Problem 24 - General Chemistry

Question

You have 0.10 -mol samples of three acids identified simply as HX, HY, and HZ. For each acid, you make up \(0.10 \mathrm{M}\) solutions by adding sufficient water to each of the acid samples. When you measure the \(\mathrm{pH}\) of these samples, you find that the \(\mathrm{pH}\) of \(\mathrm{HX}\) is greater than the \(\mathrm{pH}\) of \(\mathrm{HY}\), which in turn is greater than the \(\mathrm{pH}\) of \(\mathrm{HZ}\). a. Which of the acids is the least ionized in its solution? b. Which acid has the largest \(K_{a}\) ?

Step-by-Step Solution

Answer

HX is the least ionized. HZ has the largest \(K_a\).

Step 1: Understand the Relationship Between pH and Acidity

The pH of a solution is a measure of its acidity. Lower pH values indicate a higher concentration of \([H^+]\) ions, meaning a stronger acidic solution. Therefore, the order from strongest to weakest acid based on pH is: HZ > HY > HX.

Step 2: Relate Ionization to Acidity

Ionization refers to the degree to which an acid dissociates in solution to produce \([H^+]\) ions. A stronger acid ionizes more completely, producing more \([H^+]\) ions, and hence having a lower pH.

Step 3: Identify the Least Ionized Acid

Since HX has the highest pH among the three acids, it produces the fewest \([H^+]\) ions in solution, implying it is the least ionized. Therefore, HX is the least ionized acid.

Step 4: Determine the Largest Ka

The acid dissociation constant, \(K_a\), measures the strength of an acid in solution; larger \(K_a\) values indicate a stronger acid. Since HZ has the lowest pH, it dissociates the most leading to the largest concentration of \([H^+]\), and thus the largest \(K_a\).

Key Concepts

Acid Ionization

Acid ionization is the process by which an acid molecule donates a proton (H\(^+\)) to water, forming hydronium ions (H\(_3\)O\(^+\)). When an acid, such as HX, HY, or HZ, is placed in water, it can ionize to varying degrees.
The degree of ionization affects how much H\(^+\) is released into the solution.

• Strong acids ionize almost completely, releasing more H\(^+\) ions.
• Weak acids do not ionize completely, releasing fewer H\(^+\) ions.

The level of ionization is key to understanding the acidity and strength of an acid solution. For instance, in the problem, HX is the least ionized because it has the highest pH, indicating fewer H\(^+\) ions are in the solution compared to HY and HZ.

Acid Dissociation Constant (Ka)

The acid dissociation constant, represented as \(K_a\), is a quantitative measure of the strength of an acid in its ionized form. It determines how easily an acid donates its proton to a solvent like water. For an acid HA, the expression is:\[ K_a = \frac{[H^+][A^-]}{[HA]} \]

• Higher \(K_a\) values indicate stronger acids because they dissociate more readily, producing more H\(^+\) ions.
• Conversely, lower \(K_a\) values indicate weaker acids with less dissociation.

In the exercise, HZ has the lowest pH, indicating it produces the highest concentration of H\(^+\), hence the largest \(K_a\). This demonstrates strong acid behavior and significant dissociation.

Acidity Measurement

Acidity measurement is often achieved via the pH scale, which ranges from 0 to 14 and is based on the concentration of hydrogen ions in a solution. The pH scale operates logarithmically:\[ \text{pH} = -\log[H^+] \]

• A lower pH corresponds to higher acidity and a higher hydrogen ion concentration.
• A higher pH indicates less acidity and a lower hydrogen ion concentration.

Understanding pH is crucial for identifying the strength of acids. In our examples, since HX has the highest pH among the acids, it is identified as the weakest in terms of acidity. This simplicity in measurement makes pH an effective tool for comparing acid strengths.

Solution Chemistry

Solution chemistry involves the study of how substances dissolve, interact, and react in a solvent, typically water. This field focuses on how solutes like acids dissociate and behave in a solution.
When acids are dissolved in water, they can affect the solution’s properties through:

• Ionization, which influences the overall acidity.
• The formation of conjugate bases, products of acid dissociation.

In the given context, understanding solution chemistry helps explain why the different acids (HX, HY, HZ) have varying pH levels and \(K_a\) values. This knowledge is fundamental in predicting and explaining the behaviors of acid solutions.