Problem 57 - Chemistry An Atoms First Approach

Question

Calculate the \(\mathrm{pH}\) of each of the following solutions of a strong acid in water. a. \(0.10 \mathrm{M} \mathrm{HCl}\) b. 5.0 M HCl c. \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\)

Step-by-Step Solution

Answer

The pH of each solution is as follows: a. pH of 0.10 M HCl is 1, b. pH of 5.0 M HCl is approximately -0.70, and c. pH of \(1.0 \times 10^{-11}\) M HCl is 11.

Step 1: (Part a: Calculate [H₃O+] for 0.10 M HCl solution)

For a strong acid like HCl, the concentration of H₃O+ ions is equal to the concentration of HCl as it dissociates completely. So, in this case, [H₃O+] = 0.10 M.

Step 2: (Part a: Calculate pH of 0.10 M HCl solution)

Now we will use the pH formula: pH = -log[H₃O+] Plugging in the value of [H₃O+] = 0.10 M, we get: pH = -log(0.10) = 1 The pH of the 0.10 M HCl solution is 1.

Step 3: (Part b: Calculate [H₃O+] for 5.0 M HCl solution)

In this case as well, the concentration of H₃O+ ions is equal to the concentration of HCl, which is 5.0 M.

Step 4: (Part b: Calculate pH of 5.0 M HCl solution)

Using the pH formula, we have: pH = -log[H₃O+] pH = -log(5.0) ≈ -0.70 The pH of the 5.0 M HCl solution is approximately -0.70.

Step 5: (Part c: Calculate [H₃O+] for \(1.0 \times 10^{-11}\) M HCl solution)

Again, the concentration of H₃O+ ions is equal to the concentration of HCl, which is \(1.0 \times 10^{-11}\) M.

Step 6: (Part c: Calculate pH of \(1.0 \times 10^{-11}\) M HCl solution)

Using the pH formula, we get: pH = -log[H₃O+] pH = -log(\(1.0 \times 10^{-11}\)) = 11 The pH of the \(1.0 \times 10^{-11}\) M HCl solution is 11.

Key Concepts

Strong Acids

Strong acids play a crucial role in chemistry due to their ability to almost completely dissociate in water. This means that in a solution, almost all the acid molecules break apart into ions. For students, understanding this property simplifies many calculations, especially when dealing with concentrations and pH levels.

When you hear the term "strong acid," think of an acid that can fully ionize in water. Here are a few important characteristics of strong acids:

• They release a large concentration of hydrogen ions (\[\text{H}^+\]) in solution.
• The pH of their solutions is typically below 7.
• Examples include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and nitric acid (HNO₃).

These attributes make strong acids very reactive, and they can significantly alter the pH of solutions they are added to. Recognizing these characteristics is vital for predicting the chemistry of reactions involving acids.

HCl

Hydrochloric acid, abbreviated as HCl, is one of the most commonly known strong acids. It is widely used in laboratories and industry due to its effectiveness in various chemical processes. When you dissolve HCl in water, it ionizes completely, creating a highly acidic environment.

Let's break down what makes HCl special:

• HCl is composed of hydrogen and chlorine atoms.
• In aqueous solutions, it fully dissociates to form \[\text{H}^+\] ions and \[\text{Cl}^-\] ions.
• This complete dissociation is what qualifies it as a strong acid.

Due to these characteristics, HCl is highly effective for use in pH adjustments, cleaning tasks, and preparing acids for further reactions. Understanding its behavior in water provides insights into its widespread application in both educational and practical contexts.

Dissociation in Water

Dissociation in water refers to the process by which certain compounds, like strong acids, separate into ions when they are dissolved. This process is straightforward for strong acids, resulting in an increase of hydrogen ions (\[\text{H}^+\]) in the solution, usually directly influencing the pH.

Here's a simplified look at how dissociation works:

• When HCl is added to water, it splits into \[\text{H}^+\] and \[\text{Cl}^-\] ions.
• This separation is rapid and complete, leaving no unchanged molecules of HCl in the solution.
• The high concentration of \[\text{H}^+\] ions directly translates to a lower pH.

In summary, the dissociation of strong acids in water is critical for understanding changes in solution acidity. It informs predictions about how strong acids will behave in various chemical contexts and supports calculations involving pH and ion concentrations in solution. This foundational concept helps students grasp how acid strength relates to reactivity and acidity.