Textbook Question
Calculate 3OH-4 for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (c) a solution in which 3H+4 is 1000 times greater than 3OH-4.
Ch.16 - Acid-Base Equilibria
Chapter 16, Problem 38
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 guidance1
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.
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, \([\text{H}^+]_A = 250 \times [\text{H}^+]_B\).
Step 3: Calculate the pH of solution A using the formula: \( \text{pH}_A = -\log([\text{H}^+]_A) = -\log(250 \times [\text{H}^+]_B) \).
Step 4: Calculate the pH of solution B using the formula: \( \text{pH}_B = -\log([\text{H}^+]_B) \).
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
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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The pH Scale
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.
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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.
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Related Practice
Textbook Question
Deuterium oxide 1D2O, where D is deuterium, the hydrogen-2 isotope) has an ion-product constant, Kw, of 8.9 * 10-16 at 20 °C. Calculate 3D+4 and 3OD-4 for pure (neutral) D2O at this temperature.
Textbook Question
By what factor does [H+] change for a pH change of (a) 2.00 units? (b) 0.50 units?
Textbook Question
The average pH of normal arterial blood is 7.40. At normal body temperature 137 °C2, Kw = 2.4 * 10-14. Calculate 3H+4, 3OH-4, and pOH for blood at this temperature.