Question

Phenol red is an indicator with a \(\mathrm{pK}_{\mathrm{a}}\) of \(7.4\). It is yellow in acid solution and red in alkaline. (a) What is its \(K_{\mathrm{a}}\) ? (b) What is its \(\mathrm{pH}\) range? (c) What would its color be at \(\mathrm{pH}\) 7.4?

Short answer

Answer: The Ka value for Phenol Red is approximately \(3.98 \times 10^{-8}\), its pH range is approximately 6.4 to 8.4, and its color at pH 7.4 is orange.

Step-by-step solution

Calculate the Ka value from the given pKa value

The relationship between Ka and pKa is given by the formula: \(pK_a = -\log_{10}(K_a)\). First, we need to use the given pKa value to calculate the Ka value as follows: - Rearrange the equation for Ka: \(K_a = 10^{-pK_a}\). - Plug in the given pKa value, 7.4, and calculate Ka: \(K_a = 10^{-7.4}\).

Calculate the Ka value

Now we can calculate the Ka value using the formula: \(K_a = 10^{-7.4}\). Evaluating the expression gives us: \(K_a \approx 3.98 \times 10^{-8}\).

Determine the pH range of Phenol Red

The pH range of an indicator can be estimated by taking the pKa value ±1. This is because the pH range over which an indicator changes color depends on the concentration of the acidic and basic forms of the indicator in the solution. So, for Phenol Red, the pH range will be: \(pH = pK_a \pm 1\) \(pH = 7.4 \pm 1\) The pH range of Phenol Red is approximately 6.4 to 8.4.

Determine the color of Phenol Red at pH 7.4

At a pH value equal to the pKa of the indicator (in this case, 7.4), the concentration of the acidic form and the basic form of the indicator are equal. Phenol Red is yellow in an acidic solution and red in an alkaline solution. Since the pH value, 7.4, is equal to the pKa value, the solution is at the transition point between the acidic and basic forms of Phenol Red. At this point, the indicator will exhibit a color that is an intermediate between the acidic yellow and the basic red colors. The resulting color at pH 7.4 is orange. In summary: - (a) The Ka value for Phenol Red is approximately \(3.98 \times 10^{-8}\). - (b) The pH range for Phenol Red is approximately 6.4 to 8.4. - (c) The color of Phenol Red at pH 7.4 is orange.

Key concepts

pKa and Ka relationship

Understanding the relationship between pKa and Ka is essential in grasping how strong or weak an acid is. Both are measurements related to acidity but express in different forms.
In chemistry, the pKa value indicates the strength of an acid. It represents the negative logarithm to the base ten of the acid dissociation constant (Ka). This value allows chemists to compare the relative strength of different acids.
- **Equation:** The relationship can be expressed mathematically as follows: \( pK_a = -\log_{10}(K_a) \). With this equation, one can find Ka using the reverse equation: - \( K_a = 10^{-pK_a} \). - **Example:** For an indicator like Phenol Red with a pKa of 7.4, the Ka can be calculated as follows:
\( K_a = 10^{-7.4} \approx 3.98 \times 10^{-8} \).
This low Ka value suggests that Phenol Red is a weak acid, as it does not donate protons easily. This is a typical characteristic of indicators that change color over a pH range.

pH range of indicators

Acid-base indicators like Phenol Red have a specific pH range in which they change color. This range is centered around the pKa value of the indicator, generally extending one pH unit above and below the pKa.
- **Significance:** The color change occurs because the indicator exists in different ionic forms at different pH values, each having its color.
- **Range Calculation:** For Phenol Red, with a pKa of 7.4, the pH range is: \( pH = pK_a \pm 1 \), resulting in a range of approximately 6.4 to 8.4.
- **Importance in Experiments:** This range is critical in laboratory settings, where knowing the precise pH range for color change helps scientists determine the acidity or basicity of a given solution. Thus, it aids in identifying the endpoint of a titration or measuring pH neutralization.

color change at transition point

The transition point in acid-base indicators is pivotal as it represents the pH at the point where the indicator changes color. At this specific pH, concentrations of the acidic and basic forms of the indicator are equal. - **Phenol Red Example:** For Phenol Red, the transition point is at pH 7.4, which is equal to its pKa. At this juncture, Phenol Red exhibits an intermediate color between its acidic (yellow) and basic (red) forms.
- **Transition Color:** Here, the solution will appear orange, a blend of the yellow and red colors. This is because the hue at the transition point is a combination of both ionic forms, reflecting their equal presence.
- **Visualization in Experiments:** This helps students and scientists visually perceive the exact transition point, vital for understanding how solutions shift between acidic and basic states. Recognizing this color can significantly improve the accuracy of pH measurements in experimental applications.