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It depends a bit on the buffer itself, but it is usually true. Generally speaking, a buffer is a solution composed of a weak acid (or base) along with its conjugate base (or acid). Usually, the two components (let's call the HA and A- for a weak acid and its conjugate base) are added in equal concentrations. If this is the case, then it is also true that the pH of the solution is equal to the pKa of the weak acid, a very useful fact. If the concentration of two HA and A- are equal, then the buffer capacity should be the same using a strong acid or strong base. However, you can also make a buffer with unequal concentrations of HA and A-. This is still considered a buffer solution, and it will resist change to pH in both directions, but unequally now. If you have a higher concentration of HA than A-, then the buffer will have a higher capacity to resist pH change if you add a strong base (because the base will be deprotonating HA, which you have more of). If you added a strong acid instead, then you would protonate all the A- faster (than you would deprotonate HA with the same amount of strong base), and so it would have a lower buffer capacity. This discussion works equally well if you are using a weak base (B) and its conjugate acid (HB+) instead, except everything is switched!

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Q: Is buffer capacity the same if determined by titration with a strong base instead of a strong acid?
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What is role of buffer solution in complexometric titration?

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