1.a. Spectrophotometric determination of the dissociation
constant of an acid-base indicator
The 3′,3′′,5′,5′′-Tetrabromo-m-cresolsulfonephthalein (bromocresol green) acidbase
indicator behaves as a reversible system whose acidic form (yellow, HB-)
changes into a basic form (blue, B2-) over the pH range 3.8–5.4. The concentration of
both forms of the indicator can be determined using photometry.
The univalent anion of the indicator dissociates according to the chemical equation:
𝐵−
+ 𝐻2 𝑂  𝐵2−
+ 𝐻3 𝑂+
(1.)
yellow solution blue solution
The thermodynamic equilibrium constant of dissociation to the second degree is given
by:
𝐾𝐴 =
𝑎 𝐻3 𝑂+ 𝑎 𝐵2−
𝑎 𝐻𝐵−
(2.)
where ai (𝑖 = 𝐻3 𝑂+
, 𝐵2−
, 𝐻𝐵−
) are the activities of the ions. The relationship between
the true thermodynamic dissociation constant 𝐾𝐴 and the approximate dissociation
constant is:
𝐾𝐴

=
[𝐻3 𝑂+] [𝐵2−]
[𝐻𝐵−]
= 𝐾𝐴
 𝐻𝐵−
 𝐻3 𝑂+  𝐵2−
(3.)
where are the activity coefficients of the ions. After mathematical rearrangement,
we get:
𝐾𝐴

= 𝑝𝐻 − 𝑙𝑜𝑔
[𝐵2−]
[𝐻𝐵−]
(4.)
The ionic activity coefficients can be obtained from the extended Debye-Hückel law
(DHL). The activity  𝐵2− is given in aqueous solution at 25°C as the following:
𝑙𝑜𝑔(  𝐵2− ) = −
𝐴 (𝑧 𝐵2−)
2
√ 𝐼
1+𝐵 (𝑟 𝐵2−) √ 𝐼
= −
2.034 √ 𝐼
1+2.30 √ 𝐼
(5.)
Where 𝐴 = 0.5085, 𝐵 = 0.3281, and 𝑟 𝐵2− = 0.7Å Å, which is the effective diameter of
the ion 𝐵2−
in Ångström. The ionic strength I (at low concentrations) is given by:
(6.)
where are charge numbers of all ions 𝑖 in the solution, and are their molarities.
The activity coefficients and are equal according to the DHL; thus, the
relationship between constants and can be simplified to:
ie: 𝑝𝐾 𝐴
= 𝑝𝐾𝐴

− 𝑙𝑜𝑔 ( ) (7.)
and together with eqn (5.), results in the following:
𝑝𝐾 𝐴
= 𝑝𝐾𝐴
 2.034 √ 𝐼
1+2.30 √ 𝐼
(8.)
The thermodynamic equilibrium dissociation constant 𝐾𝐴 can be calculated using eqn
(8.) or it can be more precisely graphically evaluated from an experiment at different
ionic strengths.
KA
'
 i


k
i
ii zcI
1
2
2
1
iz ic

OH3
  HB
KA KA
'
K KA A B
 
'
 2 2
B


TASK: Evaluate the thermodynamic equilibrium dissociation constant 𝐾𝐴 of
bromocresol green to the second degree at 0.1M ionic strength.
LABORATORY AIDS AND CHEMICALS: UV/VIS spectrophotometer (minimum range
350-720 nm), 2 cuvettes, 2 volumetric flasks (50 cm3), 1 volumetric flask
(250 cm3), 3 volumetric pipettes (1, 5, 25 cm3), 1 scale pipette (10 cm3), 1.5  10-4M stock
solution of bromocresol green (CAS No: 76-60-8), 0.2M CH3COONa, 1M CH3COOH,
1M KCl, and 3M HCl.
INSTRUCTIONS:
Preparation of solutions I and II. Using a 50 cm3 flask, prepare 50 cm3 of solution I:
1.5  10-5 M bromocresol green (BG) inside 0.01 M CH3COONa at ionic strength I=0.1M
using stock solutions. Set the ionic strength to the desired value with a pre-calculated
volume of 1M KCl. Similarly, prepare 50 cm3 of solution II: 1.5  10-5 M bromocresol
green (BG) inside 0.25 M CH3COOH at ionic strength I=0.1M using KCl stock solution.
Measuring spectra of indicator at different pH. Pour all of solution I into a larger
flask (250 cm3). Take a sample of solution I, place it in a quartz cuvette and measure
the entire UV / Vis spectrum. Determine the wavelength at which the solution has a
maximum absorbance A2 (see FIG. 1). Return the content of the cuvette to the flask
with the original solution I. Add 1 cm3 of solution II to the flask and mix. The pH of the
solution is changed. Repeat sampling, spectrum measurement, sample return and
addition of 1 cm3 of solution II a total of 6 times. For the last addition, use 1 cm3 of 3M
HCl.
The solution containing an equimolar ratio of CH3COONa and CH3COOH is green in colour
and has two maxima (see FIG. 1).
DATA ANALYSIS: The ratio of the concentrations of the basic and acidic forms of
the indicator is equal to the absorbance ratio at the adsorption maximum
(compare FIG. 1):
(9.)
where 𝐴2 is the absorbance of the 𝐵2−
anion if the 𝐻𝐵−
anion is not present (i.e.,
in a very basic environment). 𝐴1 is the
absorbance of the 𝐻𝐵−
anion if the
𝐵2−
anion is not present (i.e., in a very
acidic environment). 𝐴 𝑖 is the
absorbance of the 𝐵2−
anion at a general
pH when both anions 𝐵2−
and
𝐻𝐵−
coexist in the solution.
The pH of the solutions to be monitored
is determined by the concentration of the
majority of the solution components,
which are acetic acid and sodium
acetate. They form a conjugated acidbase
buffer. The pH is given by the
Henderson-Hasselbalch eqn:
 
 
B
HB
A A
A A
i
i
2
1
2





?


FIG. 1: Evaluation of spectra of acid-base
indicator of bromocresol green obtained at
different pH.

𝑝𝐻 = 𝑝𝐾 𝐻𝐴𝑐
+ 𝑙𝑜𝑔
𝑐 𝑁𝑎𝐴𝑐
𝑐 𝐻𝐴𝑐 (10.)
where 𝑝𝐾 𝐻𝐴𝑐
= 4.76 is the negative logarithm of the dissociation constant of acetic
acid. 𝑐 𝑁𝑎𝐴𝑐
and 𝑐 𝐻𝐴𝑐
are analytical concentrations of sodium acetate and acetic acid.
REPORT: TABLE 1: The volumes of the stock solutions used to prepare solutions
I and II. A detailed calculation of the ionic strength. Common graph 1: UV/Vis
spectra for all sample solutions. Also include: wavelength of absorption maxima of
𝐵2−
and 𝐻𝐵−
, values A2 and A1 (FIG. 1). Table 2: for each sampling: addition of solution
II, experimental absorbance 𝐴𝑖, calculated ratio (𝐴𝑖 − 𝐴1) (𝐴2 − 𝐴𝑖)⁄ (use eqn (9.)),
log[(𝐴𝑖 − 𝐴1) (𝐴2 − 𝐴𝑖)⁄ ], 𝑐 𝑁𝑎𝐴𝑐
and 𝑐 𝐻𝐴𝑐
, pH value calculated using eqn (10.) and
𝑝𝐾 𝐻𝐴𝑐
from literature. (eqn (4.)), (eqn (8.)). Also include: The mean value
and its confidence interval according to the Student's t-distribution.
pKA
'
pKA
pKA
