Final answer:
When several drops of Eriochrome Black T are added to a 28.0 mL sample of 0.130 mol/L NaOH, the solution will turn blue, indicating a basic environment.
Step-by-step explanation:
The solution will appear blue, because the NaOH will create a basic environment.
Eriochrome Black T is an acid-base indicator with a pKa of 6.2. Given that the sample is a 0.130 mol/L NaOH solution, this will result in a basic environment. When NaOH (a strong base) is dissolved in water, it disassociates completely, increasing the pH of the solution significantly. Since the pH of a 0.130 mol/L NaOH solution is well above 7, it is safe to assume that the pH will be higher than the pKa of Eriochrome Black T.
Therefore, adding a few drops of Eriochrome Black T to this alkaline solution would result in the indicator showing its basic form color, which is blue. Indicators, like Eriochrome Black T, change color depending on whether they are in their acid form or base form. This color change occurs around the value of their pKa, which indicates the pH at which there is an equal concentration of the acid and base forms of the indicator.