Problem 80 - Chemistry: Structure and Properties

Question

Phenolphthalein has a pKa of 9.7. It is colorless in its acid form and pink in its basic form. For each of the pH values, calculate [In-]/[HIn] and predict the color of a phenolphthalein solution. a. pH = 2.0 b. pH = 5.0 c. pH = 8.0 d. pH = 11.0

Step-by-Step Solution

Answer

a. Ratio \(0.0002\), colorless. b. Ratio \(0.002\), colorless. c. Ratio \(0.2\), slight pink tint. d. Ratio \(20\), pink.

Step 1: Calculate the Ratio [In-]/[HIn] for pH 2.0

To calculate the ratio [In-]/[HIn] at pH 2.0, use the Henderson-Hasselbalch equation: \(\text{pH} = \text{pKa} + \log(\frac{[In^-]}{[HIn]})\). Rearrange the equation to solve for \(\frac{[In^-]}{[HIn]}\): \(\frac{[In^-]}{[HIn]} = 10^{(\text{pH} - \text{pKa})}\). Substitute pH = 2.0 and pKa = 9.7: \(\frac{[In^-]}{[HIn]} = 10^{(2.0 - 9.7)}\) which results in approximately 0.0002.

Step 2: Predict Color for pH 2.0

Since the ratio [In-]/[HIn] is much less than 1, the acid form (HIn) predominates, hence the solution remains colorless.

Step 3: Calculate the Ratio [In-]/[HIn] for pH 5.0

Using the same Henderson-Hasselbalch equation: \(\frac{[In^-]}{[HIn]} = 10^{(5.0 - 9.7)}\). The calculated ratio is around 0.002.

Step 4: Predict Color for pH 5.0

The ratio [In-]/[HIn] is still less than 1, indicating the solution is primarily in the acid form (HIn) and will remain colorless.

Step 5: Calculate the Ratio [In-]/[HIn] for pH 8.0

Apply the Henderson-Hasselbalch equation again: \(\frac{[In^-]}[HIn]} = 10^{(8.0 - 9.7)}\). This yields a ratio close to 0.2.

Step 6: Predict Color for pH 8.0

The ratio is still below 1, but because it is closer to 1, there might be a very light pink tint due to the presence of some In- ions.

Step 7: Calculate the Ratio [In-]/[HIn] for pH 11.0

By the Henderson-Hasselbalch equation: \(\frac{[In^-]}{[HIn]} = 10^{(11.0 - 9.7)}\). The calculated ratio is about 20.

Step 8: Predict Color for pH 11.0

The ratio [In-]/[HIn] is greater than 1, indicating the basic form (In-) predominates. The solution will be pink.

Key Concepts

Acid-Base Indicators

Acid-base indicators are compounds that change color based on the pH of the environment. They're helpful for visually determining whether a solution is acidic or basic. These substances have a particular pH range in which their color gradually changes due to the varying concentration of their ionized and non-ionized forms.

For instance, let’s take phenolphthalein, a commonly used laboratory indicator. It appears colorless when in acid form and transitions to pink in its basic form. This color change happens over a pH range, which for phenolphthalein is typically between pH 8.2 to 10.0. In strongly acidic solutions, the molecule is completely in its acid form, remaining colorless, while in basic solutions, its basic form dominates, and it becomes pink.

pH Calculation

pH calculation is pivotal in understanding acid-base chemistry. It is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. The pH scale ranges from 0 to 14, with lower values being more acidic, higher values more basic, and 7 considered neutral.

The Henderson-Hasselbalch equation is a mathematical expression employed to relate the pH of a solution to the pKa (an acid's dissociation constant) and the concentrations of an acid and its conjugate base. It is written as: \[\text{pH} = \text{pKa} + \text{log}(\frac{[\text{In}^-]}{[\text{HIn}]})\].

This equation allows for the calculation of the pH when the acid and base forms' concentrations are known, or vice versa. Understanding this relationship helps determine the extent of ionization of molecules like phenolphthalein in solutions with different pH values.

Phenolphthalein Color Change

Phenolphthalein is particularly interesting due to its distinct color change from colorless to pink. The underlying mechanisms are all about the ratio of acidic to basic forms, denoted as HIn for the acid form and In- for the base form. At low pH values, the concentration of HIn is high, making the solution colorless. As pH increases, more of the molecule converts to its In- form, leading to pink coloration.

Visualizing pH Changes

With phenolphthalein, this transition is evident around a pH of 8.2 and becomes distinct by pH 10. This behavior illustrates the gradual shift from acid form dominance to base form dominance, crucial for practical applications such as titrations. The precise color change occurs when the pH of the solution crosses the pKa value of the indicator.

Acidic and Basic Forms of Indicators

Acid-base indicators, including phenolphthalein, possess both acidic and basic forms, which determine their color in solution. The acid form (HIn) tends to be colorless or have a different color compared to the base form (In-).

Ions and Equilibrium

The equilibrium between these two forms is driven by the pH of the surrounding environment. In acid conditions, the equilibrium is shifted towards the acidic form, whereas in basic conditions, the basic form is favored. The Henderson-Hasselbalch equation provides a quantitative way to understand this equilibrium with respect to the color you observe in a system. The ratio of \([\text{In}^-]/[\text{HIn}]\) indicates which form is prevalent at a given pH, explaining the indicator's visible color.