Question

When a solution is titrated with an acid, an indicator In- changes from blue to yellow HIn. The Ka of the indicator is 8.2e-6. At what pH will the indicator color change first be visible?

Answer 1

The pH at which the color change of the indicator will first be visible can be estimated using the Henderson-Hasselbalch equation, which relates the pH of a solution to the ratio of the concentrations of the acid and its conjugate base. The first visible color change of the indicator will occur at a pH of 6.1.

Step-by-step explanation:

When a solution is titrated with an acid, an indicator In- changes from blue to yellow HIn.

The color change of an indicator is determined by the ratio of the concentrations of the two species In- and HIn.

In the case of the indicator in question, its Ka value is 8.2e-6.

The pH at which the color change of the indicator will first be visible can be estimated using the Henderson-Hasselbalch equation, which relates the pH of a solution to the ratio of the concentrations of the acid and its conjugate base.

In this case, we can use the equation:

pH = pKa + log([In-]/[HIn])

First, we can calculate the pKa value by taking the negative logarithm (base 10) of the Ka value: pKa = -log(8.2e-6) = 5.1

Next, we can substitute the pKa value and the ratio of [In-]/[HIn] into the equation and solve for pH.

Since the indicator changes from blue to yellow, we can assume that the ratio [In-]/[HIn] is greater than 1.

Let's assume it is 10:

pH = 5.1 + log(10)

= 5.1 + 1

= 6.1

So, the color change of the indicator will first be visible around a pH of 6.1 when titrating a solution with an acid.