Final answer:
The value of Ka for an indicator with a pH range of color change from 9.0 to 11.0 is approximately 1 × 10^-10. The pKa, representing the middle of the color change range, is around 10.0, and Ka equals 10^-pKa.
Step-by-step explanation:
The value of the Ka for an indicator can be estimated using the pH range where the color change occurs. A color change between pH 9.0 and 11.0 indicates the pKa value is in the middle of this range, around a pH of 10.0. Given that pKa is the negative logarithm of Ka (pKa = -log(Ka)), we can calculate Ka as 10-pKa or 10-10, which gives us a Ka value of 1 × 10-10. This is because the color change interval for most indicators represents the range of approximately pKa ± 1, where the concentration ratio of the deprotonated form ([In-]) to the protonated form ([HIn]) varies between 0.1 and 10.