Spectrophotometric Determination of Acid Dissociation Constant (Ka)

This report details an experiment focused on determining the acid dissociation constant (Ka) of an unknown indicator using spectrophotometry. The introduction explains the purpose of the experiment, the concepts of Ka, acid-base indicators, and the application of spectrophotometry. The experimental section outlines the procedure, including the preparation of solutions and absorbance measurements. The results section presents the experimental pKa values, calculations, and a comparison to the theoretical values, with a discussion on the sources of error, such as pH changes and contamination. The report utilizes the Henderson-Hasselbalch equation to calculate the pKa values and identify the unknown indicator as methyl red. The discussion compares the experimental and theoretical Ka values and includes a percentage error analysis. The conclusion summarizes the successful determination of the pKa value and identifies the indicator. The bibliography provides a list of cited references. The report aims to provide a comprehensive understanding of the spectrophotometric method for determining Ka values, incorporating all the necessary components of a formal scientific report.

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Determination of the Ka for an Indicator by Spectrophotometry
Introduction
This is an experiment to determine the pKa of an acid-base indicator using the
spectrophotometry method. An indicator tells the end of a titration (Daniella, and Burkina, p. 9-
4). For the acid-base titrations, either a weak acid or a weak base detects the end of the titration.
A sharp change in the color of the indicator due to a steep in the pH of the solution closer to the
equivalence point of the titration indicates the end of an acid-base titration (Danilla, and Buskina,
p. 9-4). The use and application of spectrophotometry in this experiment are to determine the
concentration of the ionized base and unionized acid forms of the indicator. In addition to that,
spectrophotometry also helps to determine the dissociation constant of the acid by using the
Henderson –Hasselbach equation (Danilla, and Buskina, p. 9-4). The main objectives of the
experiment are to determine the pKa of the acid-base indicator. Methyl red indicator, for example,
is a weak organic acid, which is red in acidic solution but changes to yellow in ionized basic
solution. Methyl red indicator is a weak acid represented as HMR dissociates in both the ionized
and unionized solution as:

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HMR ↔H+ MR-
Procedure
The wavelength of maximum absorption was first determined for the unionized and
ionized forms of the indicator both of the two solutions A and B against 0.01HCl and0.01
sodium acetate respectively and recorded. A plot the absorbance as a function of the wavelength
showing various spectrum for the indicator under study was drawn (Zayed, Mohamed, and
Mahmoud, P. 1135-1149). 30cm3, 20cm3 and 10cm3 of solution A was pipetted into three
separate 50cm3 and each solution topped up with 0.01 HCl .Similar procedure was done to
solution B but topped up with 0.01 sodium acetate solution instead and the absorbance for each
solution measured.
Results and calculations.
The table of the results drawn below indicates the pKa experimental values obtained for
each of the indicator used. Methyl red for example in a pH range of 4.4 to 6.2 gives the pKa
value of 4.95(Kirkwood, Jobie, et al.,p.2367-2375). Changing from red in an acidic solution to
yellow in basic media, indicated on the table below as (R-Y).Cresol red, Thymol blue and
Methyl yellow also behave the same way as the methyl red in acidic media turning from red to
yellow indicated as (R-Y) in the table below.
Bromophenol blue, Bromocresol green and Thymol blue indicators are all blues in basic
solutions indicated on the table as (Y-B). Methyl orange is orange in acidic solution, p-

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Nitrophenol yellow in basic media while phenolphthalein and Alizarin yellow are red and violet
in a basic media respectively.

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From the Henderson –Hasselbach equation it provides the relationship between pH and
pKa.Taking for example the methyl red ,Henderson-Hasselbach equation can be given as, pH
=pKa + log [MR-]/[HMR],when rearranged, pKa =pH -log [MR-]/[HMR] .When the
concentrations for both the ionized and unionized forms of the indicators are known then pKa
can be determined at a given pH. (Zayed, Mohamed, and Mahmoud, P. 1135-1149). The total
absorbance of the indicator at a given pH for both the ionized part and the unionized part of the
indicator can be given as,
pKa value of the indicator can then be determined using the Henderson –Hasselbach equation
Hence,
Keeping the concentration of the indicator constant, the pKa values can be obtained as,
From the Henderson –Hasselbach equation of log[MR-]/[HMR] = PH –pKa is a straight
line of the type, Y=Mx + C, where X is the pH, C is the –pKa and Y equals to the
log[MR-]/[HMR]. A plot of the log [MR-]/[HMR] vs the various pH of the given indicators give
a slope m which should always be 1 and the intercept = -pKa, the values of pKa for each of the
indicators were found by determining the intercept from the graph as shown below.

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Discussion
The ka value for the methyl red was found to be 4.7647 which is lower than the
theoretical value of 4.95.this is, therefore, confirms the unknown indicator used in this
experiment as methyl red indicator (Kirkwood, Jobie, et al.,p.2367-2375).
The percentage error found was about 41.2%. The percentage error realized was due to
the constant changing pH of the solutions and again must have been due to the contamination of
the indicators. Methyl red indicator being a weak indicator dissociating in both an ionized and
unionized solution (Kirkwood, Jobie, et al.,p.2367-2375).However, in our calculations and
determination of the pKa value, we assumed that this does not affect the overall acidity pH of the
solutions used.
Conclusion

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In summary, the objective of determining the pKa value of the unknown indicator methyl red
indicator was perfectly achieved using both graphical method and spectrophotometry method
and the unknown indicator was found to be methyl red indicator (Shokrollahi, Ardeshir, et al.,
p.67-79). The experimental value and the theoretical was calculated and compared. The
percentage error obtained showed that there were constant changes in the pH.

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Bibliography
Danilina, Elena I., and Lilia T. Agliullina. "Optimization of kinetic determination of iodate by
methyl orange oxidation in the presence of hydrazine. (2014)
Danilina, E. I., and K. A. Buskina. "Kinetic spectrophotometric determination of hydroxylamine
and nitrite ion in a mixture by their reactions with neutral red.4 (2017).
Kirkwood, Jobie, and et al. "A high-throughput colorimetric method for the determination of pH
in crystallization screens." Acta Crystallographica Section D: Biological
Crystallography70.9 (2014): 2367-2375.
Ljubas, Davor, Goran Smoljanić, and Hrvoje Juretić. "Degradation of Methyl Orange and Congo
Red dyes by using TiO2 nanoparticles activated by the solar and the solar-like
radiation." Journal of environmental management 161 (2015): 83-91.
Shokrollahi, Ardeshir, Masoud Gohari, and Foroogh Ebrahimi. "Determination of Acidity
Constants of p-Rosolic acid and Bromoxylenol Blue by Solution Scanometric
Method." Analytical and Bioanalytical Chemistry Research 5.1 (2018): 67-79.
Zayed, Mohamed, and Mahmoud Farouk. "The Use of Diphenylamine Sulfonate Redox
Indicator in Spectrophotometric Micro-determination of Non-Steroidal Anti-
Inflammatory Drugs." Egyptian Journal of Chemistry 60.6 (2017): 1135-1149.