Abstract:
Rate constants are important to quantify the rate of a chemical reaction. The protonation and deprotonation rate constants were determined of the lowest excited singlet state of 2-naphthol (ArOH) in aqueous solution. The rate constants were determined by measuring the fluorescence intensity, I_{f}, proportional to [ArOH*] at acidic, basic, and varying ammonium acetate (NH_{4}Ac) concentrations (0.01-0.11M). Radiative, k_{r}, and nonradiative, k_{nr}, were calculated to be (2.6±0.1)*10^{7} s^{-1} and (1.18±0.7)*10^{8} s^{-1} using literature values for fluorescence quantum efficiency, Φ=0.18 and the natural fluorescence,. Rate constants for unassisted, k_{d}, and acetate assisted, k_{Ac}^{–}, deprotonation were determined by a Stern-Volmer plot, intensity as a function of the [NH_{4}Ac], to be (8.1±0.3)*10^{7} s^{-1} and (2.56±0.07)*10^{9} M^{-1 }s^{-1}, respectively. Protonation constant, k_{p}, was determined to be (6.19±0.2)*10^{10} M^{-1 }s^{-1 }using the literature excited state acidity constant K_{a}^{*}= 0.00131. Nonradiative decay occurred at a faster rate than radiative decay and acetate assisted deprotonation occurred at a faster rate than unassisted. Using the Stokes-Einstein-Smolouchowski equation k_{diff} was calculated to be 7.42*10^{9} dm^{3}mol^{-1}s^{-1}. Both k_{diff} and k_{Ac}^{–} have the same order of magnitude signifying k_{Ac}– is dependent on diffusion. Rate constant results corresponded with literature values with a percent difference of 0.9%, 30%, and 11% for k_{r+} k_{nr}_{, }k_{d}, and k_{p}, respectively.
Experimental:
A series of five aqueous solutions in 25-mL volumetric flasks with varying NH_{4}Ac concentration between 0.010 and 0.10 M and ArOH stock solution (4.0*10^{-4} M) were prepared. Two solutions were made with stock solution of ~0.1 M NaOH and ~0.1M H_{2}SO_{4} to observe fluorescence in acid and base. Reagents used in Table 1 and amount stock solution used for each solution in Table 5 under appendix. Deionized water was used as a blank and fluorescence measurements were taken with a Photon Technology International fluorometer with FeliX32 analysis module computer program at excitation wavelength of 320 nm in the emission range of 330 to 600 nm.
Table 1. Reagents used for stock solution in 250 mL volumetric flasks.
Reagent | Formula |
Molecular Weight (g mol^{-1}) |
Density (g mL^{-1}) |
CAS Number | Stock Concentration (M) |
Sodium Hydroxide | NaOH | 40.00 | 2.13 | 1310-73-2 | 0.10924±0.000005 |
Ammonium Acetate | NH_{4}Ac | 77.08 | 1.073 | 631-61-8 | 0.11514±0.00006 |
Sulfuric Acid | H_{2}SO_{4} | 98.079 | 1.84 | 7664-93-9 | 0.1126±0.0002 |
2-Naphthol | C_{10}H_{7}OH | 144.17 | 1.22 | 135-19-3 | 0.00042±0.0000 |
Data
Table 2. Acetate concentration in each solution with the Fluorescence intensity, I_{f}, found in Figure 1 at 356 nm.
Solution | [Ac^{–}], M | I_{f} | ,,𝑰–𝒇–𝟎.-,𝑰–𝒇..− 𝟏 |
3 | 0.0099 | 210591 | 0.7619 |
4 | 0.0299 | 170159 | 1.1805 |
5 | 0.0598 | 153216 | 1.4216 |
6 | 0.0801 | 124891 | 1.9709 |
7 | 0.0990 | 108405 | 2.4227 |
Table 3. Least squares results from Figure 2, Stern-Volmer plot of 2-naphthol fluorescence.
LINEST RESULTS | |||
Slope (m) | 18.0 | 0.6 | y-intercept (b) |
Standard Deviation of Slope (S_{m}) | 2.0 | 0.1 | Standard Deviation of y-intercept (S_{b}) |
Linear Regression (R^{2}) | 0.9649 | 0.1 | Standard Deviation of y (S_{y}) |
Table 4. Rate constants determined compared to literature values using the same method as this experiment with percent difference.
Rate Constant | Experimental | Literature^{3} | Percent Difference |
k_{r }(s^{-1}) | (2.6±0.1)*10^{7} | k_{r+}k_{nr}=1.43*10^{8 } | 0.9% |
k_{nr} (s^{-1}) | (1.18±0.07)*10^{8} | ||
k_{d} (s^{-1}) | (8.1±0.3)*10^{7} | 6.0*10^{7} | 29% |
k_{Ac}– (M^{-1} s^{-1}) | (2.56±0.07)*10^{9} | 2.3*10^{9} | 11% |
k_{p }(M^{-1} s^{-1}) | (6.2±0.2)*10^{10} | 1.9*10^{11} | 102% |
k_{diff} (M^{-1} s^{-1}) | 7.42*10^{9} | – | – |
Note: Large percent difference for k_{p} associated with using different K_{a}^{*}
Conclusion
The protonation and deprotonation rate constants of 2-naphthol in the lowest excited singlet state in a range of acidic to basic pH solutions was determined by fluorescence study and Stern-Volmer plot, as a function of [Ac^{–}], Figure 2. The maximum emission intensity for acidic solution was determined to be at 356 nm, 420 nm for basic solution, and the isostilbic point at 387 nm, Figure 1. Fluorescence at 356 was highest in acidic solution due to deprotonation being suppressed^{1}. The rate of acetate-assisted deprotonation was determined to be faster than unassisted with k_{Ac}–= (2.56±0.07)*10^{9} M^{-1} s^{-1 }and k_{d}= (8.1±0.3)*10^{7}. Nonradiative decay occurred faster than radiative decay due to low reaction energy barrier at rates of k_{nr}= (1.18±0.07)*10^{8} s^{-1} and k_{r}= (2.6±0.1)*10^{7} s^{-1}. The diffusion rate constant, calculated from the Stokes-Einstein-Smolouchowski, was found to be 7.42*10^{9 }M^{-1} s^{-1} indicating two neutral species due to k_{diff} same order of magnitude as k_{Ac}^{–}^{1}. The percent difference for the rate constant is 0.9%, 30%, and 11% for k_{r+} k_{nr}_{, }k_{d}, and k_{p}, respectively. Difference between theoretical and experimental could be due to temperature differences while running the reactions. Determining the rate constants is important to understand reactions under variable conditions.
References
[1] M. Halpern and G.C. McBane, Experimental Physical Chemistry, 3^{rd} ed., W.H. Freedman and Company, New York, 2006. Experiment 34.
[2] Atkins, P., J. De Paula “Physical Chemistry”, 9th ed., W. H. Freeman, New York (2010)
[3] R. Boyer, G. Deckey, C. Marzzacco, M. Mulvaney, C. Schwab, and A. M. Halpern, J. Chem. Educ., 62, 630 (1985).
[4] Kestin, J.; Sokolov, M.; Wakeham, W. A. Viscosity of Liquid Water in the Range -8°C to 150°C. J. Phys. Chem. 7, 941 (1978).
[5] T. Forster, Z. Elektrochem., 54, 42 (1950).
[6] Smith, J.; Fluorescence Decay of 2-Naphthol, Handout, Print.
Appendix
Table 5. Amount of stock solution used to make solutions that were analyzed by the fluorometer.
Analyte | Soln. 1 (Acidic) | Soln. 2 (Basic) | Soln. 3 (Buffer 1) | Soln. 4 (Buffer 2) | Soln. 5 (Buffer 3) | Soln. 6 (Buffer 4) | Soln. 7 (Buffer 5) | Soln. 8 (Blank) |
ArOH | 2.5 mL | 2.5 mL | 2.5 mL | 2.5 mL | 2.5 mL | 2.5 mL | 2.5 mL | 2.5 mL |
H2SO4 | 22.5 mL | — | — | — | — | — | — | — |
NaOH | — | 22.5 mL | — | — | — | — | — | — |
NH_{4}Ac 0.01M | — | — | 2.25 mL | — | — | — | — | — |
NH_{4}Ac 0.03M |
— | — | — | 6.80 mL | — | — | — | — |
NH_{4}Ac 0.06 M |
— | — | — | — | 13.6 mL | — | — | — |
NH_{4}Ac 0.08 M |
— | — | — | — | — | 18.2 mL | — | — |
NH_{4}Ac 0.11 M |
— | — | — | — | — | — | 22.5 mL | — |
Deionized water | — | — | 20.25mL | 15.7 mL | 8.9 mL | 4.3 mL | — | 25 mL |
Total Volume | 25 mL | 25 mL | 25 mL | 25 mL | 25 mL | 25 mL | 25 mL | 25 mL |
Table 6. Fluorescence Decay for 2-Naphthol in 0.10 M H_{2}SO_{4} at 25C.^{[4]}
Time (ns) | Intensity (photons emitted nanosecond^{-1}) | Natural Log (Intensity) |
0 | 21753 | 9.988 |
1 | 18907 | 9.847 |
2 | 16380 | 9.704 |
3 | 14171 | 9.559 |
4 | 12432 | 9.428 |
5 | 10757 | 9.283 |
6 | 9288 | 9.136 |
7 | 8138 | 9.004 |
8 | 7083 | 8.865 |
9 | 6014 | 8.709 |
10 | 5350 | 8.585 |
Calculations
Fluorescence Quantum Efficiency Ф=0.18 ^{[1]}
The slope (m) of Figure 2 was used to calculate
The y-intercept (b) of Figure 2 was used to calculate
Error Calculations