Buffer range | Acids and bases | AP Chemistry | Khan Academy

Buffers consist of a significant amount of a weak acid, which we will represent as H A, and the conjugate base to the weak acid, which we will represent as A minus. Buffer solutions resist large changes in pH; however, buffers are only effective over a certain range of pH values.

We are going to use the Henderson-Hasselbalch equation to find the effective pH range of a buffer. Looking at the Henderson-Hasselbalch equation, the pH of the buffer solution is equal to the pKa of the weak acid, which would be H A, plus the log of the concentration of the conjugate base divided by the concentration of the weak acid.

It's this ratio of the concentration of the conjugate base to the concentration of the weak acid that determines if a buffer is effective or not. Buffer solutions are most effective at resisting a change in pH in either direction when the concentration of the weak acid is equal to the concentration of the conjugate base. When the concentrations are equal to each other, the ratio is equal to 1, and the log of 1 is equal to zero.

Therefore, when the concentrations are equal to each other, the pH of the buffer solution is equal to the pKa of the weak acid plus zero. So we could just say that the pH is equal to the pKa when the concentration of the weak acid is equal to the concentration of the conjugate base.

We usually try to choose a buffer with a weak acid that has a pKa value close to the desired pH of the solution. Buffers are effective at resisting large changes in pH when the pH is approximately equal to the pKa of the weak acid. However, if the concentration of one component of a buffer is more than 10 times the concentration of the other component, buffers are not effective at resisting large changes to pH.

Therefore, to find the effective pH range, we are going to use the Henderson-Hasselbalch equation to calculate the pH when the concentration of the conjugate base is 10 times the concentration of the weak acid and also to calculate the pH when the concentration of the weak acid is 10 times the concentration of the conjugate base. Doing these two calculations gives us the upper and lower limits of the effective pH range.

So, let's calculate the pH of the buffer solution when the concentration of the conjugate base is 10 times the concentration of the weak acid. Looking at the Henderson-Hasselbalch equation, if the concentration of the conjugate base is 10 times the concentration of the weak acid, the ratio is equal to 10 over 1, and the log of 10 is equal to 1.

Therefore, the pH of the buffer solution is equal to the pKa value of the weak acid plus one. This value for the pH represents the upper limit of the effective pH range. Next, let's calculate the pH of the buffer solution when the concentration of weak acid is 10 times the concentration of the conjugate base.

Looking at the Henderson-Hasselbalch equation, if the concentration of H A is 10 times the concentration of A minus, the ratio is equal to 1 over 10, and the log of 1 over 10 is equal to negative one. Therefore, the pH of the buffer solution is equal to the pKa value of the weak acid minus one.

This value for the pH represents the lower limit of the effective pH range. By the calculations that we've just done, we've seen that the effective pH range of a buffer is plus or minus 1 of the pKa value of the weak acid.

Let's use this concept of an effective pH range to choose a buffer solution. Let's say we want to buffer a solution at a pH of 9.00 at 25 degrees Celsius. Suppose that we have two choices: we could either choose an acetic acid/acetate buffer or we could choose an ammonium/ammonia buffer.

Because the effective pH range of a buffer is plus or minus 1 the pKa value of the weak acid, we don't want to choose the acetic acid/acetate buffer solution because, at 25 degrees Celsius, the pKa value for acetic acid is equal to 4.74. Therefore, this buffer would only be effective at a range of plus or minus 1 from 4.74, so about 3.74 to approximately 5.74.

The ammonium cation has a pKa value equal to 9.25 at 25 degrees Celsius. Therefore, the ammonium/ammonia buffer is effective plus or minus 1 of this pKa value, so approximately 8.25 to 10.25. Since our pH of 9 falls within that range, we would choose the ammonium/ammonia buffer.