Question

Thymolphthalein is an indicator that changes from colorless to blue at \(\mathrm{pH} 9.5\) (a) What is its \(K_{\mathrm{a}}\) ? (b) What is its pH range? (c) What is the color of a solution with a pH of 10.0 and a few drops of thymolphthalein?

Short answer

Answer: The Ka value for thymolphthalein is \(3.16 \times 10^{-10}\). The pH range for thymolphthalein is between 8.5 and 10.5. The color of a solution with a pH of 10.0 and a few drops of thymolphthalein is blue.

Step-by-step solution

Calculate the Ka

Given that thymolphthalein changes color at pH 9.5, we can calculate the pKa and Ka values. To calculate the Ka, we must first find the pKa. The pKa is the pH at which the indicator changes color, so in this case, pKa = 9.5. Now, to find Ka, we use the following formula: $$ Ka = 10^{-pKa} $$ So, $$ Ka = 10^{-9.5} $$

Calculate the Ka value

While calculating the Ka value, we get: $$ Ka = 10^{-9.5} = 3.16 \times 10^{-10} $$ Thus, the Ka value of thymolphthalein is \(3.16 \times 10^{-10}\).

Determine the pH range

The pH range of an indicator is typically within one pH unit of its pKa value. So, for thymolphthalein, the pH range can be defined as: $$ pH \: range = pKa \pm 1 $$ With pKa = 9.5, the pH range for thymolphthalein is from 8.5 to 10.5.

Determine the color of the solution at pH 10.0

Now we need to determine the color of a solution with a pH of 10.0 and a few drops of thymolphthalein. Given that the indicator changes color at pH 9.5, we can determine the color at pH 10.0 as follows: At a pH below 9.5, thymolphthalein is colorless. At a pH above 9.5, thymolphthalein is blue. Since the solution has a pH of 10.0, which is above 9.5, the color of the solution with a few drops of thymolphthalein will be blue. In conclusion: (a) The Ka value for thymolphthalein is \(3.16 \times 10^{-10}\). (b) The pH range for thymolphthalein is between 8.5 and 10.5. (c) The color of a solution with a pH of 10.0 and a few drops of thymolphthalein is blue.