ACID DISSOCIATION CONSTANT OF AN

INDICATOR DYE

by

Clarissa A. Gomez

CHE121L

ABSTRACT

Methyl red is the indicator dye used in this experiment. The maximum absorbance

obtained in its acidic form is 520 nm while 420 nm in its basic form. In the determination of

molar absorptivities using 10, 25 and 40 ml aliquots; the absorbance increases both in the acidic

and basic solution while the volume of aliquots escalates. Buffer solutions were prepared using

the Beer’s and Henderson-Hasselbalch’s equation. The isosbestic point appears at near 420 nm

which means that there is only one wavelength where two species have the same molar

absorptivity. By plotting the pH vs. absorbance of the prepared buffer solutions at two

maximum absorbance (acidic and basic), it was deduced that the spectrum of each solution is

dependent on the pH range. The obtained pka of methyl red using these data should be

compared to the theoretical pKa of methyl red which is 5.05 ± 0.05. However, this is not

achieved due to data deficiency.

INTRODUCTION

Indicators are weak organic acids (HIn) that change color when deprotonated (In-). A few drops of indicator added to the analyte solution before the beginning an acid-base titration. When enough base titrant is added to the analyte solution the equilibrium expressed in equation 1 will shift toward products. HIn(aq) In– (aq) + H+(aq) (1) The result is the formation of more of the deprotonated indicator (In ) and a corresponding color change of the analyte solution (the endpoint). A good indicator for a specific acid-base titration has an endpoint with a pH at or near the pH of the equivalence point. In this experiment, phenolphthalein indicator will be used for each titration. The pH range of the color change will be observed and compared with the pH of the equivalence point to determine if the indicator is an appropriate choice for each titration. The acid dissociation constant, Ka, is a measure of an acid’s strength. For weak acids these values are less than 1 and typically so small that they are expressed with scientific notation. Taking the negative log of the Ka results in more easily expressed pKa values ranging from 0 to 14 for weak acids. A spectrophotometer separates light into its separate colors. It is able to separate the light into colors because each color of light has a different wavelength than the other colors. The spectrophotometer can shine a narrow band of wavelengths (essentially one specific color) of light on a sample of substance and then measure how much of that light is absorbed by the sample. Different colored substances absorb varying amounts of specific wavelengths of light. Therefore, a spectrophotometer can be Used to measure how much of a substance is present. A calibration curve is a graph of absorbance, how much of a particular wavelength of light is absorbed, versus concentration (Beer’s law). A calibration curve is specific to a particular substance, and must

be created by measuring the absorbance of a large number of solutions of known concentration.

An acid is a substance which dissociates

to produce hydrogen ions, H+

, when dissolved in

aqueous solution. Once in solution, the H+

ion, which is simply a proton, immediately combines

with water to form the hydronium ion, H3O

+

. So

when aqueous H+

appears in a chemical equation, it is understood that the actual

species exists as H3O

+

. An acid is classified as

strong or weak depending on the extent to which the molecules of the acid dissociate into

H+

and its anion, A−

. A strong acid dissociates completely in water (e.g., HCl dissociates

virtually100% into H+

and its anion, Cl−

), while a weak acid dissociates only partially and forms

very little H+

(e.g., only about 3% of the dissolved molecules of acetic acid, CH

3COOH,

dissociate into H+

and the acetate anion,

CH3COO

−

). Weak acid dissociation can be

represented as a generic reversible reaction:

HA(aq) ⇔ H+

+ A–

where HA is the weak acid

and A-

is the anion, or conjugate base, of HA. For this reversible reaction, equilibrium constant can be defined:

(2)

The equilibrium constant is called the acid dissociation constant or acid ionization constant. If the undissociated acid (HA) is favored and the acid is weak, K

a is measurable

and will be much less than one. For strong

acids, the dissociated products, (H+

and A−

) are so strongly favored, that [HA] approaches zero and K

a approaches infinity. Thus strong acids, of

which there are very few, do not have values of K

a associated with them. Mathematically, it is

found that the amount of light absorbed by a specific sample depends on three things: 1) the concentration of the solution; 2) the distance the light travels through the sample; and 3) the natural ability of the specific substance to absorb light. Thus an equation can be written relating these things:

A=bc (3) where A = absorbance

= molar absorbtivity -- how well the material absorbs light

b = path length through which the light passes

c = concentration of the solution

In general, the value for b will remain the same

and the value for is constant for a specific chemical at a given wavelength of light. Because the general equation for a straight line is

y = mx + b (4)

If A is graphed against c, the result will be a

straight line with a slope of b and a y-intercept of zero. A solution that contains two colored species can also be analyzed using Beer’s Law

(A= bc). Mathematically, the concentrations of the two species can be determined if two simultaneous equations can be developed that relate the two. The two unknown concentrations are determined by taking readings on each solution twice, using two different wavelengths of light. The two species that are being studied in this experiment are the two colored forms of specific indicators that are weak acids. If there are two species, HIn and In, in a solution with absorbance AHIn and AIn, respectively, the total absorbance is A = AHIn + AIn . If the sample path length is combined

with, then = b and Beer’s Law for a two component mixture becomes

A1 = A1HIn + A1In = 1Hin [Hin] + 1In [In]

at 1 (5)

The constant does not change with concentration, but will change at different wavelengths and/or with a different absorbing

species. So, at a second wavelength 2, the following equation for Beer’s Law would be true:

A2 = A2HIn + A2In = 2HIn [HIn] + 2In [In]

at 2 (6) There are now two equations that can be used to determine the concentrations of the two different colored unknowns that are present in the solution. These equations can be rearranged to allow determination of each concentration.

[HIn] = ((A12In) ( A21In)) / ((2In 1HIn)

(1In 2HIn)) (7)

[In ] = ((A2 1HIn) – ( A1 2HIn)) / ((2In 1HIn) –

(1In 2HIn)) (8) The best wavelengths for the experiment are selected by measuring the absorbance vs. wavelength for each of the pure substances. The actual wavelengths are then chosen such that they will maximize the absorbance for each

species. The values for the four constants can be determined by doing Beer’s Law plots of absorbance vs. concentration (of pure samples) at both wavelengths and determining the slopes of the lines generated. The final set of measurements will be collected by measuring the absorbance of solutions of the weak acid at different pH’s.

EXPERIMENTAL MEHOD

To obtain the spectra of acid and base forms of the dye, first these two forms were prepared.

For the acidic solution of the dye, 0.05M HCl was used. While, 0.05M borax was utilized solution for the basic solution. Then the maximum absorbances of the solutions were determined at 20-nm intervals within the 340 – 625 nm wavelength range. In order to identify the molar absorptivities dilute solutions were prepared. Through obtaining 10, 25, and 40 mL aliquots of the solution these were diluted in a 50 mL volumetric flasks using 0.01M HCl for the acidic solution while 0.01M borax solution for dilution of basic solution. The absorbances of the six solutions were measured at the wavelengths of maximum absorption, λHIn and the λIn . After this in order to recognize the pKa of the dye using Henderson-Hasselbalch equation, five solutions at various pH values but with constant total dye concentration were prepared. It was followed by obtaining 10 mL of the original dye solution and placing it into a 100 mL volumetric flask. Then it was diluted to the mark with the buffer solution. Afterwards, their absorbanceswere obtained at λHIn and the λIn-.

RESULTS

Table 1. Wavelength and Maximum Absorption of Acidic Dye and Basic Dye Solution

(With 20 nm intervals)

λ (nm) Acidic Dye Solution Basic Dye Solution

380 - 0.034

400 0.003 0.045

420 0.008 0.050

440 0.019 0.048

460 0.042 0.042

480 0.077 0.027

500 0.110 0.011

520 0.129 0.001

540 0.118 -0.003

560 0.075 -0.004

580 0.021 -0.004

600 0.004 -0.003

620 0.001 -0.003

625 0.001 -0.003

Maximum Wavelength of Absorption for Acidic Dye Solution: 520 nm

Maximum Wavelength of Absorption for Basic Dye Solution: 420 nm

Table 2A. Wavelengths and Absorbance 2A. Wavelengths and Absorbance

of Acidic DyeTable of Basic Dye

Acid Dye Solution

λ (nm) Absorbance

505 0.119

510 0.126

515 0.128

520 0.129

525 0.128

530 0.126

535 0.123

540 0.118

Basic Dye Solution

λ (nm) Absorbance

380 0.034

385 0.037

390 0.040

395 0.044

400 0.045

405 0.046

410 0.048

415 0.050

420 0.050

Table 3A. Determination of Molar Table 3B. Determination of Molar

Absorptivities Absorptivities

Figure 1. Wavelength vs. Absorbance graph (Acidic Dye Solution)

Figure 2. Wavelength vs. Absorbance graph (Basic Dye Solution)

Absorbance of the acidic solution

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 100 200 300 400 500 600 700

Wavelength

Ab

so

rban

ce

Acidic Dye Solution

λ (nm) 10 mL 25 mL 45 mL

520 0.027 0.067 0.107

Basic Dye Solution

λ (nm) 10 mL 25 mL 40 mL

420 0.011 0.026 0.043

Absorbance of the basic solution

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 100 200 300 400 500 600 700

Wavelength

Ab

so

rban

ce

Figure 3. Wavelength vs. Absorbance graph (Acidic and Basic Dye Solution)

Table 4A. pH vs. Absorbance At maximum Table 4B. pH vs. Absorbance At maximum

Absorbance of Acidic Form Absorbance of Basic Form

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

380 400 420 440 460 480 500 520 540 560 580 600 620 625

Ab

sorb

ance

Wavelength

Basic

Acidic

0

0.01

0.02

0.03

0.04

0.05

0.06

4.4 4.8 5.6 6 6.4

Ab

sorb

ance

pH

0

0.02

0.04

0.06

0.08

0.1

0.12

4.4 4.8 5.6 6 6.4

Ab

sorb

ance

pH

Figure 4. Absorbance of acid and basic form of methyl red at two wavelengths

DISCUSSION

After the preparation of the acidic and basic solutions, their wavelength at maximum absorbance. Based on the data in Table 1, the maximum wavelength of absorption for acidic dye solution is 520 nm while 420 nm for the basic solution. The wavelength at which the absorbance is greatest needs to be determined for the reason that the spectrophotometer is more sensitive to absorbance changes at this wavelength. Although a substance will have an extinction coefficient at every wavelength, concentrations are typically measured at maxima in the absorbance spectra because this is where the absorbance changes least with changes in wavelength. From Figure 2 and 3, the Wavelength vs. Absorbance graph of acidic dye solution tends to lean on the left due to the large presence of acidic forms while in the Wavelength vs. Absorbance graph of basic dye solution tends to lean on the left ro to the large presence of its basic forms.

In the case of the dilute solutions, their molar absorptivies were obtained by using the maximum absorbance of the acidic and basic dye solution, which is 520 and 420 nm respectively. From the data gathered in Table 3A and 3B, one can see that the absorptivities of the dilute solutions by using the maximum absorbance in acidic solutions are higher than the basic solution. This can be explained through Beer’s law from equation 3. Based in this, the molar absorptivity is directly proportional to the absorbance. The capacity of the material to absorb light or its absorptivity increases as its absorbance increases as well.

The Henderson-Hasselbalch equation

which is [ ]

[ ] was used in

preparing the buffer solutions. Using the of acetic which is 4.7, buffer solutions with pH 4.4, 4.8, 5.6, and 6.4 were prepared. The ratio [In–]/[HIn] at different pH values and at

constant total dye concentration of 0.1 M were determined first, then from this the moles of the acid which is acetic acid and the base which is sodium acetate can be determined as well. In order to be prepared, their volumes must be known by using the equation for molarity, which is moles/Liter. However, after calculating the appropriate volumes for the different pH, it was found out that the amount of volumes were very small making it very difficult for the acid and the base to be pipette. So instead preparing the buffer solutions by volume, it was prepared by mass with the help of analytical balance and diluting both the acid and the base to 250 ml with distilled water.

Methyl red (4-dimethylaminobenzene-2’-carboxylic acid) is a commonly used indicator for acid-base titrations. By following the change in absorbance as a function of pH of the prepared buffer solutions we will determine the acid dissociation constant, or pKa. In this experiment we will determine this equilibrium constant, pKa', by varying the pH and measuring the ratio [In–]/[HIn . We will use acetic acid-acetate buffers to control the pH, since the Ka value for acetic acid is in the same range as the Ka' value for methyl red. The pH of these buffers force methyl red to distribute itself somewhat evenly between the two colored forms. The absorption of light is governed by the Beer-Lambert Law. The absorbance of mixtures is the sum of the separate absorbencies.

The best wavelengths to choose for the analysis are where one form absorbs strongly which is the maximum absorbance. We need to set up two equations in two unknowns, one equation

for each wavelength. Call the two wavelengths and . The two measurements then provide two simultaneous equations with two unknowns: [ ] [

]

[ ] [

]

The molar absorbance coefficients are determined from standard solutions that contain one component alone. This equations provide two equations in two unknowns. For an unknown solution, the absorbances at the two wavelengths, and , are determined

and then the two equations are solved for the unknown concentrations [ ] and [ ] at each given pH. Methyl red has a pKa of 5.1 An isosbestic point is defined as the wavelength where two species have the same molar absorptivity. At the isosbestic point the total absorbance of a solution of the two ions is independent of their relative concentrations but is dependent only upon the total dye concentration. The appearance of an isosbestic point is evidence that only two species are involved. In this experiment from Figure 3, the isosbestic point is near 420 nm. By looking at Table 4A, one can see that the absorbance decreases as the pH increases using the maximum absorbance at acidic conditions. While in Table 4B, the absorbance increases as the pH increases using the maximum absorbance at basic conditions. Equilibrium constants involving ionic species are especially sensitive to ionic strength. The ionic strength is a measure of the total ion concentration in solution. The activity of all the species in solution are a function of the ionic strength. The spectral changes are explained in terms of shifts in equilibria between different molecular and ionic species in the solutions.

Spectrophotometry involves the use of a spectrophotometer. A spectrophotometer is a photometer (a device for measuring light intensity) that can measure intensity as a function of the color, or more specifically, the wavelength of light. UV/Vis spectroscopy is routinely used in the quantitative determination of solutions of transition metals and highly conjugated organic compounds.

Spectrophotometers are most commonly used for the measurement of transmittance or reflectance of a solution or transparent material, like polished glass. However they can also be designed to measure the diffusivity on any of the listed light ranges that usually cover around 250nm - 2500nm using different controls and calibrations. Within these ranges of light, calibrations are needed on the machine using standards that vary in type depending on the wavelength of the photometric determination.

Historically, spectrophotometers use a monochromator containing a diffraction grating to produce the analytical spectrum. There are also spectrophotometers that use arrays of photosensors. Especially for infrared spectrophotometers, there are spectrophotometers that use a Fourier transform technique to acquire the spectral information quicker in a technique called Fourier Transform InfraRed.

The spectrophotometer quantitatively compares the fraction of light that passes through a reference solution and a test

solution. Light from the source lamp is passed through a monochromator, which diffracts the light into a "rainbow" of wavelengths and outputs narrow bandwidths of this diffracted spectrum. Discrete frequencies are transmitted through the test sample. Then the photon flux density (watts per metre squared usually) of the transmitted light is measured with a photodiode or other light sensor, and the transmittance value for this wavelength is then compared with the transmission through a reference sample.t

In short, the sequence of events in a spectrophotometer is as follows:

1. The light source shines through a monochromator.

2. An output wavelength is selected and beamed at the sample.

3. A fraction of the monochromatic light is transmitted through the sample and to the photodetector.

Many spectrophotometers must be calibrated by a procedure known as "zeroing." The absorbancy of a reference substance is set as a baseline value, so the absorbancies of all other substances are recorded relative to the initial "zeroed" substance.

The spectrophotometer then displays % absorbancy (the amount of light absorbed relative to the initial substance).

Beer's law relates the absorbance, the concentration of the absorbing species and the path length, such that:

A = εbc where A is the absorbance, ε, is the extinction coefficient, b is the path length (normally 1 cm) and c is the concentration of the absorbing species. Beer's law applies to solutions containing one or more absorbing species, if there is no interaction between the various species in the solution. In the case of a solution containing n species which absorb, the above equation becomes:

Atot = A1+A2+...+An = ε1bc1 + ε2bc2 + ...+ εnbcn

Beer's law in the case of a fixed path length, b, and extinction coefficient, ε, is a linear relationship between absorbance and the concentration This is not generally the case. Beer's law is successful in describing the absorption behavior of dilute solutions. One of the fundamental assumptions in the derivation of the law is that the average distance between atoms is large enough such that the charge distributions of neighboring atoms or molecules are not affected by those of its neighbors. This can alter a species' ability to absorb a given wavelength of radiation. This causes a deviation from the linear relationship because the extent of interaction depends on concentration. A similar situation can occur when the concentration of the absorbing species is low compared with the concentrations of other species. The effects of these molecular interactions become negligible at concentrations below 0.01M. Dilute solutions must therefore be used.

The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of nonlinearity include:

deviations in absorptivity coefficients at high concentrations (>0.01M) due to electrostatic interactions between molecules in close proximity

scattering of light due to particulates in the sample

fluoresecence or phosphorescence of the sample

changes in refractive index at high analyte concentration

shifts in chemical equilibria as a function of concentration

non-monochromatic radiation, deviations can be minimized by using a relatively flat part of the absorption spectrum such as the maximum of an absorption band

stray light

When an isosbestic plot is constructed by the superposition of the absorption spectra of two species (whether by using molar absorptivity for the representation, or by using absorbance and keeping the same molar concentration for both species), the isosbestic point corresponds to a wavelength at which these spectra cross each other.

A pair of substances can have several isosbestic points in their spectra.

When a 1-to-1 (one mole of reactant gives one mole of product) chemical reaction (including equilibria) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). This occurs because the two substances absorb light of that specific wavelength to the same extent, and the analytical concentration remains constant.

An isosbestic point is observed in overlaid

spectra when a chromophoric precursor is

converted to a product with a different

spectrum, so that it is often assumed that an

isosbestic point occurs only when the precursor

is quantitatively converted to a single product.

We show experimentally and by computer

simulations that more complex reactions also

exhibit isosbestic points and that the

wavelength of the isosbestic point may change.

Such wavelength changes will occur if either (i)

the molar absorbtivity of the precursor changes

or (ii) the fraction of the precursor that is

converted to multiple products changes. In the

latter case, the isosbestic wavelength and molar

absorbtivities of the precursor and product can

be used to calculate the fraction of the

precursor that is converted to products from

the relationship, f =

epsilon(Precursor)(M)/epsilon(Product)(M),

where f is the fractional conversion,

epsilon(Precursor)(M) is the molar absorbtvity

of the precursor, and epsilon(Product)(M) is the

molar absorbtivity of the product.

The requirement for an isosbestic point to occur

is that the two species involved are related

linearly by stoichiometry, such that the

absorbance is invariant for one particular

wavelength. Thus, other ratios than one to one

are possible. The presence of an isosbestic point

typically does indicate that only two species

that vary in concentration contribute to the

absorption around the isosbestic point. If a third

one is partaking in the process the spectra

typically intersect at varying wavelengths as

concentrations change, creating the impression

that the isosbestic point is 'out of focus', or that

it will shift as conditions change.[2] The reason

for this is that it would be very unlikely for three

compounds to have extinction coefficients

linked in a linear relationship by chance for one

particular wavelength.

In chemical kinetics, isosbestic points are used as reference points in the study of reaction rates, as the absorbance at those wavelengths remains constant throughout the whole reaction. Isosbestic points are used in medicine in a laboratory technique called oximetry to determine hemoglobin concentration, regardless of its saturation. Oxyhaemoglobin and deoxyhaemoglobin have isosbestic points at 590 nm and near 800 nm. Isosbestic points are also used in clinical chemistry, as a quality assurance method, to verify the accuracy in the wavelength of a spectrophotometer. This is done by measuring the spectra of a standard substance at two different pH conditions (above and below the pKa of the substance). The standards used include potassium dichromate (isosbestic points at 339 and 445 nm), bromothymol blue (325 and 498 nm) and congo red (541 nm). The wavelength of the isosbestic point determined does not depend on the concentration of the substance used, and so, it becomes a very reliable reference.

CONCLUSION

Absorption Spectroscopic methods of

analysis rank among the most widespread and powerful tools for quantitative analysis. The use of a spectrophotometer to determine the extent of absorption of various wavelengths of visible light by a given solution is commonly known as colorimetry. This method is used to determine concentrations of various chemicals which can give colors either directly or after addition of some other chemicals. Like in his experiment, the acid dissociation constant of the indicator dye based on the maximum absorbance and molar absorptivities of the acid and base forms of the dye.

Spectrophotometer was used to determine the pKa of theindicator solutions, methyl red. The method is a simultaneous photometric determination, using Beer's Law and the Henderson - Hasselbalch equation to determine the pKa of the indicator.

Methyl red is a weak organic acid which can be used as an indicator in the pH range of 4.8 to 6.0. From the prepared solutions done in this experiment, we can verify that a solution of methyl red will be red if the pH is lower than 4.8, yellow if it is above 6.0 and a mixture of both if 4.8< pH > 6.0. The color of these methyl red solutions should vary from the acidic color to the basic color. The ionization constant may be calculated from measurements of the ratio [In–]/[HIn] at known pH values. Since the two forms of methyl red absorb strongly in the visible range, the ratio [In–]/[HIn] may be determined spectrophotometrically. The absorption spectra of methyl red in acidic and basic solutions are determined, and two wavelengths are selected for analyzing mixtures of the two forms.

These two wavelengths, λIn– and λ HIn, are

chosen so that at one, the acidic form has a very large absorbancy index compared with the basic form, and at the other, the situation is reversed.

The absorbancy indices of [In–] and [HIn] -

are determined at both of these wavelengths, using several concentrations to determine whether Beer’s law is obeyed. From the data gathered in Table 3A and 3B, we can validate that molar absorptivity is directly proportional to the absorbance. Maximum absorbance was used because the wavelength at which the absorbance is greatest needs to be determined for the reason that the spectrophotometer is more sensitive to absorbance changes at this wavelength. This method is useful for studying dyes for use as indicators in acid- base titrations, or by an analogous procedure for indicators for oxidation-reduction titrations. The isosbestic point only appears at near 420 nm which means that there is only one wavelength where two species have the same molar absorptivity. Figure 4 is an example of absorbance of acid and basic form of methyl red at two wavelengths; however, it was not able to do in his experiment due to the lack of data gathered. The pka of methyl red was not able to obtain because to determine the ionization constant of methyl red, the relative amounts of HIn and In- present in solution must be obtained as a function of pH at different wavelengths.

REFERENCES

http://www.ruf.rice.edu/~bioslabs/methods/potein/protein.html#top

http://spinner.cofc.edu/genchemlab/beers.htm?referrer=webcluster&

http://www.chemistry.adelaide.edu.au/external/soc-rel/content/beerslaw.htm

http://sbio.uct.ac.za/Sbio/postgrad/modules/GRD/spectrophotometry/beer1.php

http://www.ncbi.nlm.nih.gov/pubmed/11112281

TITRATION CURVES, INDICATORSAND ACID DISSOCIATION CONSTANTS. "Chemistry with Computers.Vernier Software, Portland OR,1997