Thermodynamics of the Rhodamine B LactoneZwitterion Equilibrium An Undergraduate Laboratory Experiment Daniel A. Hindtley and Paul G. Seybold Wright State University, Dayton, OH 45435 During the course of study in hoth introductory chemistry and physical chemistry the thermodynamic concepts of enthalpy change, entropy change, and dihbs energy change for a chemical transformation are taught. Unfortunately, these concepts are usually not reinforced in the laboratory by appropriate experiments. A review of physical chemistry laboratory texts reveals primarily thermochemical experiments involving heats of solution and combustion. Thermochromic transformations nrovide an excellent ODportunity to study thermodynamic'properties because the color chanees involved allow one to follow the Droeress of the transformation with temperature. Earlier repor& have described thermochromic svstems (1, 2). An experiment to derive thermodynamic values froma thermochromic equilibrium has been reported (3); however, that experiment reauires svnthesis of the comnound and use of a scannine sp&rophbtometer with thermostatted cells, and the equE lihrium is achieved onlv slowlv (10-15 mint. In the Dresent report, an experiment ii described that uses a comm&ially available dye, attains equilihrium rapidly, employs a simple, single-beam spectrophotometer, and is suitable for hoth physical chemistry and introductory chemistry laboratories. The xanthene dye rhodamine B (RB) exhibits several interesting equilibria. In solution the spectrum of the dye is known to depend on temperature, solvent, and concentration ( 4 4 . In protic solvents RB exists as an equilihrium mixture of a colorless lactone (L) and a colored zwitterion (Z).
sary to have a reference standard. Elsewhere we suggest a molar absorptivity of 13.0 X lo4 dm3Imol.cm for the pure Z form of ~ ~ ; i o w e r v a l ucan e s he taken to indicate that some of the dye is in its L form (7). From this it is possible to calculate the equilibrium constant, K, for the L ==Z equilibrium, K = [ZlI[LJ (1) From the variation of K with temperature, the enthalpy change AHo, entropy change ASo, and Gihbs energy change AGO of the L * Z equilibrium can he determined. Experimental Procedure Use of a short-chain alcohol such as ethanol, 1-propanol, 2-propanol, 1-hutanol, or 2-methyl-1-propanol as the solvent is recommended. RB dissolves slow1.y in lonper c h a i ~ alcohols, hut the dissolution can be speedehuphy ii~mngX secondary or tertiaxy aIcoho1~are need, a trace of a Lewi base (e.g., triethylamine) should be added to the solution t, avoid contamination by the RB cation. Prepare a 50 mL -8.0 X M stock solution of RB (HC salt, MW = 479.02).' Dilute the stock solution 11100 t prepare a working solution at -8.0 X 10-6M RB.2 A sinple-beam Bausch and Lomb Spectronic 20 spectra photomiter was used in our experiment, and the foilowin instructions refer to this instrument. Other visible spectra photometers can be substituted with only minor modifica tions of the procedure. Determine the wavelength of maximum absorption (or minimum transmission) by scanning the -8.0 X 10-6M RB solution from 530 nm to 560 nm at 5-nm intervals. It is easiest to read per cent transmittance (%T) on the Spectronic 20 and convert to absorbance (A) using A = -lag (%T/100)
The position of the equilibrium has heen shown todepend on hoth solwnt hvdruecn-hond donatinr abilitv and solvrnt dielectri~/~olariz~hili& characteristics 76, 7).A S temperature increases the equilibrium shifts toward the less polar lactone. Low concentrations of dye are required because at higher concentrations two other forms of RB, the cation and the dimer, appear.
The O%T and 100%T values must he reset at each wavelength on the Spectronic 20. With the spectrophotometer set on the wavelength of maximum ahsor~tion,insert a suitable temperature prube7inta thesoiutivn and record its temperature and 17: Insert the sample w l l into an ice bath to loe,er its temperature. After a minute, remove the cell from the bath, dry it on the outside, and place it hack in the sample compartment. Record % T a t 15 OC and 20 "C as the temperature rises. Next, heat the solution to about 60 OC by carefully inserting the sample cell into a hot water bath. Avoid overheating,
'
Rhodambe B Cation
Both of these forms are, like the Z form, highly colored, and can interfere with the measurements. The strong visible absorption of the zwitterion provides a convenient handle with which to follow that L + Z equilihrium. In order to determine the concentration of Z i t is neces362
Journal of Chemical Education
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Rhodamine B (HCI salt) is available in a range of purities. Laser grade RB (99 %), Eastman Kodak Company,was used in these experiments. Students are advised to wear gloves. RB can stain not Only clothes and hands, but also glassware and analytical balances. Chemical stain remover, for example, Erada-Stain (Cambridge Chemical Products), will remove most stains if applied promptly. A Fisher Scientific Company electronic digital thermometer with a Yellow Springs Instrument thermistor probe No. 427 was used here.
1V/T(K)
Figwe 1. Absorption Spectra of modarnine B in 1-butanol from 15 OC to 55 OC.
which leads to solvent evanoration. Remove the cell, d m . it.. and insert it into the sample compartment. With the temDerature orohe in dace. monitor 90T at 5 "C intervals as the temperatke falls'from 55 'C to 30 OC. There should be enough time to replace the RB solution and perform a second experimental analysis. Frequent checks of O%T and 100%T will correct any baseline drift of the instrument. Several improvements in the above experiment can he made if desired. Desiccation of the dye and distillation of the solvents will improve the results. Use of a scanning spectrophotometer with thermostatted cells4 will produce absorption spectra similar to those found in Figure 1.
Wavelength (nrn)
-
Figure 2. Arhenius plot for the hDdarnlne B L = Z equilibrium in 1-butanoi.
Table 1. Per cent Zwltterlon (Z),Equtlibrium Constant K, and Glbbs Energy AGD tor the RB L Z Equlllbrlum In Several Solvents at 25 "C Solvent
%Z
K
AG"(Jlrnol)
Analysis ol Data From Beer's law the ahsorbance A is given as A = .be
(3)
where6 is themolarahsorptivity, b is the cell path length (1.0 em), and c is the concentration in m o l L The fraction of dye present as Z can be determined from the observed absorbance if a reference 100% Z standard is available. Elsewhere we have determined the molar absorptivity of the pure Z form to be 13.0 X 104 Llmol.cm, based on studies of RB in the strong hydrogen-bond-donating solvent trifluorethanol at 15 OC (8).The 10090 % absorbance standard A(1004) can he calculated using this r value and the known concentration c in eq 3. (For less pure dye samples A(100%) can be determined by dividing the observed absorbance of RB a t 25 OC by the fraction Z for that solvent given in Table 1). A correction should be included for expansion of the solvent with temperature. Reference 9 gives densities of alcohols a t different temneratures. Over the tem~eratureranee employed (15 "C-55 " C ) it is reasonable to assume a linenr denendence of denaitv on temoerature. The Z fracrion at each temperature is c~lculatedi s
where p(15 OC) and p(T) are the solvent densities a t 15 "C and temperature T , respectively. The fraction of lactone is calculated as
[L]= 1 - [Z] The equilibrium constant K is calculated using eq 1.
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A Varian 2300 UVIVISINIR scanning spectrophotometer wilh water-jacketed cuvenes (NSG Precision Cells. Hicksville, NY 11801) connected to a Haake temoerature bath was used.
Arrhenius Analysis All students should he able to perform this analysis. AGO, the standard Gihbs energy change, is calculated a t each temperature as where R is the gas constant and T is in kelvins. Also AGO
= AH' -
TAS"
(7)
Solving for In K one obtains In K
= ASDIR- (AHoIR)(lIT)
(8)
If AHo and AS0 are approximately constant over the temperature range examined, a plot of in K against 1/T should yield a straight line with slope equaling -(AHoIR) and intercept equaling ASoIR. Figure 2 gives such a plot for RB in 1hutauol. Regression Analysis If students have access to a computer regression program, a more accurate analysis is possible. Over the temperature range examined the dependence of the equilibrium constant can he expressed as Regression analysis can be employed to determine the coefficients A , B , and Cfrom afit of the experimental data. From eq 6, AGO = -RTA -RE
- RCIT
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Table 2. Standard Enthalpy and Entropy Changes lor the RB L =?Z Equlllbrlurn in Several Solvents, at 25 'C Arrhenius Analysis AH*(kJ/mol) AS'(J1mol.K)
Solvent
ethanol
1-propan01 2-propano1 l-butanal 2-methyl1-propanol
-18.9 -19.3 -26.9 -25.5 -26.8
Regression Analysis AH0(kJ/mol) ASO(J/rnol.K)
-56.2 -59.5 -97.8 -84.1 -88.1
-18.0 -19.8 -24.8 -23.7 -24.8
Why is the Z form of RB highly colored and the L form colorless? Discuss this in terms of the molecular structures. The zwitterion is apparently stabilized by a hydrogen bond from the alcohol solvent S (6-8)
-53.2 -61.2 -90.8 -78.2 -81.0
Why does theequilibrium shift toward the lactone as temperature increases? Discuss the magnitudes and signs of AGO, ASD, and AHo. If hoth forms of analysis were performed, was the assumption of constant AS* and AHa justified? Whatwere the sources of error in this experiment?
Since (10)
Equlpment and Chemicals Rhodamine B1 Alcohol solvents Electronic digital thermometer with thermistor probeS Bausch & Lomb Speetronie 20, or comparable spectrometer Sample cells
then And from eq 7, AH" = -RB - 2RCIT
(13)
Students should be asked to confirm these mathematical relations. AHo,AS0, and AGO can be determined for each temperature using eqs 13,12, and 7. Results Values obtained for %Z, K and AG" a t 25 O C are shown in Table 1 (8). Enthalpy changes AHo,and entropy changes ASo, for the RB L + Z equilibria in the recommended alcohols are shown in Table 2, which lists values obtained hoth from the Arrhenius analysis and the regression analysis a t 25 "C. Our experience indicates that students should he able to achieve values within 5% of the values shown. Dlscusslon This experiment was tested in our undergraduate physical chemistry laboratory. The experiment was easily completed
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in three hours and proved to he one of the more popular experiments. Students were asked to consider the following points in their discussions.
Journal of Chemical Education
Acknowledgment We thank Rubin Battino for helpful discussions on this topic. We also thank the donors of the Petroleum Research Fund, administered hy the American Chemical Society, for partial support of this work. The Varian 2300 spectrometer was p u r c h a s e d t h r o u g h N S F f u n d i n g g r a n t NSF#PRM8111214. 1. McGBI. J.J. Chem.Edue. 1971. 1971.4S.ZSO. Spears, L.G.. G., Jr.: Jr.; Soeara. Speara, L. G.dJ . Chrm. Educ. 1981.61.252. 2. Soears. 3. Byme. J.P. P. j. J. chel Chem.Edue. L97R.55.267. 4. Rametk. RamefkR R.. W.;Sandell, W.; Sa E.B . J . Am. Chem. Soc. 1356. m8.4872. 5. Kuhn. RNofuruira. 1932,20,618. 6. Rorenthal. I.; Peretz, P.; Musrksf, K. A. J . Phys. Chem. l979.83.350. 7. Hinck1ey.D. A.:Seybold,P. G.;Borria,D.P.Specrrarhim.Acto l986.42A.747. 8. Hinckley. D.A,; Seybold. P. G., to be published. 9. Wilhoit, R.C.;Zwolinski, B. J. J.Phys. Cham. Ref. Dota I973.2.Suppl. No. 1. lo. Atkim. P. W.Physied Chmiatry, 2nd d.; W. H. Freeman: Sanfianeism. 1982: pp 166,176.
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