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Equilibrium with an Acid-Base Indicator

An indicator is a weak acid which has one color when it is protonated and another color when it is deprotonated. The generalized formula, HIn, is used to represent an **In**dicator because the structures of indicators tend to be large organic molecules. For example, bromothymol blue has the structure shown below. On the left in the form it takes on in a solution with a pH below 6.8, which is yellow, and on the right the form it takes on in a solution with a pH above 6.8, which is blue.

The yellow form of bromothymol blue, which has a proton bound to the oxygen atom at upper-right. | The blue form of bromothymol blue, which has lost the proton from the oxygen atom now bound with a double-bond to the neighboring carbon atom. |

Indicators are usually used in very small amounts in solutions in which the pH is determined by other species in solution. For example, in the titration of a strong acid by a strong base bromothymol blue is used to indicate the end point. The equivalence point is the point at which the amount of base added exactly equals the amount of acid being titrated. For example, consider a titration of hydrochloric acid (HCl) with sodium hydroxide (NaOH). The reaction is: NaOH + HCl → H_{2}O + NaCl. If there is 0.010 mol of HCl in the solution being titrated then equivalence is reached when exactly 0.010 mol of NaOH has been added because there is a one-to-one molar ratio between these two species.

The end point of a titration, by contrast, is the moment when a color change is observed in the solution. This is arranged in advance by the experimenter to occur near the equivalence point. The color change occurs because of a sharp jump in the pH from the moment before a molar equivalent amount of base is added to the moment when just slightly more base than a molar equivalent has been added.

The color-change range of an indicator spans about 2 pH units. This has to do with the ratio of the concentration of the protononated form (HIn) to the concentration of the de-protonated form (In^{–}). If the concentration of HIn is ten or more times greater than the concentration of In^{–} then the color of HIn dominates. If the concentrations of HIn and In^{–} are close to being the same, that is, close to having a one-to-one In^{–}/HIn ratio, then the color observed is a mixture of the two forms’ colors. If the concentration of In^{–}HIn is ten or more times greater than the concentration of HIn then the color of In^{–} dominates.

Figuring out which form is in the majority is made simple by the use of the Henderson-Hasselbalch equation:

pH = pK_{a} + log([A^{–}]/[HA])

The pH in the solution in a titration is determined completely by the composition of the solution and is not really affected by the small amount of indicator present. In this equation the value of the pH can be substituted in and the ratio [A

Your teacher will demonstrate a titration. In the following questions you will be guided through the process of discovering how an indicator, which has a color-change range of 2 pH units, can give a titration end point that correctly identifies the equivalence point. You will need a calculator and a piece of graph paper.

- What is the ratio [In
^{–}]/[HIn] for bromothymol blue- …in a solution with a pH of 7.8? What color does the solution appear?
- …in a solution with a pH of 5.8? What color does the solution appear?

- Consider a titration of 10.00 mL of 0.10 M HCl by 0.10 M NaOH.
- What is the pH of the solution before any NaOH is added?
- What volume of NaOH solution will be needed to reach molar equivalence?

- Consider what happens when exactly 1.00 mL of 0.10 M NaOH solution is added to the 10.00 mL of 0.10 M HCl solution.
- What is the new volume of the solution?
- What happens chemically?
- Use stoichiometry to determine the new concentration of H
^{+}ions in solution. What is the pH?

- Consider what happens when exactly 5.00 mL of 0.10 M NaOH solution is added to the 10.00 mL of 0.10 M HCl solution.
- What is the new volume of the solution?
- What happens chemically?
- Use stoichiometry to determine the new concentration of H
^{+}ions in solution. What is the pH?

- Calculate [H
^{+}] and pH for the following volumes of added 0.10 M NaOH solution. Plot all values of pH on a the y-axis of a graph against the x-axis values of the volume of NaOH solution added.

- 9.0 mL of added 0.10 M NaOH solution
- 9.5 mL of added 0.10 M NaOH solution
- 9.9 mL of added 0.10 M NaOH solution
- 10.0 mL of added 0.10 M NaOH solution
- 10.1 mL of added 0.10 M NaOH solution

- 10.5 mL of added 0.10 M NaOH solution
- 11.0 mL of added 0.10 M NaOH solution
- 15.0 mL of added 0.10 M NaOH solution
- 19.0 mL of added 0.10 M NaOH solution
- 20.0 mL of added 0.10 M NaOH solution

- Calculate the ratio [In
^{–}]/[HIn] at each of the pH values you found in your calculations from the previous questions. Also, give the color of bromothymol blue that would be observed.- 0.00 mL of added 0.10 M NaOH solution
- 1.0 mL of added 0.10 M NaOH solution
- 5.0 mL of added 0.10 M NaOH solution
- 9.0 mL of added 0.10 M NaOH solution
- 9.5 mL of added 0.10 M NaOH solution
- 9.9 mL of added 0.10 M NaOH solution
- 10.0 mL of added 0.10 M NaOH solution

- 10.1 mL of added 0.10 M NaOH solution
- 10.5 mL of added 0.10 M NaOH solution
- 11.0 mL of added 0.10 M NaOH solution
- 15.0 mL of added 0.10 M NaOH solution
- 19.0 mL of added 0.10 M NaOH solution
- 20.0 mL of added 0.10 M NaOH solution

- Consider the results of your calculations and your plot of Vol. of NaOH solution vs. pH as you answer the following questions:
- What is the pH at equivalence in this titration? Remember that at equivalence there is no more remaining HCl in solution because exactly enough NaOH has been added.
- How much does the pH change from when 9.9 mL of NaOH solution were added to when 10.1 mL had been added?
- What color was the solution when 9.9 mL of NaOH solution had been added? What color was it after 10.1 mL?

- Why is bromothymol blue a good choice as an indicator for the endpoint of this titration? Does the color change correspond to the equivalence point? Justify your answer.