An acid-base indicator has a distinct visual colour transition. The acid form () is distinctly red, — Ionic Equilibrium Chemistry Question
Question
An acid-base indicator has a distinct visual colour transition. The acid form ($HIn$) is distinctly red, and the basic form ($In^-$) is distinctly blue. The indicator constant $K_{In} = 1.0 \times 10^{-5}$. A laboratory manual dictates that a visual colour change is clearly perceptible to the human eye when the concentration ratio shifts from 80% red to 80% blue. Calculate the exact $\Delta pH$ required to achieve this full visual transition.
💡 Solution & Explanation
Using the indicator equation: $pH = pK_{In} + \log\frac{[In^-]}{[HIn]}$. For 80% red (acidic form), $[In^-]/[HIn] = 20/80 = 1/4$. The pH is $pH_1 = 5 + \log(0.25) = 5 - 0.60 = 4.40$. For 80% blue (basic form), the ratio is $80/20 = 4/1$. The pH is $pH_2 = 5 + \log(4) = 5 + 0.60 = 5.60$. The total required pH change for the visual shift is $\Delta pH = 5.60 - 4.40 = 1.20$.