Due at the start of class:

1. Last week's lab and calculations
2. This week's pre-lab (objective, procedure, & pre-lab questions)

Due at the end of class:

1. This week’s data.

Weak Acid Equilibrium

In this experiment you will determine the equilibrium constant for the dissociation of the weak organic acid bromocresol green. The structural formula for this acid is.

The acidic proton is the one attached to the SO₃ group.  Symbolizing this molecule as HB, we can write the dissociation reaction of interest:

                                                            HB + H₂O  D  H₃O⁺ + B⁻                                          (1)

The dissociation constant for this reaction is:

                                                            K_a =  [H₃O⁺][B^-] = a constant value                            (2)

                                                                          [HB]

Note that water does not show up in the equilibrium expression as its molarity is approximately constant and is included in the K_a value. 

The strategy of this experiment is to adjust [H₃O⁺] to a known value by buffering the solution and to measure the ratio [B⁻]/[HB] spectrophotometrically.  This will enable us to use Equation 2 to calculate K_a.

The Use of Absorbance to Measure [B-]/[HB]

Bromocresol green is sometimes used as an acid-base indicator because its color in solution is a function of pH.  The ionized form, B^-, absorbs light in the red end of the visible spectrum, thereby appearing blue, whereas the unionized form, HB, absorbs light more from the blue end, and hence appears yellow.  Thus, as we increase or decrease [H₃O⁺] in a solution containing bromocresol green, the equilibrium shown in equation 1 will shift back and forth and the solution will appear more yellow or blue.  One can make a fair guess at the pH of a solution containing bromocresol green by comparing its color with a set of color standards.

In this experiment you will use a spectrophotometer to get a much more accurate measurement of light absorbance than can be obtained visually.  The absorption of light by a solute is proportional to the concentration of the solute, other factors being equal.  This is certainly reasonable since doubling the concentration of solute doubles the likelihood that a photon will encounter a molecule of solute and be absorbed. 

Suppose we add a known amount of bromocresol green to some water, and divide this into two solutions.  To one of these solutions we add strong acid, forcing Reaction 1 to the left so that all the bromocresol green is in the form [HB].  To the other solution we add base, forcing Reaction 1 to the right so that all the bromocresol green is in the form [B^-].  These two solutions are of equal concentration which we shall label [total].  We now measure the absorption of light by these two solutions at some wavelength A.  Let us denote the absorbance by the acid and base forms as A_HB and A_B− respectively.

Now, suppose we adjusted the pH of one of these solutions so that half of the bromocresol green was in the HB form and half in the B^- form.  Then, since these forms will continue to absorb light in proportion to their concentrations, the absorbance should be equal to ½ A_HB + ½ A_B^-.

Similarly, for the general intermediate situation, where

                                    [HB] + [B^-] = [total],                                                   (3)

we expect the observed absorbance to be given by

                                                A_observed = A_HB   [HB]     +  A_B-      [B^-]                        (4)

                                                                          [total]                  [total]

this, can be rearranged to.

                                    [B^-]    =  (A_observed  − A_HB)                                            (5)

                                                [HB]      (A_B- -  A_observed)

Equation 5 will enable you to evaluate the ratio [B-]/[HB] at intermediate pH from three absorbance measurements: one at high pH, one at low pH, and one at the intermediate pH of interest.

The remaining point to discuss is the selection of the wavelength of light to use in measuring absorbance.  A rough sketch for the absorbance as a function of wavelength for HB and B⁻ is shown below.

Note that B⁻ tends to absorb more at the longer wavelengths, HB at the shorter.  At a particular intermediate wavelength, both absorb equally.  What would happen if we chose this intermediate wavelength for the experiment?  Since both HB and B⁻ absorb equally at this wavelength, no change in absorbance would be produced by changing the pH.  Thus, A_HB, A_B−, and A_observed would be identical and equation 5 would become indeterminate.  We are best off at a λ value where pH changes are accompanied by maximum absorbance changes, that is, where the absorbance due to one form is large and that due to the other form is small.  The points marked λ_{HB and} λ_B⁻  in the figure would obviously be satisfactory choices, with λ_B⁻ being superior since the difference is greater there.

pH Control by Buffering

As indicated earlier, you will control the pH of the solutions in this experiment by using a buffer system composed of acetic acid (HOAc) and acetate ions (OAc^-).  The equilibrium between these is

                                                H₂O + HOAc  D H₃O⁺ + OAc⁻                                 (6)

With equilibrium constant

                                                [H₃O⁺] [OAc]  = K_eq                                                   (7)

                                                [H₂O] [HOAc]

Since the concentration of water remains essentially unchanged as we vary the concentrations of the other chemicals over normal ranges, we can treat [H₂O] as a constant and write

                                                K_eq [H₂O]  =  [H₃O⁺] [OAc⁻]  =  K_a  =  1.75 x 10⁻⁵                (8)

                                                     [HOAc]

K_a is called the acid dissociation constant, or ionization constant.

The basic idea involved in buffering is as follows:  Suppose we make up a solution containing relatively large amounts of HOAc and OAc^-. The system equilibrates by producing the necessary concentration of H₃O⁺ to satisfy Equation 8.   At this point, we have an H₃O⁺ concentration governed by re-arranging equation 8 to give…..

                                                            [H₃O⁺]  =  K_a  [HOAc]       K_a = 1.75 x 10⁻⁵              (9)

                                                                                    [ OAc⁻]

When fairly small amounts of H₃O⁺ are added or removed to this buffer system, the system re-equilibrates in a way to keep the concentration of H₃O⁺ almost unchanged.   The details of how a buffer system works will be seen in the next lab experiment.  However, for the purpose of this experiment you may assume that the buffer will ensure that [H₃O⁺] is determinable and is uninfluenced by the extent of ionization of bromocresol green.  You will use equation 9 to calculate the concentration of H₃O⁺ to be used in equation 2 to solve for the bromocresol green K_a value.

EXPERIMENTAL PROCEDURE:

STUDENTS SHOULD WORK IN PAIRS. SUBMIT SEPARATE REPORTS

Solution Preparation

On the front bench you will find the following solutions: 1.000 M acetic acid (HOAc), 3.0 x 10^-4 M bromocresol green solution (BCG), 0.200 M sodium acetate solution (NaOAc), and 3 M Hydrochloric acid (HCl) containing 1.5 x 10⁻⁵ M BCG. 

When you obtain your solutions, think about how much you actually need because you won’t need very much of most of the solutions.  If you only need 1 mL of a particular solution, don’t fill up your 250 mL beaker.  You can always get more if you run out.

You will prepare a total of seven solutions by the process of successive additions.  After each step you will perform one or more spectrophotometric measurements.  The procedure is as follows:

1. Use a 25-ml pipet to introduce 25.00 mL HOAc solution to a 100-mL volumetric flask.  Use a 5-mL pipet to add 5.00 mL of BCG solution to this same flask.  Dilute to the mark with distilled water.  Mix the solution thoroughly by inverting and shaking the flask a dozen times.  Pour this solution into a clean, dry Erlenmeyer flask and label it “Solution A”.

2. Rinse out your volumetric flask several times with small amounts of distilled water. Use the 5-ml pipets to add 5.00 mL BCG solution and 5.00 mL NaOAc solution to your 100-mL volumetric flask. Dilute to the mark, mix thoroughly, and pour into a second clean Erlenmeyer. Label this as "Solution 1 ".  Solution 1 is fairly basic since it contains mainly OAc⁻ which ties up much of the H₃O⁺ present in the water. This causes bromocresol green to be almost entirely in its basic (B^-) form. Record in our notebook the color of this and all subsequently prepared solutions.

3. Carefully pour some of Solution 1 into a cuvette.  Use distilled water as a blank to calibrate the spectrophotometer.  Proceed to measure the absorbance of Solution 1 at wavelengths at 25 nm intervals from 400 nm to 600 nm and at 5 nm intervals from 600 nm to 625 nm.  Determine the wavelength of maximum absorbance (subsequently referred to as λ_B-) and record the absorbance at this wavelength.  Pour the entire sample back into the Erlenmeyer so that you still have 100 mL of Solution 1.

4. Pour Solution A into a clean, dry burette and drain out a little to fill the tip.  Now position the Erlenmeyer of Solution 1 to receive 2.00 mL of Solution A.  Mix well.  This is Solution 2.  Measure its absorbance at λ_B−.  Recover the sample in the Erlenmeyer so as to have 102.00 mL of Solution 2.  Record the color of the solution.

5. To Solution 2 add 2.00 mL of Solution A.  This is Solution 3.  Mix well and measure the absorbance at all fourteen wavelengths used for Solution 1. If λ_B- is not one of these fourteen wavelengths, make the measurement at λ_B- as well.  Recover the sample so as to have 104.00 mL of Solution 3. Record the color of the solution.

6. To Solution 3, add 2.00 mL of Solution A. This is Solution 4. Mix it well and measure its absorbance at λ_B-.  Recover the sample so as to have 106.00 mL of Solution 4. Record the color.

7. To Solution 4 add 2.00 mL of Solution A to give 108.00 mL of Solution 5. Mix well and measure the absorbance at λ_B-, retaining the sample. Record the color.

8. To 108.00 mL of Solution 5 add 2.00 mL of Solution A to give 110.00 mL of Solution 6. Mix well and measure the absorbance at λ_B-, retaining the solution. Record the color.

9. To 110.00 mL of Solution 6, add 1.00 mL of 3 M HCl containing 1.5 x 10^-5 M BCG. This is Solution 7. Mix well and measure the absorbance at all of the wavelengths used for Solutions 1 and 3. The presence of the strong acid causes this solution to contain BCG entirely in its acid form (HB). Record the color.

TREATMENT OF DATA

1. Determine the [HOAc] and [OAc⁻] for each of the five buffered solution (numbers 2-6).  In all solutions, the OAc⁻ ion that is present comes from Solution 1 and the HOAc is from successive additions of Solution A. This means that the number of moles of OAc- remains unchanged in all seven solutions, but the VOLUME changes (102 mL, 104 mL, etc.) so the concentration will decrease.  For determining the HOAc concentration in each solution, the total volume is changing as above (102 mL, 104 mL, etc.) but the amount of HOAc added is also changing (you are adding 2 mL, 4 mL, etc).   These can be treated as solution dilution problems.  

2. Calculate [H₃O⁺] for each of the five buffered solutions (numbers 2-6). You can calculate this from Equation 9, once you determine the [HOAc] and [OAc⁻] above.

3. Using the spectroscopy data, calculate the ratio of [B-]/[HB] for all five buffered solutions.

4. Calculate five values for K_a of bromocresol green.  Calculate the average Ka and also the deviation of each value from this average.  Square each deviation (to make them all positive), average the five squared deviations, and take the square root of this average.  This number is called the root-mean-square-deviation or standard deviation, and is important in the statistical treatment of multiple determinations of a single quantity.  In a large set of measurements having a normal ("bell shaped") distribution, about 90% of the measurements fall within two standard deviations of the average. [Five points is a rather small number so the standard deviation is less meaningful in this case.]

5. Graph your absorbance data vs. wavelength for Solutions 1, 3, and 7 (all on one graph).  Indicate the position of λ_B- on the graph.  In the discussion, comment on how the curve for Solution 3 compares to the curves for Solutions 1 and 7, why is this?

6. Calculate the pH of each solution 2 through 6 and include a table of your color observations at the different pH values.

Prelab Questions

1. Why does bromocresol green appear blue in basic solution and yellow in acids?

2. What is the purpose of the acetate ions and acetic acid used in this experiment?

3. Approximately what quantity of each of the following solutions will you need:

1.000 M acetic acid (HOAc)

3.0 x 10^-4 M bromocresol green solution (BCG)

0.200 M sodium acetate solution (NaOAc)

3 M Hydrochloric acid (HCl) containing 1.5 x 10⁻⁵ M BCG

Postlab Questions

1. What two properties (one chemical and one physical) combine to make bromocresol green useful as an acidity indicator?  (Hint:  contrast with HCl.)

2. What criteria are used to select a wavelength for measuring absorbances in these solutions?  Why?

3. Based on your color observations, for what pH range would bromocresol green be appropriate as an indicator? 

4. Calculate at what pH would the concentration of B⁻ and HB be equal? (not pH 7).  Can you suggest any reason for this pH lying in the pH range of question 3?

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