# Is a buffer solution really inactive beyond a range of pKa±1?

I have learnt from several books that the range of a buffer solution is always from $\ce{pH = pKa - 1}$ to $\ce{pH = pKa + 1}$. But is there any solid reason to this and any exception?

• Did you derived that expression for buffer solution? Then you will find some reason… – Fawad Feb 16 '17 at 17:07
• I have read so in several books. – Aaron John Sabu Feb 16 '17 at 17:11
• Similar or possibly duplicate questions here, here, and here. The best answer is probably at that second link. – hBy2Py Feb 16 '17 at 17:31
• This question is more quantitative than the others, though -- so there may be opportunity for new content in an answer here. – hBy2Py Feb 16 '17 at 17:45

The 10:1 ratio is really just something convenient for the chemists. The buffer still works outside this range. True, its effectiveness against base addition decreases with the amount of available acid at high pH, and vice versa for acid addition at low pH. But if enough capacity remains, you can still live with the buffer even outside the 10:1 range.

Er, actually you do. Our main blood buffer, based on dissolved carbon dioxide as the acid and bicarbonate as the base, has about 20 times as much bicarbonate as carbon dioxide (https://en.m.wikipedia.org/wiki/Bicarbonate_buffer_system). Factors other than what a laboratory chemist calls "optimal" should be given their due. Metabolic processes commonly produce (weak) acids, and the solubility of carbon dioxide is more limited than that of bicarbonate salts. Both of these factors make a base-rich buffer desirable.

What I think Fawad was asking hints you can derive the result of +-1 pH around the pKa yourself from the Henderson-Hasselbach (H-H) equation. BY that equation, the ratio of the anion form of the buffer to the acid salt form of the buffer, is plugged into the equation and solves as pKa+1 if the anion to salt ratio is 10:1, because the log(10)=1. IF the ratio were 1:10, then log(0.1)=-1 giving a pH of pKa-1. SO that's where the idea that buffers work best in a range +-1 around pKa of the buffer.

PRACTICALLY when the ratio of the buffer's two forms of anion and acid salt are close to 1:1 (e g. 50% each form) the buffer chemical equilibrium easily absorbs added acid or base by absorbing the donated protons or hydroxyls. In the H-H equation that solves to a pH equal to the buffer's pKa , since log(1)=0.

SO close to the pKa the buffer as its strongest buffering. PH of +-1 is outer limit for efficient buffering based on the implied ratio of 10:1 FOR the buffer components. It is theoretical and approximate though. You should try to plot titration curves of your buffer versus added acid or base.

IF that is not deep enough answer for you, read further into Henderson-Hasselbach, buffering prediction, and titration curves of buffer systems. You might be interested to read about Dr. Good' s buffers too.

• Why should it be particularly 10:1, is there any reason for that? - This was my question. – Aaron John Sabu Feb 18 '17 at 10:26