Problem 11 - Chemistry and Chemical Reactivity

Question

What is the pH of a 0.0075 M solution of HCl? What is the hydroxide ion concentration of the solution?

Step-by-Step Solution

Answer

pH is approximately 2.12; hydroxide ion concentration is \( 1.33 \times 10^{-12} \) M.

Step 1: Understanding HCl as a Strong Acid

HCl is a strong acid, meaning it completely dissociates in water. For every mole of HCl, one mole of hydrogen ions \( (H^+) \) is produced. Therefore, the concentration of \( H^+ \) ions in a 0.0075 M HCl solution is 0.0075 M.

Step 2: Calculating the pH

The pH of a solution is calculated using the formula \[ \text{pH} = -\log[H^+] \]. Substitute the concentration of \( H^+ \) into the formula: \[ \text{pH} = -\log(0.0075) \]. Calculating this gives a pH of approximately 2.12.

Step 3: Relating pH to the Hydroxide Ion Concentration

The relationship between \( H^+ \) and \( OH^- \) ion concentrations is given by the formula \[ [H^+][OH^-] = 1 \times 10^{-14} \]. Using this, calculate the \( OH^- \) concentration: \[ [OH^-] = \frac{1 \times 10^{-14}}{0.0075} \].

Step 4: Calculating the Hydroxide Ion Concentration

Plugging the values into the formula gives: \[ [OH^-] = \frac{1 \times 10^{-14}}{0.0075} = 1.33 \times 10^{-12} \]. Thus, the hydroxide ion concentration of the solution is approximately \( 1.33 \times 10^{-12} \) M.

Key Concepts

pH calculation

The pH of a solution is a measure of its acidity or basicity, determined by the concentration of hydrogen ions (\( H^+ \)) present. It is calculated using the formula \( \text{pH} = -\log [H^+] \). This means we take the negative logarithm (base 10) of the hydrogen ion concentration.
For example, in a 0.0075 M solution of hydrochloric acid (HCl), which is a strong acid, the concentration of \( H^+ \) ions is also 0.0075 M because strong acids completely dissociate in water.
Applying our formula: \( \text{pH} = -\log (0.0075) \), the pH is approximately 2.12.
This lower pH indicates a rather acidic solution, typical for a solution with a high \( H^+ \) ion concentration.

strong acids

Strong acids, like hydrochloric acid (HCl), fully dissociate into their constituent ions when dissolved in water.
This means that each molecule of a strong acid releases one or more \( H^+ \) ions.
Common examples of strong acids include:

• Hydrochloric acid (HCl)
• Nitric acid (HNO3)
• Sulfuric acid (H2SO4)
• Perchloric acid (HClO4)

In a 0.0075 M solution of HCl, the concentration of \( H^+ \) ions is also 0.0075 M.
This fundamental property simplifies acid-base calculations significantly, allowing for direct determination of pH or related metrics from the given concentration.

hydroxide ion concentration

The concentration of hydroxide ions \( (OH^-) \) in a solution is an important aspect of its chemical behavior, especially in relation to its acidity or basicity.
For any aqueous solution, the product of the hydrogen ion concentration \( [H^+] \) and the hydroxide ion concentration \( [OH^-] \) is constant at room temperature: \( [H^+][OH^-] = 1 \times 10^{-14} \).
This relationship helps us find the \( OH^- \) concentration if we know the \( H^+ \) concentration, or vice versa.
In the given example of a 0.0075 M HCl solution, we can calculate \( [OH^-] \) using the formula: \( [OH^-] = \frac{1 \times 10^{-14}}{0.0075} \), resulting in an \( [OH^-] \) of approximately \( 1.33 \times 10^{-12} \) M.
This very low hydroxide ion concentration is typical of acidic solutions and highlights the inverse relationship between hydrogen and hydroxide ions in water.