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

Buffer capacity (\( \beta \)) measures how much a buffer solution resists a change in pH when a small amount of strong acid or base is added. In the form used for this question, it is written as \( \beta = \frac{\Delta pH}{\Delta B} \), the ratio of the observed pH change (\( \Delta pH \)) to the quantity of acid or base added (\( \Delta B \)). The other expressions either invert this relationship or introduce unrelated terms such as volume or a variable \( \Delta E \) that do not belong in the buffer capacity relationship.

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

Answer 2

Another way to confirm this is by checking the units and dimensional sense of each option in the context of a buffer resisting pH change.

1. \( \beta = \frac{\Delta pH}{\Delta B} \): Here, the numerator is a (dimensionless) pH change and the denominator is an amount of acid/base, so \( \beta \) reflects how much the pH shifts per mole of acid or base added — matching the relationship intended in this formulation.
2. \( \beta = \frac{\Delta B}{\Delta V} \): Here, the ratio compares an amount of acid/base to a volume change, which describes concentration, not the buffer's resistance to pH change.
3. \( \beta = \frac{\Delta B}{\Delta pH} \): This flips numerator and denominator relative to the form used in this question, so it does not match the expression being tested here.
4. \( \beta = \frac{\Delta B}{\Delta E} \): The term \( \Delta E \) has no defined role in buffer chemistry, so this option can be ruled out on that basis alone.

Only the pH-change-over-amount-added form matches the buffer capacity expression used in this question.

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