Question

An amount of \(0.15\) mole of pyridinium chloride has been added into \(500 \mathrm{ml}\) of 0.2 M pyridine solution. Calculate pH and hydroxyl ion concentration in the resulting solution assuming no change in volume. \(K_{\mathrm{b}}\) for pyridine \(=1.5 \times 10^{-9}\). \((\log 2=0.3, \log 0.3=0.48)\) (a) \(9.0\) (b) \(5.0\) (c) \(8.64\) (d) \(5.36\)

Short answer

The pH of the solution is 9.00, and the hydroxide ion concentration is approximately 1.0 x 10^{-5} M.

Step-by-step solution

Determine the initial moles of pyridine and pyridinium ion

Calculate the moles of pyridine before the pyridinium chloride is added by multiplying the concentration of pyridine by the volume of pyridine solution. Volume should be converted from milliliters to liters by dividing by 1000. Also, determine the moles of pyridinium ion added directly.

Calculate the change in moles after reaction

Since pyridinium ion is the conjugate acid of pyridine base, they will react with each other, reducing the moles of both. The limiting reagent will react completely and the excess reagent will determine the moles left.

Calculate new concentrations

Use the moles of pyridine and pyridinium ion remaining after the reaction to determine the new concentrations, considering the volume of the solution remains the same.

Write the hydrolysis reaction of the pyridinium ion

Pyridinium ion will react with water to yield pyridine and hydronium ion, which contributes to the pH of the solution. The equilibrium expression for this reaction can be written in terms of Kb for pyridine.

Write expression for Kb and solve for hydroxide ion concentration

Use the Kb expression and the concentrations obtained from step 3 to calculate the hydroxide ion concentration in the solution.

Calculate pOH and then pH

With the hydroxide ion concentration, calculate pOH using the formula pOH = -log[OH-]. Then, find the pH using the formula pH + pOH = 14.

Key concepts

Acid-Base Equilibrium

Understanding the acid-base equilibrium is essential when calculating pH in chemistry problems. In an aqueous solution, acids and bases can donate or accept protons, respectively, leading to a dynamic state where the concentrations of all species involved in the reaction reach a stable ratio known as the equilibrium state.

Acid-base equilibrium is governed by an equilibrium constant, which for weak acids is represented as Ka and for weak bases as Kb. The equilibrium constant is a reflection of the tendency of the conjugate base to recombine with a proton and form the acid (or vice versa for bases). This tendency determines the pH of the solution, which is a measure of acidity or basicity.

In the given exercise, pyridine acts as a base, and pyridinium ion acts as its conjugate acid. The pH calculation involves figuring out how the addition of pyridinium chloride shifts the equilibrium state and alters the pH of the pyridine solution. By understanding acid-base equilibrium, students can predict the direction in which reactions will proceed and calculate the resulting pH.

Hydrolysis Reaction

A hydrolysis reaction is a specific type of acid-base reaction that involves a salt reacting with water to form the acid or base from which it is derived. In the context of the given problem, pyridinium chloride is the salt derived from pyridine and hydrochloric acid.

During hydrolysis, the pyridinium ion (conjugate acid of pyridine) reacts with water to produce pyridine and hydronium ions. This reaction is important because the generated hydronium ions (H3O+) increase the acidity of the solution, thereby affecting the pH. The equilibrium expression of this hydrolysis reaction is tied to the base dissociation constant (Kb) of pyridine, which ultimately helps in calculating the hydroxide ion (OH-) concentration in solution.

The chemical equation for this hydrolysis reaction is:

\[C5H5NH^+ + H2O \rightleftharpoons C5H5N + H3O^+\]

Here the Kb value is necessary to find the concentration of OH- ions, which in turn allows us to calculate pOH and subsequently pH. Understanding hydrolysis reactions is therefore crucial for solving many chemistry problems involving salts of weak acids or bases.

Conjugate Acid-Base Pair

The concept of a conjugate acid-base pair is vital to any discussion on pH calculations. A conjugate acid-base pair consists of two species that transform into each other by the gain or loss of a proton (H+). In the case of the given exercise, pyridine and pyridinium ion form such a pair.

When pyridine (C5H5N) accepts a proton, it becomes its conjugate acid, pyridinium ion (C5H5NH+). Conversely, when pyridinium ion donates a proton, it reverts to pyridine. Understanding these pairs allows us to determine the direction in which an equilibrium will lie and calculate concentrations of acids, bases, and their conjugates at equilibrium.

The relationship within the conjugate acid-base pair also provides insight into the strength of the acid or base in question. A strong acid has a weak conjugate base, while a weak acid has a strong conjugate base, and the same is true for bases and their conjugates. In our example, since pyridine is a weak base with a small Kb value, its conjugate acid, pyridinium ion, is relatively strong, affecting the pH more significantly when introduced into the solution.