EXPT. 5 DETERMINATION OF pKa OF AN INDICATOR USING SPECTROPHOTOMETRY
Determination of pKa of an Indicator Using Spectrophotometry
Structure 5.1
Introduction Objectives
5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9
5.1
Principle Spectrophotometri c Determination Determi nation of pKa Value of Indicator Requirements Solutions Provided Procedure Observations and Calculations Calc ulations Result Precautions
INTRODUCTION
You have so far learnt about and performed the quantitative determination of inorganic and organic species using UV-VIS spectrophotometry in this laboratory course. In this experiment you would learn about an application of spectrophotometry in the determination of a physical constant for an organic compound. You would learn about and carry out the determination of the pK a of an acid-base indicator. You know that an indicator is used for the visual detection of the end point of a titration. The indicator used in acid-base titrations is either a weak acid or weak base which has distinctly different colours in the ionised and unionised form. The end point in an acid-base titration is indicated by a sharp change in the colour of the indicator due to a steep change in the pH of the solution near the equivalence point of the titration. Spectrophotometry can be used to determine the concentrations of the ionised (basic) and unionised (acidic) forms of the indicator which in turn is used for the determination of the acid dissociation constant using Henderson-Hasselbach equation. In the next experiment you would learn about the application of IR spectrometry in the detection of the functional group in an organic compound.
Objectives After studying and performing this experiment you should be able to: •
pK a of explain the principle underlying the spectrophotometric determination of pK an acid-base indicator,
•
state and explain Henderson-Hasselbach equation,
•
prepare a series of buffer solutions and measure the absorbance of the indicator solution as a function of pH,
•
compute the relative concentrations of the ionised and unionised forms of the indicator by simultaneous equation method and determine the pK a value of the indicator using Henderson-Hasselbach equation, and
•
determine graphically, the pK a of an acid-base indicator using the pH versus absorbance data.
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SpectroscopicMethods Lab.
HO O
Methyl red
N N
N
2-(4-dimethylaminophenylazo)benzoic acid
5.2
PRINCIPLE
As mentioned in the introduction, an acid-base indicator is either a weak acid or a weak base that has distinctly different colours in the ionised and unionised forms. One form of an indicator may be colourless but the other must be distinctly coloured. Let us take the example of the indicator methyl red. It is a two colour indicator; red in its unionised (acidic) and yellow in its ionised (basic) form. Methyl red is a weak organic organic acid which can be used as an indicator in the pH range of 4.4 to 6.2. This implies that a solution of methyl red will be red if the pH is lower than 4.8 and yellow if it is above 6.2. On the other hand, if the pH of the solution is in this range (4.4< pH > 6.2), the colour will be an appropriate mixture of both the colours. Methyl red is a weak acid and can be represented as say, HMR. The dissociation of the indicator can be expressed as given below. +
HMR Unionised
H
+
MR Ionised
MR represents the ionised or the basic form of the indicator. The acid form (HMR) of the indicator is zwitterionic in nature and is a resonance hybrid of two closely related structures; the basic form on the other hand is an anionic species. The structures of the acidic and basic forms and the equilibrium between them are as given below. O
O O N
O + N
N
N
H
N
H
Acid form (RED)
+ H
+ N
OH
O O N N
N
Base form (YELLOW)
You have learnt earlier that Henderson – Hasselbach equation provides the relationship between pH and p K a value of an indicator. For methyl red we can write the Henderson – Hasselbach equation as given below. −
pH
=
pK a
+
log
[MR ] [ HMR]
… (5.1)
It can be rearranged as following, −
pK a
=
pH − log
[MR ] [ HMR ]
… (5.2)
−
or
2
log
[ MR ] [ HMR ]
=
pH − pK a
… (5.3)
Thus, if we know the concentrations of the ionised and unionised forms of the indicator at a given pH, we can determine the p K a value of the indicator. As bot h, the ionised as well as the unionised forms of methyl red are coloured, their concentrations can be determined by measuring the absorbances at the wavelengths of maximum absorption of the two forms with the help of a spectrophotometer or a colorimeter. These can then be used to compute the pK a value of methyl red using Henderson-Hasselbach equation. This forms the basis of the spectrophotometric determination of the p K a value of the indicator.
5.3
SPECTROPHOTOMETRIC DETERMINATION OF pKa VALUE OF INDICATOR
A typical spectrophotometric determination of the pK a value of the indicator consists of the following steps.
Determination of pKa of an Indicator Using Spectrophotometry
It may be noted that the ionised form has small absorption at the wavelength of maximum absorption of the unionised form. Similarly, the unionised form also absorbs to some extent at the wavelength of maximum absorption of the ionised form.
Step 1: Obtaining the absorption spectra of the pure unionised unionised and ionised forms forms of the indicator to determine the wavelengths of their maximum absorption and the corresponding molar a bsorption coefficients A solution of a known concentration of the indicator is prepared in acidic solution (low pH) such that the indicator exists almost exclusively in the unionised form and the spectrum is obtained. Similarly, a spectrum is obtained for a solution of a known concentration of the indicator in a basic solution (high pH) such that the indicator exists almost exclusivel exclusivel y in the ionised ionised form. The schematic schematic spectra of the unionised and the ionised forms of the indicator are given in Fig. 5.1.
Fig. 5.1: Schematic spectra of of ionised (basic) form (blue curve) and unionised unionised (acidic) form (black curve) of methyl red indicator
These spectra are then analysed to determine the wavelengths of maximum absorption respectively for the unionised and ionised forms of the indicator. Let these be represented as λmax,HMR , and λmax, MR respectively. For convenience convenience let us us simplify the −
expressions as
λHMR
and λMR ; the subscript max and the charge on the ionised form
being dropped. The molar absorption coefficients of the unionised and ionised forms at the two wavelengths of maximum absorption obtained above are determined using BeerLambert’s law. You know that the expression for the Beer-Lambert’s law can be written as follows.
3
SpectroscopicMethods Lab.
A = ε bc
… (5.4)
In the expression, A is the absorbance, is the molar absorption coefficient, b is the thickness or the path length (in cm) of the sample and c is the concentration of the absorbing species in moles per litre. For a unit path length at a given concentration the molar absorption coefficient can be written as given below. ε =
A
… (5.5)
c
The four molar absorption coefficients for the unionised and ionised forms of the indicator at the two wavelengths, λ HMR and λ MR can be defined as follows.
ε
MR , λMR
ε
ε
ε
AMR, λ
=
MR , λ HMR
HMR , λ MR
MR
… (5.6)
c =
=
HMR , λ HMR
AMR,λ
HMR
c AHMR, λ
=
MR
c AHMR, λ
HMR
c
… (5.7)
… (5.8)
… (5.9)
These are determined by using the absorption values at the wavelengths of maximum absorption of the unionised and ionised forms in the spectra obtained above. Step 2: Verification of the Beer-Lambert’s Beer-Lambert’s law for the unionised and ionised forms of the indicator at the wave lengths, λ HMR and λ MR The Beer’s law can be verified by measuring the absorbances of a series of solutions of varying concentration obtained by diluting the stock solution of the indicator in the unionised and ionised forms using the cuvettes of path length equal to 1cm. These absorbance values are then plotted against relative concentrations of the solution. The linear plot so obtained establishes the validity of the Beer’s law. The slope of the line obtained gives the molar absorption coefficients. Step 3: Obtaining the absorption values of the indicator at different pH val ues A small but fixed amount of the indicator solution is added to a series of buffer solutions having pH spread over the indicator range (p K a ± 1) such that the indicator exists in varying proportions of the ionised and unionised form. As the K a value for acetic acid is in the same range as that for methyl red, we will use acetic acid-acetate buffers to control the pH. The absorption values of these solutions at λ HMR and λ MR , the wavelengths of maximum absorption of the unionised and ionised form of the indicator respectively are measured with the help of a suitable spectrophotometer or colorimeter. Step 4: Manipulating the data obtained in step 1-3 to obtain the p K a value The data obtained in the steps 1-3 can be used to determine the pK a value of the indicator. This can be achieved in a number of ways. Two of these are described as follows.
4
A.
Simultaneous Equations Method
You would recall from Experiment 3 of this course that when the analyte contains a mixture of two species whose spectra overlap to certain extent then the concentrations of these can be obtained by b y solving a set of simultaneous equations. As in the present case also the two species present in the solutions of the indicator at a given pH have overlapping regions in their spectra, we can compute their concentrations in the same way. The relevant equations can be worked out as follows.
Determination of pKa of an Indicator Using Spectrophotometry
In the mixtures of the acidic and basic forms of methyl red, the total absorbance at the wavelengths of maximum absorptions of the two forms viz., λ HMR and λ MR can be written as follows.
A λ
=
HMR
A λ
=
MR
−
εMR , λ
[MR ]
HMR
−
εMR , λ
[ MR ]
MR
εHMR , λ
+
HMR
εHMR , λ
+
MR
[HMR]
… (5.10)
[ HMR ]
… (5.11)
Solving these simultaneous equations we get the expressions for the concentrations of the two species as follows.
[ HMR ] =
A λ . ε MR , λ MR
εMR , λ
HMR
[ MR ] =
HMR
. ε HMR , λ
MR
A λ . εHMR , λ MR
HMR
εHMR , λ
HMR
. εMR , λ
MR
. εMR , λ
−
A λ
−
ε MR , λ
− −
HMR
MR
MR
A λ
HMR
. ε HMR, λ
… (5.12)
HMR
. εHMR , λ
MR
εHMR , λ
MR
. εMR , λ
… (5.13)
HMR
These equations can be used to obtain an expression for the ratio of the ionised and the unionised form of the indicator in a given mixture. The expression comes out to be as follows. −
[ MR ] [ HMR ]
=
A λ
HMR
. εHMR , λ
MR
A λ . ε MR , λ MR
HMR
−
A λ . ε HMR , λ
−
MR
A λ
HMR
HMR
.εMR , λ
… (5.14)
MR
This can then be used to obtain the pK a value of the indicator by using the HendersonHasselbach equation, viz., −
pK a
=
pK a
=
pH − log
[ MR ]
… (5.2)
[ HMR ]
Thus, pH - log
[ A λ
HMR
. ε HMR , λ
MR
[ A λ . εMR , λ MR
HMR
−
A λ . εHMR , λ
−
MR
A λ
HMR
HMR
.ε MR , λ ]
]
…. (5.15)
MR
In this experiment the concentration of the indicator is to be kept constant in all the absorbance measurements. As we do not need t he absolute values of the concentrations of the unionised and ionised forms of the indicator we just need their ratio. Therefore, we can do away with the determination of the molar absorption coefficients mentioned above, instead use the absorbance values for the total concentration of the indicator in the unionised and ionised forms at the λHMR and λMR . These can be obtained by
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SpectroscopicMethods Lab.
extrapolating the linear plots obtained for the verification of Beer’s law to relative concentration of 1.0. Accordingly, Equations 5.10 and 5.11 get modified as follows.
A λ
HMR
A λ
MR
u
−
A
=
[ MR ]
MR , λHMR
Au
=
−
MR , λMR
[ MR ]
+
+
u
AHMR, λ
HMR
[ HMR]
… (5.16)
u AHMR [ HMR ] ,λ
… (5.17)
MR
Where, the terms containing the superscript ‘u’ pertain to the absorbance values at relative concentration of 1.0 or unity. The final expression for the p K a value then can be written as follows.
pK a
=
pH − log
u
[ A λ
HMR
. AHMR, λ
MR
u [ A λ . AMR , λ MR
HMR
u
A λ . AHMR, λ
−
MR
A λ
−
HMR
HMR
]
… (5.18)
u . AMR ] , λ MR
Graphical Method Recall that according to the H enderson- Hasselbach equation, −
log
[MR ] [HMR ]
=
… (5.3)
pH − pK a
This represents an equation of a straight line of the type, Y= mX + C. where, −
Y equals, log [MR ] ; X = pH and C = [ HMR ]
−
pK a . Thus in a plot of log
slope would be equal to 1 and the intercept would be equal to
−
−
[MR ] versus pH the [HMR]
pK a as shown in −
Fig.5.2. Thus, the pK a can be found by determining the intercept of the plot of log [MR ]
[ HMR]
versus pH. Also, the line would cross the pH axis at pH = p K a ( as at this stage the concentrations of the ionised and unionised forms would be equal, [ MR ] = [HMR ] , −
making the log term equal to z ero.
−
log
Fig. 5.2:
6
[MR ] [HMR ] versus pH plot for the indicator
The pK a can be obtained either as the point of intersection of the line with the X-axis or from the intercept on the Y-axis.
5.4
REQUIREMENTS
Apparatus
Chemicals
Spectrophotometer/ Filter photometer
1
Matched cuvettes
2
Hydrochloric acid
pH meter with glass electrode
1
Sodium acetate
Volumetric flasks (1 litre)
1
Acetic Acetic acid a cid
3
1
3
8
Volumetric flasks (50 cm )
6
Volumetric flasks (250 cm ) Volumetric flasks (100 cm ) 3
3
Pipettes (10, 20 cm )
1each
Burette stand with clamp
1
5.5
Determination of pKa of an Indicator Using Spectrophotometry
Ethanol
Methyl red indicator
SOLUTIONS PROVIDED
i)
Sodium acetate (0.04M): It is prepared by accurately weighing 3.28 g of 3 anhydrous sodium acetate and transferring to a 1 dm volumetric flask containing 3 about 100 cm of distilled water. After dissolving dissolving the salt the volume is made up to the mark with distill ed water.
ii)
Sodium acetate solution (0.01M): It is prepared by diluting 250 cm of the 0.04 3 M sodium acetate solution prepared above to 1 dm by distilled water.
iii)
Acetic acid solution (0.02M): It is prepared by mixing 1.2 cm of glacial acetic 3 3 acid with 100 cm of distilled water in a 1dm volumetric flask and making up the volume with distilled water.
iv)
Hydrochloric acid solution (0.1M): It is prepared by transferring 9 cm of 3 3 concentrated hydrochloric acid to a 1dm volumetric flask containing 500 cm of distilled water. After mixing the volume is made up by distilled water.
v)
Hydrochloric acid solution (0.01M): It is prepared by diluting 100 cm of the 3 0.1 M hydrochloric acid solution prepared above to 1 dm by distilled water.
vi)
Methyl red indicator (stock) solution: solution: It is prepared by dissolving 0.1 g of pure 3 3 crystalline methyl red in 30 cm of 95% ethanol and making up to 100 cm with distilled water.
vii)
Methyl red in acidic form (Solution A): A): It is prepared by mixing 10 cm3 of the 3 indicator solution prepared in (vi) above with 10 cm of 0.1 M HCl solution and 3 diluting to 100 cm with distilled water in a volumetric v olumetric flask.
3
3
3
3
B): It is prepared by diluting 10 cm3 of the viii) Methyl red in basic form (Solution B): indicator solution prepared in vi) above with 0.01 M sodium acetate solution to 3 100 cm in a volumetric flask.
5.6
PROCEDURE
You would recall from section 5.3 that a typical spectrophotometric determination of the pK a value consists of four steps. Th ese are as follows. a)
Determine the wavelengths of maximum absorption for the unionised and ionised forms of the indicator, 7
SpectroscopicMethods Lab.
-
b)
Verification of Beer’s law for unionised (HMR) and ionised (MR ) forms at the wavelengths of their maximum absorptio n,
c)
Obtaining the absorption values of the indicator at different pH values,
d)
Manipulating the data obtained in step 1-3 to obtain the p K a value of the indicator.
Follow the instructions given below in the sequential order to accomplish these tasks. a)
Determination of the wavelengths of maximum absorption for the unionised and ionised forms of the indicator 1.
Record the absorption spectrum of ‘solution A’ in the range 350 – 610 nm against 0.01 M HCl.
2.
In case the instrument is of manual type, measure the absorption value after every 10 nm over the spectral spectral range and record the readings in columns columns 2, 5 and 8 of the Observation Table 5.1.
3.
Similarly, measure the absorption value for solution B against 0.01 M sodium acetate after every 10 nm over the spectral range and record the readings in columns 3, 6 and 9 of of Observation Table 5.1.
4.
Draw the spectrum of solution A and solution B by plotting the absorbance as a function of the wavelength in the graph provided in Fig.5.3. You may use two different colours to draw the spectra for solution A and solution B respectively.
5.
Select the wavelength which gives maximum absorbance for solution A and solution B and r ecord the same as λ HMR and λ MR respectively.
b)
Verification of Beer’s law for HMR and MR at λ HMR and λ MR 1.
Pipette out 40.0 cm3, 20.0 cm3 and 10.0 cm3 of solution A into three 3 separate 50 cm volumetric flasks and make up the volume in each case with 0.01 M HCl solution. Label these solutions as A1, A1, A2 and A3 respectively. These solutions would have concentrations equal to 0.8, 0.4 and 0.2 times the concentration of the stock solution A.
2.
Similarly, pipette out 40.0 cm , 20.0 cm and 10.0 cm of solution B into 3 three separate 50 cm volumetric flasks and make up t he volume in each case with 0.01 M sodium acetate solution. Label these solutions as B1, B2 and B3 respectively. These solutions would have concentrations equal to 0.8, 0.4 and 0.2 times the concentration of the stock solution B.
3.
Measure the absorbances of the solutions A1, A2 and A3 at λHMR and λMR using 0.01 M HCl as the reference and record your observations in Table 5.2.
4.
Similarly, Measure the absorbance values for the solutions B1, B2 and B3 at λ HMR and λ MR using 0.01 M sodium acetate as the reference and record your observations in Observation Table 5.2.
5.
Plot the absorbance values obtained in step 3 and 4 against the corresponding relative concentrations in the graph provided in Fig.5.4.
6.
The linearity of the plot so obtained establishes the validity of the Beer’s law.
7.
Extrapolate the linear plots obtained above to compute the absorbance values of the unionised and ionised forms of the indicator at λ HMR
3
and λ MR and record the same. 8
3
3
c)
d)
Determination of pKa of an Indicator Using Spectrophotometry
Obtaining the absorption values of the indicator at different pH val ues 1.
Prepare four solutions of the indicator in buffer solution of different pH values by mixing sodium acetat e, acetic acid, methyl red and water as detailed in column 2 to 5 of the Observation Table 5.3. Use 100 cm3 volumetric flasks labelled as 1, 2, 3 and 4 for this purpose.
2.
Measure the pH values of these solutions with the help of a suitably calibrated pH meter. Record these values in the column 6 of Table 5.3.
3.
Measure the absorbance values of these soluti ons at λ HMR and λ MR against water as a blank. blank. Record the same under column 7 and 8 of Observation Table 5.3.
Calculation of p K a value for the indicator from the data obtained −
Calculate the values of [MR], [HMR], and [ MR ] respectively from the
1.
[HMR ]
observed absorbance values at different pH values using equations given under step D of Section Section 5.6. Record the same in Observation Observation Table 5.4. 2.
Use these to calculate p K a value with the help of Henderson-Hasselbach equation and record in Observation Table 5.4.
3.
Find average value and report the result.
4.
Plot a graph between pH (x-axis) and log [MR ] (y-axis) in Fig.5.5.
−
[HMR]
Determine the pK a value from the point of intersection of the line and the pH axis and also in terms of the intercept on the y-axis and report the result.
5.7 A.
OBSERVATIONS AND CALCULATIONS Determination of the wavelengths of maximum absorption for the unionised and ionised forms of the indicator Observation Table 5.1: Absorbance values of the solution A and solution B at different wavelengths Column 1
2
Wavelength (nm)
Absorbance Solution A
3 Solution B
4
5
Wavelength (nm)
Absorbance Solution A
6 Solution B
7 Wavelength (nm)
8
Absorbance Solution A
350
440
530
360
450
540
370
460
550
380
470
560
390
480
570
400
490
580
410
500
590
420
510
600
430
520
610
9 Solution B
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SpectroscopicMethods Lab.
B.
Spectra for unionised form of the indicator (solution A) a nd ionised form of the indicator (solution B) using the data recorded recorded in Table 5.1
e c n a b r o s b A
350
400
450
500
550
600
650
Wavelength (nm) Fig. 5.3: Visible spectra for methyl red in t he unionised unionised and ionised f orms
From the spectra obtained above, the wavelengths of maximum absorption for the unionised and ionised forms of the indicator methyl red are as follows. For unionised form,
λHMR
= ………nm
For unionised form,
λMR
=……….nm
C.
-
Verification of Beer’s law for HMR and MR at the λ HMR and λ MR Observation Table 5.2: Absorbance values of the solution A and solution B at different wavelengths For Unionised form, HMR
Solution
Volume of Volume of Solution A 0.01 M HCl
Relative concentration
A1
40
10
0.8
A2
20
30
0.4
A3
10
40
0.2
Absorbance λ HMR
λ MR
-
For ionised form, MR Solution
10
Relative concentration
B1
Volume of Volume of Solution B 0.01 M CH3COONa 40 10
B2
20
30
0.4
B3
10
40
0.2
0.8
Absorbance λ HMR
λ MR
Determination of pKa of an Indicator Using Spectrophotometry
e c n a b r o s b A
0
0.2
0.4
0.6
0.8
1.0
Relative concentration λ λ Fig. 5.4: Absorbance values (at HMR and MR ) versus relative concentration plot for methyl red in the unionised and ionised forms
The absorbance values at λ HMR and λ MR for unionised and ionised forms of methyl red at relative concentration of 1.0 are found to be as given below.
A
u
A A
D.
u
u
A
HMR, λMR
HMR, λHMR =
MR, λHMR
u
=
MR, λMR
= =
Obtaining the absorption values at
λHMR
and
λMR
for the indicator at
different pH values. Observation Table 5.3: Absorbance values of the indicator solution in buffer solutions of different pH values Column 1
2
S.No.
3
4
5
6
Volume of 0.02 M CH3COOH
1
25.0
50.0
10.0
To make up to the mark
2
25.0
25.0
10.0
To make up to the mark
3
25.0
10.0
10.0
To make up to the mark
4
25.0
5.0
10.0
To make up to the mark
(cm )
8
Absorbance
0.04 M CH3COONa 3 (cm )
3
7
Indicator
Water
Stock
(cm3)
pH
λHMR
λMR
3
(cm )
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SpectroscopicMethods Lab.
E.
Calculation of p K a value for the indicator from the data obtained a)
Simultaneous Equation Method −
[MR ]
The values of [MR], [HMR],
, can be calculated from the observed [HMR] absorbance values at different pH values using the following equations.
[HMR] =
A λ
MR
u . AMR, λ
u
u
AMR, λ
HMR
[MR] =
[MR - ] [HMR]
A λ
MR
. AMR, λ
MR
u . AHMR, , λ
HMR
=
HMR
u . AMR, λ
MR
u
u
AMR, λ . AHMR, λ
−
−
MR
A λ
HMR
HMR
u . AHMR, λ
MR
u
u u u AHMR λ . AMR, − A . AMR, λMR λHMR HMR, λMR HMR
A λ =
HMR
u . AHMR, , λ
MR
u
A λ . AMR, λ
HMR
MR
pK a
A λ
−
HMR
pH − log
[ A λ
HMR
−
−
A λ
MR
λ HMR,
u [ A λMR . AMR, λHMR
HMR
u
A
u . AHMR, λMR
u . AHMR, λ
− −
. AMR, λ
MR
u A λMR . AHMR, ] λHMR
u A λHMR . AMR, ] λMR
Observation Table 5.4: Computation of the pKa values of methyl methyl red indicator using Handerson-Hesselbalch equation. S.No.
pH
[MR]
[HMR]
−
−
[ MR ]
log
[ HMR]
[ MR ] [ HMR]
−
pK a
=
pH − log
[ MR ] [ HMR]
1
2
3
4
Average value of p K a
The average value of p K a from the simultaneous equation method is found to be = b)
Graphical method −
Graph between pH and log
12
[ MR ] [ HMR]
Determination of pKa of an Indicator Using Spectrophotometry
4.5
5.0
5.5
6.0
6.5
pH
−
Fig. 5.5: Plot of
log
[MR ] [HMR]
versus pH to determine the pKa of methyl red.
The value of p K a from the graphical equation method is found to be =
5.8
RESULT
The pK a of the indicator (methyl red) using simultaneous equation method is found to be =
…………………..
The pK a of the indicator (methyl red) using graphical method is found to be =
…………………..
13
