Chapter U6.123, Problem 2E

Interpretation Introduction

Interpretation: Whether the value of K_a of an acid-base indicator changes when the indicator is added to an acid or a base or not needs to be explained.

Concept Introduction:An acid-base indicator is a visual indicator that signals the end of an acid-base titration by a color change. The color change of the indicator depends on the pH of the medium. An acid-base indicator shows different colors in acidic and basic mediums and the color change depends on the concentration of H+ ions in the solution.

Answer to Problem 2E

The value of K_a of an acid-base indicator doesn’t change when the indicator is added to an acid or a base; however, the concentrations of the unionized and the ionized forms of the indicator change.

Explanation of Solution

An acid-base indicator is a weak acid that undergoes partial ionization in an aqueous solution as below.

  $\text{HIn }\left(aq\right)\rightleftharpoons {\text{ H}}^{+}\left(aq\right)+{\mathrm{In}}^{-}\left(aq\right)$

Here HIn is the unionized indicator and In- is the ionized indicator.

The equilibrium constant for the above ionization is the acid ionization constant, K_agiven by the expression

  $K_a=\frac{\left[H^{+}\right]\left[I{n}^{-}\right]}{\left[HIn\right]}$

Here, K_a is a thermodynamic equilibrium constant and hence, depends only on the temperature. The addition of an acid or a base to an indicator doesn’t change the temperature of the medium; hence, K_a doesn’t change. However, depending on the pH of the medium, the concentrations of HIn and In- change.

Conclusion

The addition of the indicator to an acid or a base doesn’t change the K_a of the indicator.