Determining the Acid Dissociation Constant of 2-Naphthol in the Ground and Excited State by Application of the Förster cycle


The physical and chemical properties of molecules as a function of electronic states is important in understanding chemical reactions. In this experiment, electronic spectroscopy was carried out on 2-naphthol and its conjugate base naphthoxy in varying pH solutions (2.00-11.80) to determine the acid dissociation constant in the ground, pKa, and lowest excited singlet state, pKa*. Beer’s law was used to determine the molar absorptivity of 2-naphthol and its conjugate base and then applied to determine the concentration of free acid and conjugate base in the buffered solutions. The concentrations were plotted as a function of pH, in a Henderson-Hasselbalch plot to determined the pKa. The Förster cycle was applied, taking into account the enthalpy change and neglecting entropy. The absorbance and fluorescence spectra of the acidic and basic solutions were used to determine the 0-0 energies, 0-0. The acid dissociation constants were determined to be 2.97 pKa* and 9.47 pKa. The pKa and pKa* corresponded well with literature values of 9.45 and 3.0 with a 0.2 and 1.0% difference, respectively. It was determined that 2-naphthol is a weaker acid in the ground state than the excited state due to pKa > pKa*.


The electronic structure of a molecule determines its physical and chemical properties. Absorption of a photon with energy equal to the difference in the quantum levels leads to the excitation of an electron from the ground to the first excited singlet state, S0 -> S1. The change in electron distribution can result in chemical reactions while in the excited state. The excited state is relatively short lived with a lifetime of 10-6 to 10-11 seconds so measuring excited state properties is difficult. Decay from the excited state can occur through radiative, ejection of a photon, or non-radiative, transfer of energy, processes. The radiative process fluorescence, S1->S0, is an effective method to measure properties of excited states.

In this experiment we consider the interaction of a fluorophore, 2-naphthol, with its surrounding environment and determine its acid dissociation constant in the ground and first excited singlet state. 2-naphthol can be an acid or a base in aqueous solution,

The dissociation of 2-naphthol varies according to electronic state of the molecule.

Figure 1. Schematic diagram of S0 and S1 states of 2-naphthol and its conjugate base

The energy of deprotonation, , changes depending if the molecule is in the ground or excited state. The free energy of deprotonation of ArOH can be expressed in terms of enthalpy and entropy,


for the S0 and S1 states, respectively. In pure solvents the effects of excitation on entropy are small as the number of microstates do not vary. It can be assumed that is the same in the ground and excited state.

The pKa can be determined by finding the concentration of the free acid and conjugate base in varying pH solutions by applying Beer’s law. A Henderson-Hasselbalch plot is then applied to determine the pKa. The Förster cycle can be used to determine the pKa* by finding the energy gap between the ground and first excited singlet state,

The energy gap can be determined from UV-Vis and fluorescence spectroscopy. Like stated earlier, only photons with energy equal to the energy gap between quantum levels can be absorbed. Some of the absorbed energy is lost due to vibrational relaxation. When the photon is released again through fluorescence at a specific wavelength, the wavelength corresponds to the energy gap of S1->S0 state. For this reason an overlay of the fluorescence and absorbance spectra of the acidic and basic solution allows the determination the 0-0 energies where the spectra of ArOH and ArO intersect. The 0-0 energies can then be used to determine


Table 1. Reagents used in this experiment

Reagent Chemical Formula Molecular Weight CAS Stock Solution Concentration (M)
Ammonium Chloride NH4Cl 53.49 12125-02-9 0.1
Ammonium Hydroxide NH4OH 35.04 1336-21-6 0.1
Sodium Hydroxide NaOH 40.00 1310-73-2 0.02
Hydrochloric Acid HCl 36.46 7647-01-0 0.02
2-Naphthol 144.17 135-19-3 4.16 x 10-4

Three buffer solutions were prepared from stock solutions, Table 1, in 100 mL volumetric flasks, Table 2. To determine pKa five solutions of 2-naphthol were prepared. The first two solutions were made to predominately contain either the free acid or conjugate base of 2-naphthol by adjusting the pH to 2 using HCl and 11.8 with NaOH. Three solutions were made with intermediate pH by using (NH4OH/NH4CL) buffer solution. A Jasco-530 UV-Vis spectrophotometer was used to obtain absorbance data and a Photon Technology International fluorometer was used with the FeliX32 analysis module computer program for fluorescence measurements. Optimal excitation wavelength was determined to be 320 nm and emission scans were obtained from 330 to 500 nm. Absorption scan range was between 300 and 380 nm.

Table 2. Concentration of ammonium chloride, ammonium hydroxide, and water used to make the buffered solutions.


Buffer 1



Buffer 2



Buffer 3



0.1 M NH4Cl

20 mL

10 mL

10 mL

0.1 M NH4OH

10 mL

10 mL

20 mL

Deionized Water

70 mL

80 mL

70 mL

Total Solution Volume

100 mL

100 mL

100 mL

Table 3. The concentration of each reagent used to make the five solutions analyzed.


Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

4.0 x 10 -4 M ArOH

5 mL

5 mL

5 mL

5 mL

5 mL

0.02 M HCl

20 mL

0.02 M NaOH

20 mL

2:1 NH4OH/NH4Cl

20 mL

1:1 NH4OH/NH4Cl

20 mL

1:2 NH4OH/NH4Cl

20 mL

Total Volume

25 mL

25 mL

25 mL

25 mL

25 mL


Absorbance and fluorescence spectra were obtained of 2-napthol in varying pH solutions (2.0-11.8) and used to find the  of absorbance and emission. It was necessary to correct the fluorescence spectra due to non-ideal response of the instrument. Beer’s law was used to determine the molar absorptivity of 2-naphthol in the acidic and basic solution. The molar absorptivity was then used to determine the concentration of ArOH and ArO in the buffered solution. The concentration could be used in a Henderson-Hasselbalch plot to determine the pKa. The pKa* was determined by applying the Förster cycle.

The absorbance spectrum in Figure 2 shows the characteristics of an excited state reaction. The isosbestic point at 326 nm indicates a closed system. The fluorescence spectrum of 2-naphthol in varying acidic, basic, and buffered solutions is observed in Figure 3. The fluorescence wavelength of protonated 2-naphthol was determined to be 356 nm from solution 1, 2-naphthol with HCl at a pH of 2. The fluorescence wavelength of deprotonated 2-naphthoxy was determined to be 416 nm from the spectrum of solution 2 containing NaOH with a pH of 11.8. The buffered solutions 3-5 displayed both free acid and conjugate base absorption.

From solution 1,  was determined to be 527 cm-1 M-1 and  was determined to be 1057 by Eq. 6. The molar absorptivities were used to determine the concentration of each species of 2-naphthol in the buffered solutions. The pH was graphed as a function of the log of the concentrations to make a Henderson-Hasselbalch plot.




Log([ArO-]/[ArOH]) pH
1 8.00 x 10-5 0


2 0 8.00 x 10-5


3 2.64 x 10-4 1.52 x 10-4



4 3.19 x 10-4 9.66 x 10-5



5 3.62 x 10-4 5.42 x 10-5



Table 5. The least squares results from Figure 4












The pKa was determined from the y-intercept of the Henderson-Hasselbalch plot to be 9.47.

The 0-0 energies were determined from an overlay of the fluorescence and absorbance spectra of the acidic and basic solutions, Figures 6 and 7, respectively. It was determined that the 0-0 energy for the acidic solution 1 was 333 nm and 371 nm for the basic solution 2 which were converted to wavenumbers of 30030 and 26954 cm-1, respectively. The spectroscopic energy difference, , was determined from the 0-0 energies to be 3076 cm-1. Using Equation 4, it was determined that the pKa* was 2.97, Table 6.

Table 6. The pKa and pKa* found from this experiment compared to literature values with the calculated percent difference.




Percent Difference










In the buffered solutions emission is observed from both species. At pH below 3 the reaction is reversible but at above pH 6 the reaction becomes irreversible, Figure 2. From the fluorescence spectrum Figure 3, it is observed that in acidic solution the emission came from the 2-naphthol with a  emission of 356 nm and in basic solution emission occurs from the naphtholate anion at 416 nm. From Figure 6 and 7, a Stokes’ shift is observed where fluorescence occurs at a lower wavelength than absorption. This occurs due to the loss of energy through vibrational relaxation and rearrangement of the molecule. The fluorescence spectrum appears to be a mirror image of the absorption spectrum which is due to the same electron transition being involved S0 and S1 in both absorption and emission.

From this experiment it was determined that the pKa of the ground state of 2-napthol is 9.47. The pKa* of the lowest excited state of 2-naphthol was determined to be 2.97. Both of these values correspond to literature values of 9.45 and 2.97 for pKa and pKa* with 0.2 and 1.0% difference, respectively. Comparing the two pKa values shows that 2-naphthol is a stronger acid in the excited state. This is due to the degenerate singlet excited state having a less polar long axis and a more diffuse nature.[4] Deprotonation occurs more readily in the excited state because the electrons on the hydroxyl group are shifted into the aromatic ring making the hydroxyl group more acidic. The electron density increases around the oxygen atom because it is more electronegative than the hydrogen, pulling the shared electrons closer to the oxygen.

The Ka is calculated from the equation, . It was determined that Ka is 3.55 x 10-10 and Ka* is 1.07 x 10-3. From Figure 1 it is seen that as the Ka increases the enthalpy change of the system increases, so  is a lot larger than . The entropies of the system, as stated in the introduction, can be assumed to be the same due to the solvent being pure. This results in both the ground state and lowest excited energy level having the same microstates. If the molecule reacted with the solvent in any way then would have to be taken into consideration.

Molecules with similar behavior to 2-naphthol are 2-napthoic acid, acridine, and quinolone. The protolytic reactions in water are,

Figure 8. The protolytic reactions for a. 2-naphthoic acid b. acridine c. quinoline in aqueous solution.

Applying the results of this experiment to 2-napthoic acid, acridine, and quinolone, it can be concluded that pKa*>pKa for all the molecules. The 2-naphthoic acid has a carboxylic acid group which is an electron acceptor. These molecules have a vacant π orbitals into which electrons can be transferred in the excited state increasing electron density and resulting in weaker dissociation.[5] Acridine and quinolone both have electron donor group amine. When electron donors have a lone pair of electons in an aromatic ring system they tend to become more conjugated in the excited state.[5]

The difference between the experimental and the literature value was minimal. The variance could have occurred from an inconsistent temperature during the trials from this experiment. According to the Van’t Hoff equation, all equilibrium constants varying with temperature. The temperature of the solutions was not held at a consistent temperature. The Förster cycle is also not reliable in estimating the precise pKa* value but rather is effective in determining the direction of change in the pKa.


UV-Vis and fluorescence spectroscopy were used to determine the acid dissociation constant of 2-naphthol in the ground and lowest excited singlet state by application of the Förster cycle. The pKa of 2-napthol in the ground state was 9.47 compared to the lowest excited singlet state pKa* of 2.97. Both the ground and excited state acid dissociation constants correlated with literature values with a 0.2 and 1.0% difference, respectively. From the acid dissociation constants it was determined that 2-naphthol is a stronger acid in the excited state. This information can be used in reactions that require deprotonated 2-naphthol in a relatively acidic solution. The pKa determined in this experiment can now be used in further study of 2-naphthol and the deprotonation and protonation rate constants in the ground and excited state.


[1] Halpern, A. M; Reeves, J. H, Experimental Physical Chemistry, Scott, Foresman and Company, Boston, 1988.

[2] Rosenberg, L. J.; Brinn, I.; Excited State Dissociation Rate Constants in Naphthols. J. Phys. Chem. 1972; 76 (24), 3558-3562.

[3] Park, H.; Mayer, B.; Wolschann, P.; Köhler, G., Excited-State Proton Transfer of 2-Naphthol Inclusion Complexes with Cyclodextrins. J. Phys. Chem. 1994; 98 (24), 6158-6166.

[4] Lakowics, J. R., Principles of Fluorescence Spectroscopy; Kluwer: New York, 1999.


The concentration of the original solutions

The molar absorptivity

The concentration of ArOH in the buffered solutions at equilibrium,

The Concentration of ArOat equilibrium