See explanation below.
Work Step by Step
1. BUFFER RANGE AND BUFFER COMPONENT RATIO : The range of pH over which the buffer will act effectively, is called the buffer range. It's value is largest when the buffer component ratio is 1. It's value gradually decreases as the Buffer Component Ratio deviates from 1. Practically, If one component of the buffer ratio is more than 10 times the other, the buffer becomes ineffective. That is, if the ratio of A- and HA is between 0.10 and 10, then only, the buffer action will be effective. 2. Now, pH = pKa + log ( [A-] / [HA] ) We know, Log 10 = 1 Log 0.1 = -1 So, when [A-] / [HA] is at the maxima, i.e. 0.1 or 10, pH = pKa + log ( [A-] / [HA] ) = pKa + log 0.1 = pKa - 1 OR pH = pKa + log ( [A-] / [HA] ) = pKa + log 10 = pKa + 1 In short, buffer has a usable range within 1 pH value of the acid component (Ka).