Question

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

Short answer

The \(\mathrm{p}_{a}\) (pKa) for bromcresol green is \(4.68\).

Step-by-step solution

Understand the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by: \[pH = pKa + \log\frac{[A^-]}{[HA]}\] where pH is the solution's pH, pKa is the acidity constant of the weak acid, \([A^-]\) is the concentration of the conjugate base, and \([HA]\) is the concentration of the weak acid.

Identify the information given in the problem

We know that when the pH is 4.68, the acid (HA) and base (A-) forms of bromcresol green are present in equal concentrations. This means that at this point, the ratio \(\frac{[A^-]}{[HA]}\) is equal to 1.

Use the Henderson-Hasselbalch equation to find the pKa

Since \(\frac{[A^-]}{[HA]} = 1\), we can rewrite the Henderson-Hasselbalch equation as follows: \[pH = pKa + \log(1)\] Note that the logarithm of 1 is equal to 0, so the equation simplifies to: \[pH = pKa\] We are given the pH as 4.68, so the acidity constant (pKa) for bromcresol green is: \[pKa = 4.68\] The \(\mathrm{p}_{a}\) for bromcresol green is \(4.68\).

Key concepts

Acid-Base Indicators

Acid-base indicators are chemical compounds that change color in response to changes in pH, which is a measure of how acidic or basic a solution is. These indicators are often weak acids or bases themselves. The color change occurs because the indicator molecule transforms between its acid form and its base form at a certain pH level.

Some common examples of acid-base indicators are litmus, phenolphthalein, and methyl orange. Each indicator has its own unique range of pH over which it changes color, which makes each suitable for different types of chemical reactions.

• Litmus turns red in acidic conditions and blue in basic conditions.
• Phenolphthalein is colorless in acidic solutions and turns pink in basic solutions.
• Methyl orange turns from red in acidic solutions to yellow in neutral to basic solutions.

When using an acid-base indicator, it's essential to know its pH range and corresponding color changes to interpret the results effectively.

pKa Calculation

Understanding the calculation of pKa is crucial for predicting how a weak acid or base will react in solution. pKa is the negative logarithm of the acid dissociation constant (Ka), which describes how easily an acid donates a proton to become a base.

The equation for this process involves using the Henderson-Hasselbalch equation: \[\text{pH} = \text{pKa} + \log\frac{[A^-]}{[HA]}\] where \([A^-]\) is the concentration of the conjugate base and \([HA]\) is the concentration of the acid.

In simple terms, the pKa value helps us determine at what pH the acid and base forms of a substance are present in equal amounts. When these concentrations are equal, \(\log\frac{[A^-]}{[HA]} = 0\), simplifying the relationship to \(\text{pH} = \text{pKa}\). This relationship is especially useful in chemistry when preparing buffer solutions, as it tells us the point at which the mixture resists changes in pH.

Bromcresol Green

Bromcresol green is a specific type of acid-base indicator used in various laboratory and educational settings due to its clear color change within a convenient pH range. This indicator transitions from yellow to blue across its operational pH range of approximately 3.8 to 5.4, which makes it suitable for identifying the acidity of a given solution.

In a pH of around 4, bromcresol green appears green. This is because the yellow form of the acid and the blue form of the base are blended. The color change makes it easy for users to visually judge whether a solution is more acidic or basic than its neutral point.

By understanding the pKa of bromcresol green, which is \(4.68\) as given by the exercise, you can accurately predict when the solution will appear green, highlighting the concept of neutralization through the Henderson-Hasselbalch equation. This kind of practical application helps in making lab work more intuitive.