Problem 109 - Chemistry and Chemical Reactivity

Question

(a) What is the pH of a 0.105 M HCl solution? (b) What is the hydronium ion concentration in a solution with a pH of \(2.56 ?\) Is the solution acidic or basic? (c) A solution has a pH of 9.67. What is the hydronium ion concentration in the solution? Is the solution acidic or basic? (d) A 10.0 -mL sample of \(2.56 \mathrm{M}\) HCl is diluted with water to \(250 .\) mL. What is the pH of the dilute solution?

Step-by-Step Solution

Answer

(a) pH = 0.979. (b) [H₃O⁺] = 2.75×10⁻³ M, acidic. (c) [H₃O⁺] = 2.14×10⁻¹⁰ M, basic. (d) pH = 0.99.

Step 1: Calculating the pH of 0.105 M HCl solution

HCl is a strong acid which completely dissociates in water. The concentration of hydronium ions [H₃O⁺] is the same as the concentration of the HCl solution. Thus, [H₃O⁺] = 0.105 M. The formula for pH is \( \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \). Calculate the pH: \( \text{pH} = -\log_{10} (0.105) \approx 0.979 \).

Step 2: Calculating hydronium ion concentration from pH of 2.56

The formula that relates pH to hydronium ion concentration is \( [\text{H}_3\text{O}^+] = 10^{-\text{pH}} \). For a pH of 2.56, we calculate \( [\text{H}_3\text{O}^+] = 10^{-2.56} \approx 2.75 \times 10^{-3}\, \text{M} \). Since the pH is less than 7, the solution is acidic.

Step 3: Calculating hydronium ion concentration from pH of 9.67

Using the same formula as in Step 2, for a pH of 9.67, we calculate \( [\text{H}_3\text{O}^+] = 10^{-9.67} \approx 2.14 \times 10^{-10}\, \text{M} \). The pH being greater than 7 indicates the solution is basic.

Step 4: Calculating the pH of diluted HCl solution

First, calculate the new concentration of HCl after dilution using the formula \( C_1V_1 = C_2V_2 \), where \( C_1 = 2.56 \text{ M} \), \( V_1 = 10.0 \text{ mL} \), and \( V_2 = 250.0 \text{ mL} \). Therefore, \( C_2 = \frac{2.56 \times 10.0}{250.0} = 0.1024 \text{ M} \). The concentration of hydronium ions is 0.1024 M because the acid is strong and fully dissociates. Calculate the pH: \( \text{pH} = -\log_{10} (0.1024) \approx 0.99 \).

Key Concepts

Hydronium Ion Concentration

Hydronium ion concentration, denoted as \([\text{H}_3\text{O}^+]\), is a key aspect in determining the acidity or basicity of a solution. The hydronium ion is formed when a hydrogen ion, \(\text{H}^+\), released by an acid in water, combines with a water molecule to form \(\text{H}_3\text{O}^+\). This ion is crucial in defining pH, which is a measure of how acidic or basic a solution is.

For instance, in a strong acid like hydrochloric acid (HCl), which fully dissociates in water, the concentration of hydronium ions is equal to the concentration of the acid itself. This is because each molecule of HCl releases one \(\text{H}^+\) that combines with water to form \(\text{H}_3\text{O}^+\).

To calculate the hydronium ion concentration from pH, you can use the formula:

• \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\)

This relationship helps us convert between pH values and hydronium ion concentrations, allowing for a deeper understanding of the solution's properties.

Acidic vs Basic Solutions

Whether a solution is acidic or basic is primarily determined by its pH level. The pH scale ranges from 0 to 14:

• A pH less than 7 indicates an acidic solution.
• A pH of 7 indicates a neutral solution, like pure water.
• A pH greater than 7 indicates a basic (or alkaline) solution.

An acidic solution has a higher concentration of hydronium ions \([\text{H}_3\text{O}^+]\). For example, a pH of 2.56 suggests an acidic solution as it is below 7, with a hydronium ion concentration that can be calculated to ensure it's greater than the concentration in a neutral solution.

Conversely, a basic solution has a lower \([\text{H}_3\text{O}^+]\) and a pH above 7, such as a solution with a pH of 9.67. Understanding these differences aids in predicting the chemical behavior of the solution.

Dilution Calculations

Dilution involves reducing the concentration of a solute in a solution by adding more solvent, typically water. This is crucial in chemistry for adjusting the strength of solutions for various experiments and applications.

To calculate the new concentration after dilution, you can use the formula:

• \(C_1V_1 = C_2V_2\)

Where:

• \(C_1\) is the initial concentration,
• \(V_1\) is the initial volume,
• \(C_2\) is the new concentration, and
• \(V_2\) is the new volume.

For example, if you have a \(10.0\,\text{mL}\) sample of \(2.56\,\text{M}\) HCl and dilute it to \(250.0\,\text{mL}\), the new concentration \(C_2\) is \(0.1024\,\text{M}\).

This process is vital for accurately preparing solutions of desired concentrations, ensuring consistency and reliability in scientific experiments.