See explanation below.
Work Step by Step
1 To see a distinct color in a mixture of two colors, we need one of the colors to have about 10 times the intensity of the other. The concentration ratio is given by [HIn] / [In-] For one of these to be the case, the concentration ratio [HIn] / [In-] has to be either greater than 10 or less than 1/10. i.e. [HIn] / [In-] > 10 OR [HIn] / [In-] < 1/10 pH = pKa + log([HIn] / [In-]) Thus, when [HIn] / [In-] = 10, pH = pKa + 1 And, when [HIn] / [In-] = 1/10 pH = pKa - 1 In short, pH = pKa +/- 1, thus giving a pH range of about 2 units.