1. Acid-base Equilibria
1.a. Photochemical determination of dissociation constant of
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)
at pH range 3.8–5.4. The concentration of both
forms of the indicator can be determined by the photometric method.
The univalent anion of the indicator dissociates according to the chemical equation:
+−−
+⇔+ OHBOHHB 3
2
2 (1.1.)
yellow solution blue solution
The thermodynamic equilibrium constant of the dissociation to the second degree is
given by:
K
a a
a
A
H O B
HB
=
+ −
−
3
2.
(1.2.)
where ai
(𝑖𝑖 = 𝐻𝐻3 𝑂𝑂+
, 𝐵𝐵2−
, 𝐻𝐻𝐵𝐵−
) are the activities of the ions. The relationship between
thermodynamic dissociation constant KA and dissociation constant KA
'
obtained
from concentrations is:
[ ][ ]
[ ]
′ = =
+ −
−
−
+ −
K
H O B
HB
KA A
HB
H O B
3
2
3
2
.
.
γ
γ γ
(1.3.)
where γ i are the activity coefficients of the ions. After mathematical rearrangement,
we get:
[ ]
[ ]
pK pH
B
HB
A′ = −
−
−
log
2
(1.4.)
The activity coefficients of ions can be obtained by use extended Debye-Hückel law
(DHL). The activity −2
B
γ is given in aqueous solution at 25°C by expression:
( )
I
I
IrB
IzA
B
B
B
30,21
034,2
1
log
2
2
2
2
+
−=
⋅⋅+
⋅⋅
−=
−
−
−g (1.5.)
where 5085,0=A , 3281,0=B , 7,02 =−
B
r Å is effective diameter of the ion 𝐵𝐵2−
in
Ångström. The ionic strength 𝐼𝐼 is (at low concentrations) given by:
∑=
=
k
i
ii zcI
1
2
2
1
(1.6.)
where iz are charge numbers of all ions i in the solution, ic are their molarities.
The activity coefficients +
OH3
γ and γ HB− are equal according DHL thus relationship
between constants KA and KA
'
can be simplified to:
K KA A B
= −
'
γ 2 ie: 𝑝𝑝𝐾𝐾 𝐴𝐴
= 𝑝𝑝𝐾𝐾𝐴𝐴́ − 𝑙𝑙𝑙𝑙𝑙𝑙 � −2
B
γ � (1.7.)

and together with eqn (1.5.) it gives:
pK pK
I
I
A A= +
+
' ,
,
2 04
1 2 3
(1.8.)
The thermodynamic equilibrium constant of the dissociation 𝐾𝐾𝐴𝐴 can be calculated
using eqn (1.8.) or it can be graphically evaluated more precisely from an experiment
at different ionic strength.
TASK: Evaluate thermodynamic equilibrium constant of dissociation 𝐾𝐾𝐴𝐴 of
bromocresol green to the second degree at ionic strength 0,1M.
LABORATORY AIDS AND CHEMICALS: UV/VIS spectrophotometer (minimum range
350-720 nm), 2 cuvettes, 2 volumetric flasks (50ml), 1 volumetric flask (250ml),
3 volumetric pipettes (1, 5, 25ml), 1 scale pipette (10ml), 1,5.10-4
M stock solution of
bromocresol green (CAS No: 76-60-8), 0,2M CH3
COONa, 1M CH3
COOH, 1M KCl,
and 3M HCl.
INSTRUCTIONS:
Preparation of solutions I and II. Prepare 50 ml (use flask of same volume) of
solution I of concentration 1,510-5
M bromocresol green (BG) inside 0,01 M
CH3
COONa at ionic strength I=0,1M from stock solutions. Set the ionic strength to
the desired value with a pre-calculated volume of 1M KCl. Prepare 50 ml of solution II
of concentration 1,510-5
M bromocresol green (BG) inside 0,01 M CH3
COONa at
ionic strength I=0,1M from stock solutions.
Measuring spectra of indicator at different pH. Pour whole solution I into larger
flask (250 ml). 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 FIGURE 1). Return the content of
the cuvette to the flask with the original
solution I. Add 1 ml of solution II to the
flask and mix. The pH of solution is
changed. Repeat sampling, spectrum
measurement, sample return and
addition of 1 ml of solution II. Repeat
this procedure 6 times. The last
addition is done with 1ml of 3M HCl.
The solution containing the equimolar
ratio CH3COONa and CH3COOH is
green in color and has two maximas
(see FIGURE 1).
DATA ANALYSIS: The ratio of the
concentrations of the basic and acid forms of the indicator is equal to the
absorbance ratio at the adsorption maximum (compare FIGURE 1):
[ ]
[ ]
B
HB
A A
A A
i
i
2
1
2
−
−
=
−
−
(1.9.)
?


FIGURE 1: Evaluation of spectra of acid-base
indicator of bromocresol green obtained at
different pH.

where 𝐴𝐴2 is absorbance of 𝐵𝐵2−
anion if the anion 𝐻𝐻𝐵𝐵−
is not present (ie in a far basic
environment). 𝐴𝐴1 is absorbance of 𝐻𝐻𝐵𝐵−
anion if the anion 𝐵𝐵2−
is not present (ie in a
far acidic environment), 𝐴𝐴𝑖𝑖 is absorbance of 𝐵𝐵2−
anion at a general pH when both
anions 𝐵𝐵2−
, 𝐻𝐻𝐵𝐵−
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 conjugated acid-base buffer. The pH is given by Henderson-Hasselbalch eqn:
𝑝𝑝𝑝𝑝 = 𝑝𝑝𝑝𝑝 𝐻𝐻𝐻𝐻𝐻𝐻
+ 𝑙𝑙𝑙𝑙 𝑙𝑙
𝑐𝑐 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
𝑐𝑐 𝐻𝐻𝐻𝐻𝐻𝐻
(1.10.)
where 𝑝𝑝𝑝𝑝 𝐻𝐻𝐻𝐻𝐻𝐻
= 4,76 is the negative logarithm of the dissociation constant of acetic
acid. 𝑐𝑐 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
and 𝑐𝑐 𝐻𝐻𝐻𝐻𝐻𝐻
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. The detailed calculation of the ionic strength. Common graph 1:
UV/VIS spectra for all sample solutions. Next: wavelength of absorption maxima of
𝐵𝐵2−
and 𝐻𝐻𝐵𝐵−
, value A2 and A1 (FIGURE 1). Table 2: for each sampling: addition of
solution II, experimental absorbance 𝐴𝐴𝑖𝑖, calculated ratio (𝐴𝐴𝑖𝑖 − 𝐴𝐴1) (𝐴𝐴2 − 𝐴𝐴𝑖𝑖)⁄ (use eqn
(1.9.)), log[(𝐴𝐴𝑖𝑖 − 𝐴𝐴1) (𝐴𝐴2 − 𝐴𝐴𝑖𝑖)⁄ ], 𝑐𝑐 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁
and 𝑐𝑐 𝐻𝐻𝐻𝐻𝐻𝐻
, pH value calculated using eqn
(1.10.) and 𝑝𝑝𝑝𝑝 𝐻𝐻𝐻𝐻𝐻𝐻
from literature. pKA
'
(eqn (1.4.)), pKA (eqn (1.8.)). Next: The
mean value pKA and its confidence interval according to the Student's t-distribution.
