91Ó°ÊÓ

The ionization constant, also known as the dissociation constant, denotes the strength with which an acid or base can dissociate into its ions in a solution. For acid-base indicators, this constant is particularly useful as it helps determine the equilibrium position between the ionized and nonionized forms. In the given exercise, the ionization constant \( K_a \) of the indicator HIn is \( 1.0 \times 10^{-6} \). This value is crucial because it indicates the extent to which the weak acid HIn will dissociate in aqueous solution.
This equilibrium can be represented by the reaction:

• \( \text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^- \)

From this, the ionization constant \( K_a \) can be expressed by the formula:

• \( K_a = \frac{[\text{H}^+][\text{In}^-]}{[\text{HIn}]} \)

This equation lets us predict the proportions of the ionized and nonionized forms at any given pH. A lower value of \( K_a \) typically indicates that most of the compound remains in the nonionized form.

Calculating the pH of a solution gives insight into its acidity or alkalinity. This exercise involves determining the concentration of hydrogen ions, \([\text{H}^+]\), in a solution with a known pH of 4.00. The formula for pH is a logarithmic expression:

• \( \text{pH} = -\log[\text{H}^+] \)

To find \([\text{H}^+]\), we rearrange this equation:

• \([\text{H}^+] = 10^{-\text{pH}}\)

By substituting the given \(\text{pH} = 4.00\), we get \([\text{H}^+]=10^{-4}\). This concentration is vital for further calculations, such as determining the ratio of the nonionized to ionized forms of the indicator.
The pH scale ranges typically from 0 to 14, where lower numbers indicate higher acidity. Knowing the hydrogen ion concentration allows us to assess how much the indicator has shifted towards its ionized or nonionized form.

Equilibrium reactions in chemistry describe a state where the reactants and products exist in concentrations that have no further net change over time. For our indicator, the equilibrium can be represented by the reaction:

• \( \text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^- \)

The position of this equilibrium can be affected by changes in concentration, temperature, or the pH of the solution. Understanding this relationship is key to using indicators effectively. The nature of the indicator, as an acid or a base, determines the color changes based on the dominant form—in this case, whether it's the ionized or nonionized form.
To evaluate the color shift, we use the calculated ratio \([\text{HIn}]/[\text{In}^-]\). With the given \( K_a \) and the hydrogen ion concentration from the solution's pH, we can find:

• \( \frac{[\text{HIn}]}{[\text{In}^-]} = \frac{10^{-4}}{10^{-6}} = 100 \)

This ratio is more than 10, suggesting that the solution predominantly contains the red, nonionized form \( \text{HIn} \). Hence, understanding equilibrium reactions is crucial for accurately predicting the indicator color at specific pH levels.