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The buffer capacity is equal to
\[
  A.\dfrac{{\Delta n}}{{\Delta pH}} \\
  B.\dfrac{{pH}}{{\Delta n}} \\
  C.{\text{ }} \pm 1p{K_a} \\
  {\text{D}}{\text{. None of these}} \\
 \]

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Last updated date: 13th Jun 2024
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Answer
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Hint: We can define buffer capacity as the moles of acid required to change the \[pH\]of the solution by 1, in the given liter of buffer solution.

Complete step by step answer:
Let’s start by discussing the buffer capacity and buffer.
Therefore, we can define Buffer capacity as the moles of acid or base required to change the pH of the solution by 1. It is a unitless quantity. When we add acid or base into the system we notice a change in \[pH\] which can be bigger or smaller depending on the initial condition of the solution (its \[pH\], concentration, etc.). The buffer capacity helps us estimate how much change will be there when we add 1 mole of acid or base. A buffer is a solution that resists the change in when acid or base is added to the system. So, that means as long as the buffer is not completely consumed the \[pH\] of the solution will not change. After the buffer is being depleted, drastic \[pH\] change is observed.
Now, coming back to the question, we already know that buffer capacity is the moles of acid or base required to change the \[pH\] of the solution by 1 or we can say that it is the mole of acid or base added divided by the change in pH multiplied by the volume of buffer in liter. For example, we added 2 moles of acid in 1 liter of solution and the change in \[pH\] is 1. So the buffer capacity will be 2.
Now, Buffer capacity = $\dfrac{{{\text{Number of moles of O}}{{\text{H}}^{\text{ - }}}{\text{ or }}{{\text{H}}^{\text{ + }}}{\text{ added}}}}{{{\text{Change in pH }} \times {\text{ Volume of Buffer in litres}}}}{\text{ = }}\dfrac{{\Delta {\text{n}}}}{{\Delta {\text{pH}}}}$
So, the answer to this question is A. \[\dfrac{{\Delta {\text{n}}}}{{\Delta {\text{pH}}}}\]

Note:
We can use buffer capacity in the analysis of water samples in order to determine the water quality. Also, we must know that the buffer capacity is a quantitative measure of resistance to \[pH\] change upon the addition of \[{H^ + }\] or \[O{H^ - }\] ions. Mainly we are using buffer capacity for river water. Because the stable \[pH\] of river water important for the local ecosystems is conserved in order to keep Columbus flourishing.