Problem 5 - General Chemistry: Principles and Modern Applications

Question

With which of the following bases will the ionization of acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH},\) proceed furthest toward completion (to the right): (a) \(\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{NH}_{3} ;\) (c) \(\mathrm{Cl}^{-}\) (d) \(\mathrm{NO}_{3}^{-} ?\) Explain your answer.

Step-by-Step Solution

Answer

The ionization of acetic acid proceeds furthest toward completion with \(NO_3^-\) as the base.

Step 1: Identifying the Bases

Here, the substances \(H_2O\), \(NH_3\), \(Cl^-\), and \(NO_3^-\) are given. In the context of the Bronsted-Lowry theory, these could act as bases, as they have the potential to accept protons.

Step 2: Analyzing the Proton Affinity of the Bases

Given that acetic acid is a weak acid, it will ionize most readily with the base that has the greatest proton affinity. Water and ammonia are both neutral molecules which can act as bases, but their proton affinity is less than that of the negatively charged ions \(Cl^-\) and \(NO_3^-\). Consequently, we can eliminate \(H_2O\) and \(NH_3\).

Step 3: Final Comparison Between \(Cl^-\) and \(NO_3^-\)

Comparing \(Cl^-\) and \(NO_3^-\), the chloride ion is less likely to accept a proton because it is a conjugate base of hydrochloric acid \(HCl\), which is a strong acid. The nitrate ion \(NO_3^-\) is the conjugate base of the weak acid \(HNO_3\). A strong acid has a weak conjugate base and vice versa. Therefore, \(NO_3^-\) has a greater proton affinity than \(Cl^-\).

Key Concepts

Acetic Acid

Acetic acid is a common organic acid that you might find in your kitchen as vinegar. It has the formula \( \text{CH}_3\text{COOH} \). This molecule is made up of carboxylic group \( \text{COOH} \) which is responsible for its acidic properties. Like many other acids, acetic acid can donate a proton (\( \text{H}^+ \)) during a reaction.
In solution, acetic acid partially ionizes, meaning not all molecules lose a proton. This is because it is a weak acid. This partial ionization is often represented as a reversible reaction:

• \( \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \)

In this equilibrium, the ionization extent can change depending on what substance the acetic acid encounters. The completion of this reaction depends on the nature of the base it reacts with.

Bronsted-Lowry Theory

The Bronsted-Lowry Theory is fundamental in understanding acid-base reactions. This theory defines an acid as a proton donor and a base as a proton acceptor. It provides insight into how acetic acid ionizes.
When acetic acid donates a proton, the base in the solution must be ready and willing to accept it. Not all bases are equal in this aspect, and their ability to accept protons is called proton affinity. This is where the Bronsted-Lowry theory helps predict which substances will effectively remove protons from acetic acid through ionization.
An example using this theory is the comparison between \( \text{NH}_3 \) and \( \text{NO}_3^- \) as bases. Though both can accept protons, their differences in proton affinity direct the reaction's equilibrium position.

Proton Affinity

Proton affinity is a crucial concept that describes how readily a base will accept a proton. It's like saying how eager a base is to grab a proton from acetic acid. The higher the proton affinity, the more likely the base will encourage the ionization of the acid.
In examining ammonia \( \text{NH}_3 \) and water \( \text{H}_2\text{O} \) as bases, their neutral charge makes them less competitive in grabbing protons compared to ions like \( \text{Cl}^- \) and \( \text{NO}_3^- \).
However, proton affinity is not merely about charge but also about how stable a base becomes after gaining a proton. As such, even between \( \text{Cl}^- \) and \( \text{NO}_3^- \), the nitrate ion is more willing to accept a proton due to its lesser stability as a conjugate base.

Conjugate Base Comparison

Conjugate bases are what remain after an acid donates a proton. Their strength is closely linked to the strength of the original acid. A weak acid like acetic acid produces a reasonably strong conjugate base \( \text{CH}_3\text{COO}^- \), and vice versa.
In comparing conjugate bases like \( \text{Cl}^- \) and \( \text{NO}_3^- \), understanding the strength of their corresponding acids helps. \( \text{Cl}^- \) is the conjugate base of \( \text{HCl} \), a strong acid. Whereas \( \text{NO}_3^- \) is tied to \( \text{HNO}_3 \), a weaker acid.
The strength of these conjugate bases gives insight into proton affinity. Generally, the weaker the original acid, the stronger the resulting conjugate base. This principle helps determine how far the ionization of acetic acid proceeds.