Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Keywords: Equilibrium Constant, pH, indicator, spectroscopy
Objectives:
Prepare all solutions for measurement of the equilibrium constant for
bromothymol blue
Make a series of spectroscopic measurements on the solutions and from this data,
determine the equilibrium constant for bromothymol blue.
Bromothymol blue is a chemical indicator used to detect weak acids and bases. It works
as an indicator by displaying a change in color from the protonated form (HBB) to the
non-protonated form (BB-). This is illustrated below in the pH dependent equilibrium
between the two forms.
HO
O
OH
Br
Br
+
H2O
OH
Br
Br
+
H3O
+
O
S
O
SO 3
O
-
Figure One: Equilibrium of bromothymol blue (yellow and blue forms)
Obviously, this equilibrium is pH dependent and under acidic conditions, the
bromothymol blue will be protonated and as a result, the solution will be yellow. Under
basic conditions, the deprotonated form results in a blue solution. But these are the two
extreme cases and it is found that between pH 6 to 8, the solution appears green, a color
resulting from the presence of both protonated and deprotonated forms of bromothymol
blue. Towards pH 6, the solution is a more greenish yellow while towards pH 8, the
solution is more of a bluish green.
Hence the color of the solution can be used as a visual guide to the relative amounts of
protonated and deprotonated forms of bromothymol blue. The absorbance spectra of each
of these are thus shown below:
Bromothymol Blue- 1
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Figure Two: Absorbance Spectra of Bromothymol Blue (yellow and blue forms)
The blue form, BB-, has an absorbance maximum at about 616 nm. The yellow form,
HBB, has its maximum absorbance at 432 nm. In this experiment, we will measure the
absorbance of the yellow form at 453 nm, where the absorbance is still strong and the
absorbance of the blue BB- is minimal (as can be seen in the spectra in Figure Two at 432
nm, BB- also absorbs).
In this experiment, we will consider the equilibrium between the two forms
HBB (yellow) H2O
⇋ H3O+ + BB-(blue)
(1)
The equilibrium expression, Kc, for the HBB/BB- equilibrium (Eq. 1) is:
Kc
[ H 3O ][ BB ]
[ HBB ]
(2)
The value of Kc should be independent of all factors except a change in temperature. At
high pH, the concentration of the blue form, [BB-], is large and [HBB] is small, and at
low pH, [HBB] is large and [BB-] is small. In this experiment, you will be working with
a solution that is green in color, so that neither [HBB] nor [BB-] is much larger than the
other.
Bromothymol Blue- 2
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Both the yellow and blue forms of bromothymol blue have Beer’s law expressions that
relate absorbance (A) to concentration ([ ], in molarity) at their respective wavelengths:
A453nm
For the yellow form, HBB:
yellow
453nm
b [ HBB ]
(3)
and for the blue form, BB-:
A616 nm
blue
616 nm
b [ BB ]
(4)
where ε is the molar absorptivity (L mol-1cm-1) and b is the pathlength in cm.
Solving Equations 3 and 4 for [HBB] and [BB-], respectively, gives:
A453nm
[ HBB]
yellow
453nm
(5)
b
A616nm
[ BB ]
blue
616nm
(6)
b
These two equalities can be substituted into the Kc expression (Eq. 2) and the b’s cancel:
[ H 3O ]
Kc
A616nm
blue
616 nm
A453nm
yellow
453nm
b
[ H 3O ] A616nm
A453nm
yellow
453nm
blue
616 nm
(7)
b
Note that it is not necessary to know the concentrations of [HBB] or [BB-] in the green
solution, only the ratio A616 nm/A453 nm.
There are five values from Eq. 7 that you must obtain to determine Kc for bromothymol
blue. These are summarized in Table 1. You will determine three of these values for a
solution that is green in color, meaning that both yellow HBB and blue BB- are present in
reasonable quantities (not almost zero as would be the case in either the blue or yellow
solutions at high and low pH values, respectively).
Bromothymol Blue- 3
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Table 1: Quantities measured for the determination of Kc
Quantity
How we measure it:
[H 3O ]
Use a pH meter to determine
the pH of the green solution
green
A616nm
Determine the absorbance of
the green solution at 616 nm
yellow
453 nm
Discussed below
green
A453nm
Determine the absorbance of
the green solution at 453 nm
blue
616 nm
Discussed below
The Kc expression given above (Eq. 7) is now re-written with “green” labels indicating
that you will determine absorbance values at two wavelengths for the green form of your
bromothymol blue solution:
Kc
The value for
yellow
453 nm
green
[ H 3O ] A616
nm
green
A453
nm
yellow
453 nm
blue
616 nm
(8)
will be determined when the solution is completely yellow (low pH;
blue
~100% HBB and negligible BB-) and the value for 616
nm will be determined when the
solution is completely blue (high pH; ~100% BB ). This is because we need to relate the ε
values to concentration via the Beer’s law equation (A = ε x b x M) and unless the
equilibrium is shifted almost 100% one way or the other, we will not know the
concentration exactly.
The experiment is designed so that we will prepare three solutions, each with the
identical concentration of bromothymol blue. We will measure out equivalent amounts of
bromothymol blue solution into three beakers. Into one beaker you will add an exact
volume of an acid, HCl(aq); into another, you will add the same volume of a base,
NaOH(aq); into the third solution, you will add the same volume of a buffer solution with
a pH of approximately 6.5. The first solution will be yellow, the second solution will be
blue and the third solution will be green. All three solutions will therefore have the
same total concentration of bromothymol blue [either as HBB (yellow solution), BB(blue solution), or a combination of HBB and BB- (green solution)].
Bromothymol Blue- 4
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
The absorbance at 453 nm of the yellow solution is due entirely to the “yellow” form
(HBB); while the absorbance at 616 nm is due entirely to the “blue” form (BB-). We can
write a Beer’s law expression for the absorbance of each solution at each wavelength:
yellow
A453
nm
blue
A616
nm
yellow
453 nm
b [ HBB ( yellow)]
blue
616 nm
b [ BB (blue)]
(9)
(10)
Since we have designed the experiment such that all HBB and BB- originates from the
same source, the concentration of bromothymol blue in the yellow solution equals the
concentration of bromothymol blue in the blue solution:
[ HBB ( yellow)] [ BB (blue)]
(11)
which, upon substitution of Eq. 9 and 10 into Eq. 11, gives:
yellow
A453
nm
yellow
453nm
blue
A616
nm
blue
616 nm
b
b
(12)
The b values cancel and Eq. 12 is rearranged:
yellow
A453
nm
yellow
453nm
blue
616 nm
(13)
blue
A616
nm
yellow
The labels “yellow” and “blue” on A453nm and A616nm denote that these are the
absorbance values of the yellow and blue solutions, at their respective wavelengths. The
above ratio of ε values can be substituted into the Kc expression (Eq. 8):
Kc
green
[ H 3O ] A616
nm
green
A453
nm
yellow
453 nm
blue
616 nm
blue
green
yellow
[ H 3O ] A616
A453
nm
nm
green
blue
A453
A616
nm
nm
(14)
From Eq. 14, you should see how we can determine Kc from only absorbance values and
the [H3O+], obtained from a pH measurement on the green solution.
Bromothymol Blue- 5
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Experimental
Prepare a buffer solution by dissolving approximately 0.4 g of sodium phosphate
monobasic, NaH2PO4 and 0.8 g of sodium phosphate dibasic, Na2HPO4 in approximately
50 mL water. Stir to completely dissolve both salts. (Note: a buffer is a solution which
can maintain a constant pH unless significant amounts of acid or base are added)
Add 20 drops of bromothymol blue indicator to the buffer solution and stir to mix the
indicator uniformly through the solution. The solution should appear green in color.
If the solution is green, you can skip this step. If the solution is blue, add 1 M HCl(aq), a
drop at a time, with thorough mixing, until you obtain a shade of green. If the solution is
yellow, add 1 M NaOH (aq), a drop at a time, again with thorough mixing, until you
obtain a shade of green. Determine the pH of buffer solution. the buffer solution using a
calibrated pH meter. Record the pH and temperature of this solution.
Use a volumetric pipet to transfer 10.00 mL of the green, buffered solution to each of
three clean and dry 100 mL beakers.
Using a 2.00 mL volumetric pipet, transfer 2.00 mL of 1.0 M HCl into one of the three
beakers. The solution should turn yellow. This solution will be referred to as “Yellow.”
Clean and rinse the 2.00 mL volumetric pipet and then use it to transfer 2.00 mL of 1.0 M
NaOH into one of other beakers. The green solution should turn blue. This solution will
be referred to as “Blue.”
Clean and rinse the 2.00 mL volumetric pipet and then use it to transfer 2.00 mL of
distilled water into the remaining beaker. The green solution should remain green. This
solution will be referred to as “Green.”
Note: Even though you prepared your solutions in beakers rather than volumetric flasks,
they all contain the same final volume of solution (12.00 mL) and the same number of
total moles of bromothymol blue (delivered with the 10.00 mL pipet). This gives an
equivalent total concentration of bromothymol blue in each beaker.
On the Ocean Optics spectrometer, measure the spectra for the green, yellow and blue
solutions and save copies of the spectra – you will replot these in Excel and use them to
extract the data needed to determine the equilibrium constant.
Safety / Waste Disposal
The materials used in this reaction should be collected in the waste container in the hood
at the end of the experiment.
Bromothymol Blue- 6
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Data Analysis
You should now have all of the measurements you need to calculate the equilibrium
constant for bromothymol blue. Equations 1, 2 and 14 are rewritten below.
H2O+ + BB-(blue)
HBB(yellow) + H2O
Kc
green
[H3O ]A616nm
green
A453nm
Kc
[H 3O ][BB (blue)]
[HBB(yellow)]
yellow
A453nm
blue
A616nm
You could simply plug values from the table into the Kc expression, however a more
accurate result is obtained by subtracting the small absorbance of yellow HBB at λ = 616
nm (where blue BB- absorbs) from absorbance of the green solution, and similarly
subtracting the small absorbance of blue BB- at λ = 453 nm (where yellow HBB absorbs)
from the absorbance value of the green solution. One can see these small absorbances in
Figure 2. At 616 nm, the absorbance of the yellow solution is small and could probably
be ignored. However, when a measurement is made at 453 nm, one can see that the blue
solution also has an absorbance. Because Beer’s law is additive, Atotal = A1 + A2 + . . .
+ An, we can modify the original equilibrium expression (Eq. 14):
Kc
green
[H3O ]A616nm
green
A453nm
yellow
A453nm
blue
A616nm
by subtracting the small absorbance of blue at λ = 453 nm, and subtracting the small
absorbance of yellow at λ = 616 nm from the “green” solution (where both yellow and
blue are present) absorbance data:
Kc
green
[ H 3O ]( A616
nm
green
( A453
nm
yellow
yellow
A616
nm ) ( A453nm )
blue
blue
A453
nm ) ( A616nm )
Perform the calculation of Kc in your laboratory notebook and report your pKc value
(remember pKc = -logKc) to two decimal places.
Bromothymol Blue- 7
(15)
Chem(bio) Week 2: Determining the Equilibrium Constant of Bromothymol Blue
Grading of Experiment
I’m not really wanting to throw a full blown report at you for this as this is very much a
collect and analyze data style experiment and so as a result, 50 points will be awarded for
handing in an overlay spectrum with your blue and green and yellow spectra plotted on a
single graph and with the calculations to get K shown below. I’ll also have a post-lab
quiz for this one – will open at end of lab and you will have a few days, I’ll have exact
timing in lab.
Wiki Component
Theoretically, the equilibrium constant determined by every group should be the same.
Right? Well let’s find out how much variation there is? There will be a table on the wiki
for you to enter your data on (there will be a slight temperature variation, something you
will learn more about later in the semester so you should include the temperature in your
data.
Reference:
The Equilibrium Constant for Bromothymol Blue: A General Chemistry Laboratory
Experiment Using Spectroscopy.
Elsbeth Klotz, Robert Doyle, Erin Gross, and Bruce Mattson, Journal of Chemical
Education 2011 88 (5), 637-639.
Bromothymol Blue- 8