Consider two solutions, solution A and solution B. The concentration of 3H+4 in solution A is 250 times greater than that in solution B. What is the difference in the pH values of the two solutions?

Verified step by step guidance

1. Step 1: Understand the relationship between hydrogen ion concentration and pH. The pH of a solution is calculated using the formula: \( \text{pH} = -\log[\text{H}^+] \), where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter.
2. Step 2: Let \([\text{H}^+]_B\) be the concentration of hydrogen ions in solution B. Then, the concentration of hydrogen ions in solution A, \([\text{H}^+]_A\), is 250 times \([\text{H}^+]_B\). Therefore, \([\text{H}^+]_A = 250 \times [\text{H}^+]_B\).
3. Step 3: Calculate the pH of solution A using the formula: \( \text{pH}_A = -\log([\text{H}^+]_A) = -\log(250 \times [\text{H}^+]_B) \).
4. Step 4: Calculate the pH of solution B using the formula: \( \text{pH}_B = -\log([\text{H}^+]_B) \).
5. Step 5: Determine the difference in pH between the two solutions by subtracting the pH of solution B from the pH of solution A: \( \Delta \text{pH} = \text{pH}_A - \text{pH}_B \).

Key Concepts

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate basicity. The scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration.

Hydrogen Ion Concentration

Hydrogen ion concentration ([H+]) is a measure of the amount of hydrogen ions present in a solution. It directly influences the pH value; higher concentrations of H+ result in lower pH values, indicating stronger acidity. In this question, the concentration of H+ in solution A is significantly greater than in solution B.

Logarithmic Relationship of pH and [H+]

The relationship between pH and hydrogen ion concentration is logarithmic, expressed by the formula pH = -log[H+]. This means that if the concentration of H+ in solution A is 250 times greater than in solution B, the difference in pH can be calculated using this logarithmic relationship, leading to a specific numerical difference in their pH values.