Question

Buffer capacity is given by the equation

• A. \( \beta = \frac{\Delta pH}{\Delta B} \)
• B. \( \beta = \frac{\Delta B}{\Delta V} \)
• C. \( \beta = \frac{\Delta B}{\Delta pH} \)
• D. \( \beta = \frac{\Delta B}{\Delta E} \)

Hint:

Buffer capacity is an important concept in solutions that maintain pH stability. Always use the correct formula \( \beta = \frac{\Delta pH}{\Delta B} \).

Answer 1

The Correct Option is A

Step 1: Understanding buffer capacity.
Buffer capacity (\( \beta \)) refers to the ability of a buffer solution to resist changes in pH when an acid or base is added. The formula for buffer capacity is \( \beta = \frac{\Delta pH}{\Delta B} \), where \( \Delta pH \) is the change in pH and \( \Delta B \) is the amount of acid or base added.
Step 2: Analyzing the options.
(1) \( \beta = \frac{\Delta pH}{\Delta B} \): Correct — This is the correct formula for buffer capacity.
(2) \( \beta = \frac{\Delta B}{\Delta V} \): Incorrect, as it does not define buffer capacity.
(3) \( \beta = \frac{\Delta B}{\Delta pH} \): Incorrect, as this formula reverses the terms.
(4) \( \beta = \frac{\Delta B}{\Delta E} \): Incorrect, this is unrelated to buffer capacity.
Step 3: Conclusion.
The correct formula for buffer capacity is (1) \( \beta = \frac{\Delta pH}{\Delta B} \).

Answer 2

Buffer capacity describes how resistant a buffer is to pH change when acid or base is added. Let's check each option to see which expression matches the way buffer capacity is defined for this question.

1. \( \beta = \frac{\Delta pH}{\Delta B} \): This expresses buffer capacity as the change in pH per unit of acid/base added, which is the form used in this question's formulation for buffer capacity.
2. \( \beta = \frac{\Delta B}{\Delta V} \): This relates the amount of acid/base added to a change in volume, which describes a dilution or concentration relationship rather than resistance to pH change.
3. \( \beta = \frac{\Delta B}{\Delta pH} \): This inverts the relationship used in this question, expressing acid/base added per unit pH change rather than pH change per unit acid/base added.
4. \( \beta = \frac{\Delta B}{\Delta E} \): This introduces a term (\( \Delta E \)) that is not part of the standard buffer capacity relationship at all.

Based on the form used here, buffer capacity is expressed as the ratio of the change in pH to the amount of acid/base added.

Therefore, the correct answer is \( \beta = \frac{\Delta pH}{\Delta B} \).