Question

Given two solutions, 0.10 \(\mathrm{M} \mathrm{HCl}\) and 0.10 \(\mathrm{M}\) HF, which solution has the greater concentration of \(\mathrm{H}^{+}\) ions? Calculate pH values for the two solutions, given that \(\left[\mathrm{H}^{+}\right]=7.9 \times 10^{-3} \mathrm{M}\) in the 0.10 \(\mathrm{M} \mathrm{HF}\)

Short answer

The HCl solution has a pH of 1.0, and the HF solution has a pH of 2.1. Since the HCl solution has a lower pH, it is more acidic and has a higher concentration of H+ ions compared to the HF solution.

Step-by-step solution

Calculate the H+ Concentration in HCl Solution

HCl is a strong acid, which means it fully dissociates in water into H+ and Cl- ions. Therefore, the concentration of H+ ions in the HCl solution will be the same as the concentration of HCl: 0.10 M.

Calculate the pH of the HCl Solution

To find the pH of the HCl solution, use the pH formula: pH = -log[H+]. Substitute the given H+ concentration (0.10 M) into the formula: pH = -log(0.10) = 1.0

Calculate the pH of the HF Solution

We're given the concentration of H+ ions in the HF solution, which is 7.9 x 10^-3 M. Use the pH formula again to find the pH of the HF solution: pH = -log(7.9 x 10^-3) ≈ 2.1

Compare the pH Values and H+ Concentrations

Now that we have the pH values for both solutions, we can compare them: - HCl solution: pH = 1.0 - HF solution: pH = 2.1 The HCl solution has a lower pH, meaning it is more acidic and therefore has a higher concentration of H+ ions compared to the HF solution.

Key concepts

pH calculation

Calculating the pH of a solution helps us understand its acidity or alkalinity. pH is a scale used to specify the acidity or basicity of an aqueous solution. It is a dimensionless number generally ranging from 0 to 14. To calculate pH, you use the formula:

• \( \text{pH} = -\log[\text{H}^+] \)

The pH value tells you how acidic or basic a solution is.
For instance, a pH of 1 is very acidic, whereas a pH of 14 is very basic. A neutral solution, like pure water, has a pH of 7.
The pH scale is logarithmic, so a change in one pH unit represents a tenfold change in the concentration of hydrogen ions \(\text{H}^+\) in the solution.

strong acid

A strong acid completely dissociates in solution. This means it splits into its ions – specifically, it releases all of its hydrogen ions \(\text{H}^+\) into the solution.
Examples of strong acids include hydrochloric acid (HCl), sulfuric acid (H2SO4), and nitric acid (HNO3).

• For a strong acid like HCl, if you have a 0.10 M solution, the concentration of \(\text{H}^+\) ions will also be 0.10 M.

This is because each molecule of strong acid dissociates completely to release one \(\text{H}^+\) ion.
Due to this full dissociation, strong acids generally have very low pH values, indicating high acidity.

weak acid

A weak acid does not fully dissociate in solution. This means that only a fraction of its molecules release hydrogen ions \(\text{H}^+\) into the solution.
Examples of weak acids include acetic acid (CH3COOH) and hydrofluoric acid (HF).

• For weak acids, the concentration of \(\text{H}^+\) ions in the solution is typically much lower than the initial concentration of the acid.

Let's take HF as an example: in a 0.10 M HF solution, the \(\text{H}^+\) ion concentration might be 7.9 x 10^-3 M, as seen in our calculation.
This partial dissociation results in higher pH values compared to strong acids of the same concentration.

H+ concentration

The concentration of hydrogen ions \(\text{H}^+\) is crucial in determining the acidity of a solution.
This is because the pH of a solution is directly related to the \([\text{H}^+]\) concentration. As mentioned before, the pH is calculated as \(\text{pH} = -\log[\text{H}^+]\).

• A higher concentration of \(\text{H}^+\) ions means a lower pH, indicating a more acidic solution.
• For example, in a 0.10 M HCl solution, the \(\text{H}^+\) concentration is 0.10 M, resulting in a pH of 1.0.
• Conversely, a lower \(\text{H}^+\) concentration, such as 7.9 x 10^-3 M in HF, results in a pH of 2.1, which is less acidic.

Understanding \([\text{H}^+]\) helps us appreciate how acidic a solution is and how the strength of the acid affects the overall pH.