Question

The acid-base indicator bromcresol green is a weak acid. The yellow acid and blue base forms of the indicator are present in equal concentrations in a solution when the pH is \(4.68 .\) What is the p \(K_{a}\) for bromcresol green?

Short answer

The pKa for bromcresol green is 4.68, which is calculated using the Henderson-Hasselbalch equation: \(pH = pKa + log\frac{[A^-]}{[HA]}\). Given that the acid and base forms of the indicator are present in equal concentrations at pH 4.68, the ratio \(\frac{[A^-]}{[HA]}\) is equal to 1, simplifying the equation to \(4.68 = pKa\).

Step-by-step solution

Understand the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation relates the pH, pKa, and the ratio of conjugate base concentration ([A-]) to weak acid concentration ([HA]): pH = pKa + log\(\frac{[A^-]}{[HA]}\) In this problem, we know the pH and the concentrations of the conjugate base and weak acid forms are equal, which makes the ratio \(\frac{[A^-]}{[HA]}\) equal to 1.

Insert the given values into the equation

Now, substitute the given pH value and the equal concentration ratio into the Henderson-Hasselbalch equation: \(4.68 = pKa + log\frac{[A^-]}{[HA]}\) Since \(\frac{[A^-]}{[HA]}\) = 1, we can write the equation as: \(4.68 = pKa + log(1)\)

Calculate the pKa value

We know that log(1) = 0, so our equation simplifies to: \(4.68 = pKa\) The pKa for bromcresol green is 4.68.

Key concepts

pKa calculation

To find the pKa value of a compound such as bromcresol green, we use the famous Henderson-Hasselbalch equation. This equation is crucial in chemistry, particularly when you're dealing with buffer solutions and acid-base indicators. The formula is given as: \[ \text{pH} = \text{pKa} + \log \left(\frac{[A^-]}{[HA]}\right) \]Here,

• pH represents the acidity or basicity level of your solution.
• pKa is the negative logarithm of the acid dissociation constant, a key characteristic of acids.
• [A^-] stands for the concentration of the conjugate base.
• [HA] represents the concentration of the weak acid form of the compound.

When solving problems related to pKa, especially when the concentrations of the acid and its conjugate base are equal, the log term becomes zero. Why? Because the log of 1 is 0. This is what simplifies the equation, making the pH equal to the pKa value. This is exactly what we used to determine that the pKa for bromcresol green is 4.68.

acid-base indicators

Acid-base indicators are fascinating tools in chemistry that tell us where our solution stands on the pH spectrum. They act almost like magical color-changing lights. These indicators are usually weak acids or bases, and they exhibit different colors based on whether they are in their protonated or deprotonated forms. Some common characteristics of these indicators include:

• They have specific pH ranges where they change color.
• They operate based on the principle of ionization, meaning the compound loses or gains protons.
• The color change is due to the change in structure of the indicator molecule between its acid or base forms.

For example, in bromcresol green, it transitions from yellow in acidic solutions to blue in basic solutions. The point where the color changes, like around a pH of 4.68 for bromcresol green, is closely related to the pKa of the indicator. This is incredibly useful when trying to identify the pH range of your mixture using visible changes.

bromcresol green

Bromcresol green is a specific type of acid-base indicator frequently used in various titrations and pH analyses. Its colorful behavior in different pH environments makes it an excellent choice for educators and chemists alike to visually demonstrate pH levels. When we say that bromcresol green is a "weak acid," we mean that it doesn’t completely dissociate in solution. Rather, it partially ionizes, which plays a crucial role in its function as a pH indicator. Some important points about bromcresol green include:

• It appears yellow in acidic solutions, specifically when the pH is below 3.8.
• Soon after passing the midpoint, or near its pKa value of 4.68, it starts turning into its basic form, appearing blue in a solution with a pH above 5.4.
• Its color change is reversible, enabling it to be used repeatedly for multiple tests.

Choosing the right indicator like bromcresol green depends on the specific pH range you want to measure. Its specific transition range makes it perfect for examining solutions where slight pH changes occur around the pKa value.