An acid type indicator, HIn differs in colour from its...

An acid type indicator, HIn differs in colour from its conjugate base $\left(\mathrm{In}^{-}\right)$. The human eye is sensitive to colour differences only when the ratio $[\operatorname{In}] /[\mathrm{HIn}]$ is greater than 10 or smaller than $0.1$. What should be the minimum change in the $\mathrm{pH}$ of the solution to observe a complete colour change $\left(K_{\mathrm{a}}=1.0 \times 10^{-5}\right)$ ? (a) $0.0$ (b) $1.0$ (c) $2.0$ (d) $5.0$

Key Concepts

Henderson-Hasselbalch Equation

This equation, pH = pKa + log([A-]/[HA]), is fundamental in acid-base chemistry because it relates the pH of a solution to the pKa of the acid and the ratio of the concentrations of its conjugate base and acid forms. It is used to determine the extent of dissociation of acids and the resulting concentrations of the species in solution, which in turn affects observable properties like color change in indicators.

Acid-Base Indicator

Acid-base indicators are compounds that change color in response to changes in the pH of a solution. They exist in different forms (acid form and conjugate base form) that have distinct absorption spectra, leading to different visible colors. This property is exploited to signal pH changes in chemical systems.

Acid Dissociation Constant (Ka) and pKa

Ka is the equilibrium constant for the dissociation of a weak acid in solution, reflecting its strength. pKa, which is the negative logarithm of Ka, provides an easily understood value. Knowing the pKa of an indicator helps predict at what pH levels the indicator will change color, based on the relative amounts of the acid and conjugate base present.

Color Change Thresholds and pH Range

In the context of indicators, the human eye can detect a color change only when the ratio of the concentrations of the indicator's forms exceeds a certain threshold (greater than 10 or less than 0.1). This translates into a required change in pH, calculated using the logarithmic relationship of the concentration ratio in the Henderson-Hasselbalch equation, often resulting in a minimum observable pH transition of about 2 units.

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