INTRODUCTION
An indicator is a weak acid or base whose conjugate forms have different colors. In this experiment, the indicator, also used as a biological stain, is Neutral Red (3-amino-7-dimethylamino-2-methylphenazine hydrochloride) (NR), which has the structure (protonated form) and acid dissociation equilibrium shown below.

HNR⁺ +  H₂O =  H₃O⁺ +  NR
Figure 1. The structure and acid dissociation of Neutral Red
(3-amino-7-dimethylamino-2-methylphenazine hydrochloride).

The thermodynamic acid dissociation constant for HNR⁺ is given in terms of activities

which reduces to

because the pure solvent is taken to be standard state (a = 1). The activity is a concept of "effective concentration" which is envoked to correct for non-ideal solution behavior which is expected in aqueous electrolytes. This non-ideality may be represented by an activity coefficient, g , which is the ratio of the activity over the physical concentration.

where c_i is the molar concentration of species i. The equation for K_a is, therefore,

The activity coefficient of a neutral molecule in a dilute solution may be taken as unity. The activity coefficient of an ion is determined by the total ionic atmosphere of the solution, called the ionic strength, µ,

where c_i is the concentration of ion i, z_i is its charge, and the sum is taken over all ions in solution. Several equations can be used for calculation of activity coefficients, but a very common one is the extended Debye-Huckel equation:

where z is the charge of the ion of interest, and a is the radius of the solvated ion (ion plus its tightly bound sheath of water molecules; a = ca. 900 pm for H₃O⁺; a = ca. 700 pm for a large cation like HNR⁺). A and B are factors which depend on the density (A only) and dielectric constant of the solvent and the temperature. Values of at 25 ^oC for various ionic strengths and a's are conveniently obtained from the literature [1].

If the ionic strength is held constant for all measurements involving K_a^µ, a "concentration" dissociation constant, valid only at that ionic strength, may be used:

In this experiment, the K_a^µ=0.10 will be measured at a total ionic strength of 0.10M, maintained by adding an inert salt, NaCl, to all solutions.
 

The [H₃O⁺] will be controlled by a buffer of NH₃OH⁺/NH₂OH created by incremental addition of standard 0.10M NaOH to a known number of moles of either NH₃OH⁺ (K_a^µ=0.10 for NH₃OH⁺ at 25^oC and µ = 0.1M is 1.07 x 10^-6). As described further below, the addition of NaOH will increase the solution volume, necessitating a correction for dilution in the calculation of all concentrations.
 

The [NR]/[HNR⁺] ratio will be determined spectrophotometrically. If a solution with a total indicator concentration of c_T is made very acidic, all of the indicator exists as HNR⁺. The absorbance of the solution at a given wavelenght of light, l, is given by

where e_HNR+ is the molar absorptivity of HNR⁺ at wavelength l and b is the cell path length. If, by making the solution very basic, the same concentration of indicator is converted entirely to the NR form, the absorbance at the same wavelength is given by

where e_NR is the molar absorptivity of NR. At an intermediate pH the absorbance is

where the total concentration can be defined under any conditions as:

For a given c_T, equations 8-11 can be combined to give

If possible, the ratio should be evaluated at multiple wavelengths, including one where HNR⁺ absorbs appreciably but NR does not, and one where NR is a much stronger absorber than HNR⁺, and one where the two species absorb at approximately the same extinction (What is this point called??). The p_CH's (-log[H₃O⁺]) of the solutions should be in the transition range of the indicator, so that both HNR⁺ and NR exist in appreciable concentration. With a spectrophotometer having a conventional sample holder (cuvette) a series of separate solutions must be prepared. However, if the instrument is equipped with a fiberoptic probe, the experimental procedure can be greatly simplified. A single solution containing the indicator plus NH₃OH⁺ is prepared and known increments of NaOH are added to convert the respective acid to its conjugate base form. This addition changes the total volume and decreases c_T, but equation 12 can still be used if the absorbance values are corrected for the dilution effect.

Referring to equation 7, K_a^µ is numerically equal to [H₃O⁺] when [NR]/[HNR⁺] is one. This can be evaluated graphically by converting equation 7 to logarithmic form:

Thus, a plot of the logarithm of the [NR]/[HNR⁺] ratio versus p_CH (-log [H₃0⁺]) has an ideal slope of unity. If this condition holds, the y-intercept gives the negative of pK_a directly. However, usually the experimental slope is not exactly 1.000. Extrapolation from the p_CH's of the measurements to p_CH = zero (which is typically a factor of 10⁶ in concentration for this study) results in a very large error in pK_a^µ. On the other hand, data are obtained on both sides of the x-intercept, which is determined with very little uncertainty. Therefore, better results are obtained by solving the least-squares equation for the x-intercept (the value of the p_CH when [NR]/[HNR⁺] is one).

DESCRIPTION OF THE EXPERIMENT
The pK_a of Neutral Red will be determined in a strictly aqueous environment, by measuring the equilibrium dissociation spectrophotometrically as a function of pH at fixed ionic strength.

PROCEDURE
(Note: This procedure has been designed for use on the Spectral Instruments^TM model SI 440 spectrophotometer, which is equipped with a fiberoptic probe and a CCD detector for convenient and rapid operation. The fiberoptic probes must be handled carefully to avoid damage.)

1. Turn on the system at the power strip, press the ON pad on the temperature controller, and flip the toggle switch on the spectrophotometer module to the ON position. Click 'Cancel' when the password request appears. Click the 'SI 430-440', Windows icon. The SI main front panel display will appear. Click 'Initialize' (lower right). Within a few seconds, an audible internal switch will be heard. Then, click 'Wavelength Range' and make sure it is set to 400 to 720 nm with the lamp cutoff wavelength at 400 nm. Make sure that the 'Precision' is set to 'Normal' (20 readings of the CCD are signal averaged). Allow time for warmup. (The tungsten lamp requires 30 minutes to stabilize; baseline drift may occur otherwise.) Insert a diskette in the A drive.
 

2. To choose wavelengths and evaluate A_HNR+ and A_NR, it is necessary to prepare two indicator solutions--one containing only HNR⁺ and the other containing only NR--for each solution system. Prepare solutions in 50 mL volumetric flasks as follows, using 0.10 M NaCl for all final dilutions:

HNR⁺: 5 mL Neutral Red (provided as a 0.01% solution in 0.10 M NaCl) + 5 mL 0.10 M HCl

NR: 5 mL NR + 5 mL 0.10 M NaOH

Transfer some of each solution to appropriately labelled beakers. (These solutions do not require temperature control.)
 

3. Immerse the fiberoptic probe in deionized H₂O and stir gently with the probe to dislodge any bubbles. Click 'Blank' to acquire the blank spectrum to be used by the software for absorbance calculation. These data are used until the wavelength range is changed or until a new blank is acquired. Click 'Lock Blank' to prevent accidental repeat of the blank measurement. (If a new blank is needed later, first click 'Unlock Blank'.)
 

4. Remove the probe from the water and gently blot the probe with a bed of Kimwipes^TM to remove liquid remaining on the mirror. Gently dry the outside of the probe.
 

5. Acquire and save the spectrum for each solution as follows: Immerse the dry probe in the sample, and click 'Sample'. Then click the red 'Save' box on the lower right of the display, and save the spectrum on your floppy (A drive) using an appropriate filename. (The 'Save' box will return to background color after the spectrum has been stored.).
 

6. After you have obtained the two spectra for each system, click the 'Open' box (next to 'Save') and recall the HNR⁺ spectrum. Under 'Reference Spectrum' click 'Set' and toggle the adjacent reference button to 'On'. Now recall the NR spectrum for the same system. Use the cursor to locate the l_max for each form and the absorbance of each form at each wavelength (two total wavelengths and four total absorbance values). Choose several other wavelengths at which to make absorbance measurements, including a wavelength at which minimal absorption occurs in either species occurs which can be used for baseline correction. (The baseline tends to shift a little during the experiment. To correct for this, the absorbance at 700 nm, for example, where neither form absorbs, can be subtracted from each measured absorbance to improve the accuracy of the analysis.) Click 'Print' on the right panel (not on the Windows File pulldown) to obtain a hard copy. Toggle the reference button to 'Off'.
 

7. Obtain a 100-1000 µL Eppendorf pipettor, and practice using it on the 200 and 1000 µL settings. Determine the exact volumes dispensed by weighing samples of water. If necessary, adjust the micrometer dial to dispense volumes of 0.2000±0.0001 mL and 1.000±0.001 mL. Use the same tip for all calibrations.
 

8. Solutions for K_a^µ determination will be prepared directly in the jacketed vessel. pipet 5 mL NR, 5 mL 0.1 M NH₃OH⁺Cl^- (record the exact concentration), plus 40 mL (2x20mL) 0.10 M NaCl (50 mL total). Immerse the probe and turn on the stirrer. Locate the 'Wavelength'/ 'Absorbance' table on the computer display, and enter the two chosen wavelengths plus 700 nm. Then click 'Sample'. Record the three absorbances from the table, and store the spectrum on the floppy. Click 'Save Setup' to keep the same wavelengths in the table for all spectra.
 

9. Add 2000 µL (2.000 mL) of the standard base (record the exact concentration). Obtain and save the spectrum and record the three absorbances.
 

10. Repeat this procedure using increments which will give the total volumes listed in Table 1. Save each new spectrum to your floppy disk. Use the same pipet tip for all additions of NaOH. Rinse and blot dry the probe and the cell.
 

11. When you have finished with all the additions, click on the "Export Files" button located to the right of the Save button. A window will open called "File Dialog". Select the A: drive and select the folder containing the saved spectra. A list of all your saved files should appear. Using the shift key and the left-mouse button, select all the spectra files and click "OK." A new window will open which will give you the option of saving the files in either a text or excel spreadsheet format. Choose the one most applicable to you.
 

12. When you have completed all measurements and created your spreadsheet file(s), ask your TA if the spectrometer is to be shut down. If so, click 'File' and 'Close' in the upper left corner of the display. When the Windows descktop appears, click 'Start' and 'Shut Down'. Answer 'Yes' to the query. Turn off the spectrophotometer module, the water bath, and the power strip.
 

Table 1. Suggested total volumes (in mL) of standard 0.1 M NaOH.
 

DATA ANALYSIS
1. Derive equation 12 in the Introduction section of your report.

2. Correct all absorbance readings for the baseline offset at 700 nm. Then correct for dilution by multiplying by the ratio of the total volume to the initial volume.

3. Use equation 12 to calculate the [NR]/[HNR⁺] ratio resulting from each addition of standardized NaOH. (Omit the data for 0.000 mL.) For Systems 2 and 3, use the data for both wavelengths. Omit the l_max for NR. (In water, NR tends to form aggregates (7), leading to a complication in the analysis of the data due to the change in optical properties of the dye upon aggregation. Why does HNR⁺ not aggregate?)

4. Calculate the concentrations of buffer species (NH₃OH⁺ & NH₂OH. Calculate [H₃O⁺] from the buffer properties.

4. Determine the pK_a^µ for Neutral Red in each system and estimate the error limits in the determination by a graphical method (equation 13).

5. Consult reference 1 or another suitable source for the activity coefficents of H₃O⁺ and HNR⁺, and calculate the thermodynamic K_a for this indicator and estimate the error limits of this measurement and the correction for non-ideal activities in the system.
 

DISCUSSION AND CONCLUSION
What is an indicator and how do they work? How do the values of the pK_apK_a's of indicators determine their use? How do uncertainties in the pK_a values of an indicator translate into uncertainties in experiments that use them? How important are corrections for activities in titrations? What theories exist for the estimation of activity coefficients in electrolytes? How well do they work?

REFERENCES
1. Harris, D.C. Quantitative Chemical Analysis, 5th Ed., W.H. Freeman: New York, 1999, p 180.
2. van Stam, J.; Depaemelaere, S.; De Schryver, F. J. Chem. Educ., 1998, 75, 93-98.
3. Hartley, G.S.; Roe, J.W. Trans. Faraday Soc., 1940, 36, 101-109.
4. Mukerjee, P.; Banerjee, K. J. Phys. Chem. 1964, 68, 3567-3573.
5. Fernández, M.S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755-1761.
6. Hartland, G.V.; Grieser, F.; White, L.R. J. Chem. Soc., Faraday Trans. 1, 1987, 83, 591-613.
7. Drummond, C.J.; Grieser, F.; Healy, T.W. J. Chem. Soc., Faraday Trans. 1, 1989, 85, 551-560.