Question

The \(\mathrm{pH}\) of a \(0.0642-M\) solution of a monoprotic acid is 3.86. Is this a strong acid?

Short answer

The acid is not strong; it is weak because it ionizes only 0.215% in solution.

Step-by-step solution

Calculate the concentration of hydrogen ions

The pH is given by the formula \( \mathrm{pH} = -\log[H^+] \). We can rearrange this to find \([H^+]\): \([H^+] = 10^{-\mathrm{pH}}\). Insert the given pH of 3.86 into the formula: \([H^+] = 10^{-3.86} \approx 1.38 \times 10^{-4}\, M\).

Compare with initial acid concentration

We need to compare the concentration of hydrogen ions to the initial concentration of the acid. The initial concentration is \(0.0642\, M\).

Determine the degree of ionization

Calculate the degree of ionization: \( \frac{[H^+]}{\text{initial concentration}} = \frac{1.38 \times 10^{-4}}{0.0642} \approx 0.00215 \). This is approximately 0.215%.

Assess if the acid is strong

A strong acid fully dissociates in solution, typically having a degree of ionization close to 100%. The ionization of this acid is only 0.215%, indicating it is a weak acid.

Key concepts

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is key to grasping the \(\text{pH}\) concept. When we talk about the concentration of hydrogen ions \( [H^+] \), we are essentially referring to how many hydrogen ions are present in a solution. The \(\text{pH}\) scale, ranging from 0 to 14, is used to measure the acidity or alkalinity of a solution. A lower \(\text{pH}\) value indicates a higher concentration of hydrogen ions, making the solution more acidic.

To find the concentration of hydrogen ions from \(\text{pH}\), we use the formula: \( [H^+] = 10^{-\text{pH}} \). For example, if the \(\text{pH}\) is 3.86, the hydrogen ion concentration can be calculated as \(10^{-3.86}\), resulting in \(1.38 \times 10^{-4}\,M\). This shows the solution's acidity level based on its hydrogen ion count.

Degree of Ionization

The degree of ionization is a measure that helps us understand how much an acid dissociates in water. When acids dissolve, they can release hydrogen ions into the solution, and this process is called ionization. The degree of ionization is calculated by dividing the concentration of hydrogen ions by the initial concentration of the acid.

Using our example, the degree of ionization is given by the formula: \( \frac{[H^+]}{\text{initial concentration}} \). For the acid in question, with \( [H^+]\) calculated as \(1.38 \times 10^{-4}\,M\) and an initial concentration of \(0.0642\,M\), the degree is approximately 0.00215 or 0.215%.

This figure reveals how little the acid has dissociated, helping us categorize the acid as weak or strong.

Strong Acid vs Weak Acid

To determine if an acid is strong or weak, we assess its ionization in water. A strong acid almost completely dissociates, meaning it releases a high number of hydrogen ions compared to its initial amount. Usually, strong acids will have a degree of ionization close to 100%.

On the other hand, weak acids only partially dissociate. This means only a small fraction of the acid molecules release hydrogen ions. To gauge an acid's strength, you compare its degree of ionization.

In our example, a 0.215% ionization is far from the full dissociation expected from a strong acid. This low percentage indicates that we are dealing with a weak acid. Understanding this difference helps in predicting the behavior of the acid in various solutions and reactions.