Question

The indicator methyl red has a \(\mathrm{pK}_{\mathrm{HIn}}=4.95 . \mathrm{It}\) changes from red to yellow over the pH range from 4.4 to 6.2 (a) If the indicator is placed in a buffer solution of \(\mathrm{pH}=4.55,\) what percent of the indicator will be pre- sent in the acid form, HIn, and what percent will be present in the base or anion form, In \(^{-2}\) (b) Which form of the indicator has the "stronger" (that is, more visible) color- -the acid (red) form or base (yellow) form? Explain.

Short answer

a) 39.81% of the indicator will be in the anion form (In-) and 60.19% will be in the acid form (HIn). b) The acid form (red color) will be more visible.

Step-by-step solution

Calculate the ratio of the concentrations of base and acid form

Using the Henderson-Hasselbalch equation: \(pH = pKa + log(\frac{[In^-]}{[HIn]})\), the ratio of the concentrations of the base and acid forms can be determined. It comes out to be \(\frac{[In^-]}{[HIn]} = 10^{pH - pKa} = 10^{4.55 - 4.95} = 10^{-0.4}\).

Calculate the percentage of each form

The fraction of the form is given by the ratio of its concentration to the total concentration. Here, the percentage of In^- is given by \(\frac{[In^-]}{[HIn] + [In^-]} * 100\%\). Substitute the value from step 1 into this expression to yield the percentage: \(\frac{10^{-0.4}}{1 + 10^{-0.4}} * 100\% = 39.81\%\). The remaining (100%- 39.81% = 60.19%) will be in the acid form HIn.

Decide which form of the indicator has stronger color

Looking at the pH range where methyl red changes color (4.4 to 6.2), the indicator will exhibit an intense red color (in the acidic form) in solutions of pH less than 4.4 and an intense yellow color (in the base form) in solutions with pH greater than 6.2. At pH 4.55, the solution is closer to 4.4. This suggests that the acid form with red color will be more visible than the base form with yellow color at this pH.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is an essential tool in chemistry, particularly in the study of buffer solutions and the behavior of acid-base indicators. It is given by the formula:\[ pH = pKa + \log\left(\frac{[In^-]}{[HIn]}\right) \]This equation helps us understand the relationship between the pH of a solution, the pKa of the indicator, and the ratio of the concentrations of its acid and base forms.

• **pH** is a measure of how acidic or basic a solution is.
• **pKa** is the negative logarithm of the acid dissociation constant (Ka), indicating how easily an acid donates a proton.
• **[In^-]** and **[HIn]** represent the concentrations of the base (anion) form and acid form of the indicator, respectively.

The Henderson-Hasselbalch equation allows one to calculate what percentage of an indicator is in its acid or base form, as demonstrated in the original step-by-step solution. By inputting the pH and pKa into the equation, we determine that the concentrations ratio is \(10^{-0.4}\), reflecting the balance between the acid and base forms at a specific pH.

Methyl Red Indicator

Methyl Red is a common pH indicator used in various chemical experiments. It is particularly useful because it changes color in a specific pH range, making it easy to visually determine the acidity or basicity of a solution. The transition range for Methyl Red is between **pH 4.4** and **pH 6.2**, where it shifts from a red color in acidic solutions (lower pH) to a yellow color in basic solutions (higher pH). Key characteristics of Methyl Red include:

• **Red color**: Dominant in solutions with pH less than 4.4.
• **Yellow color**: Dominant in solutions with pH greater than 6.2.
• **Transition range**: This is the range where the indicator changes color, providing a useful visual cue for the approximate pH of the solution.

At a pH of approximately 4.55, as mentioned in the original problem, Methyl Red will present a mix of its red and yellow forms. According to the solution steps, since the pH is closer to 4.4 than 6.2, the red (acid) form is more predominant, thus being "stronger" in appearance.

pH and pKa relationship

Understanding the pH and pKa relationship is crucial in determining how acid-base indicators function. The pKa value provides insight into the strength of an acid; specifically, it tells us at what pH a given compound will donate or accept protons.

The following points elaborate on this relationship:

• **Low pKa value**: Indicates a stronger acid that donates protons easily.
• **High pKa value**: Indicates a weaker acid.
• **pH = pKa**: This state means that the concentrations of the acid and base forms of the indicator are equal.

The closer the pH is to the pKa of an indicator, the more balanced the ratio of its acid and base forms. As seen in the case of Methyl Red, its pKa is 4.95, and at a pH of 4.55, a majority of the compound will be in its red, acidic form. The pH being less than the pKa suggests that the acid form (red) predominates, making it more visible in the solution.