: m{C_5H_5N} + m{H^+} ightarrow m{C_5H_5NH^+}
• Reverse Potential: The reaction equilibrium can shift back if conditions favor the reverse process, which is the release of m{H^+} from m{C_5H_5NH^+}.

Understanding conjugate acid-base pairs is important because they define the buffering capacity of the solution and its behavior around the equivalence point.

Pyridine Titration

Pyridine titration involves titrating a weak base (pyridine) with a strong acid (hydrochloric acid). This process requires careful consideration of the chemical characteristics of pyridine and the titrant solutions.
The steps include:

• Initially, pyridine (m{C_5H_5N}) is present and defines the solution's basicity through its m{K_b} value.
• As hydrochloric acid is added, it reacts with pyridine, progressively increasing the concentration of the conjugate acid, m{C_5H_5NH^+}.
• Close to the equivalence point, the solution's pH experiences significant shifts due to the nature of pyridinium ion formation.
• Post-equivalence, excess m{H^+} from hydrochloric acid further alters the solution’s pH.

The titration of pyridine with hydrochloric acid demonstrates essential principles of acid-base chemistry, specifically highlighting the shifts in pH and the role of conjugate species within buffer systems.