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?

Step by Step Solution: Step 1. Use the Henderson-Hasselbalch equation to find the Kₐ of Phenol red. Step 2. pKₐ = -log(Kₐ) Step 3. 7.4 = pKₐ Step 4. Kₐ = 10^(-7.4) Step 5. Kₐ = 3.98 x 10^(-8) Step 6. Use the formula: pH = pKₐ + log([A⁻]/[HA]) to find the pH range for Phenol red. Step 7. Since Phenol red is yellow in acidic solutions and red in alkaline solutions, it is safe to assume that its transition occurs around its pKₐ, or pH 7.4. Step 8. Therefore, the pH range for Phenol red is approximately 6.4 to 8.4. Step 9. At pH 7.4, the solution will transition from slightly more yellow to slightly more red, but it will appear closer to red. Final Answer: a) Kₐ = 3.98 x 10^(-8), b) pH range is approximately 6.4 to 8.4, c) The color of Phenol red at pH 7.4 will be slightly more red.