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Experiment 8

Thermodynamics of the Rhodamine B Lactone-Zwitterion Equilibrium

By Maritza Adom & Nelia Rahmany

Introduction

-Rhodamine B is used for staining proteins in the biochemical field

-Prominent characteristics:

-Fluorescent in a basic environment

-Highly aromatic

-Relatively affordable

-Temperature-dependent color change

(thermo-optical capacity)

Introduction

A high [L] ratio causes the solution be colorless

A high [Z] ratio causes the solution to take a bright fushia-red hue

[L] & [Z] Forms

Zwitterionic form carries covalently attached cation and anion, or both positive and negative charges

Lactone form is characterized by a lactonic C-O bond forming a fifth ring in the compound

[L] & [Z] Forms

Molecular Interactions providing Thermo-optical Effect

-The equilibrium between form [L] and [Z] isdependent on the temperature of the solution.

*Increase in temperature:

-Ethanol loses its proton and is unable to act as a H bond donor.

-Inhibition of the selective interaction between ethanol and Rhodamine B

-Sovent cannot stabilize the charges which forces the Carbonyl group to take a more stable conformation: Neutral lactonic C-O bond.

-Shifts the equilibrium towards [L].

*Decrease in temperature:

-Ethanol acts as a H bond donor/acceptor

-Increased selective interaction between ethanol and Rhodamine B

-Ethanol stabilizes the Carbonyl group, allowing for the +/- charges of the Zwitterion to coexists

-Shifts the equilibrium towards [Z]

Molecular Interaction

0.0248 g of the Rhodamine B dye

Experimental

1/100 dilution with Ethanol

Experimental

-Weight mass of solid Rhodamine B dye

-Preparation of a stock solution of approximately 8.00x10-6 M in Ethanol

Using The Vernier LabQuest2:

-Calibration:

Blank the SpectroVis Plus using a cuvette filled wih Ethanol

-Full Spectrum Mode:

Add Rhodamine B solution (Room Temperature) to cuvette and Record maximum wavelength of its spectrum.

-Time Based Mode:

-Heat Rhodamine B solution to 60.0 ⁰C in a water bath.

-Transfer to a cuvette and inserted into the spectrophotometer

-Add the Vernier temperature probe to the cuvette

-Record temperature and corresponding absorbance at 2.0 ⁰C intervals as the is solution cooled, to room temperature (down to 25.0 ⁰C or below)

Full spectrum mode Settings:

Sample Time: 50 ms

Wavelength Smoothing: 1

Samples to Average: 6

Wavelength range: 380-900 nm

Calculations

1. Beer's Law

A(100%) = ε*b*C

where A(100%): Standard absorbance for Rhodamine B

b: Spectroscopic path length (b=1 cm)

ɛ: molar absorptivity specific to the Zwitterionic form of Rhb (ɛ = 13.0 X 104 L/mol•cm)

2. Finding [Z] using Relative Absorbance

[Z]= A(T) / (A(100%)

where [Z]: Fraction of Zwitterion in the solution

A(T): Absorbance Recorded from the SpectroVis

3. Relationship between [L] and [Z]

[L] = 1-[Z]

where [L]: Fraction of Lactone in the Solution

5. Finding the Equilibrium Constant

K= [Z] / [L]

where K: Equilibrium constant

Calculation of Thermodynamic Values

Quantification of Thermodynamic Values

6. Gibbs–Helmholtz Equation

∆G° = —RT ln K

where ∆G°: Gibb’s Free energy

R: Ideal gas law constant

T: Absolute temperature

K: Equilibirum Constant

7. Clausius-Clayperon Relationship

ln(K)= [(∆S°)/R] - [(∆H°)/RT]

where ∆S°: Entropy at equilibrium

∆H⁰: Enthalpy at equilibrium

Results

Preparation of the Stock Solution

Results & Discussion

Note: The final concentration was kept low to prevent the formation of other possible forms of the Rhodamine B complex:

-Cation form (+1 charge on Nitrogen)

- Dimeric form (two Rhodamine B molecules bridged together)

Application of Beer's Law to find Standard Absorbance

Standard Absorbance

-Beer’s law can only be applied because thermo-optical capacity of Rhodamine B

-The A(100%) computed for the standard solution at room temperature is relatively high which means:

-Zwitterionic form proeminent at room temperature

-[Z] form includes conjugated double bonds (notice the center ring double bond) while the Lactone form includes isolated double bonds.

-Conjugated double bonds absorb the visible light, the electrons contained in the molecule increase in energy level which in turn causes the red color associated with the [Z] form.

Equilibrium Analysis using recorded Temperature and Absorbance

Fraction of [Z], [L], and constant K

-Ethanol is a polar solvent with H-bond donor/acceptor capacity

-H-bonds stabilize the [Z] form, which explain why [Z] is much higher than [L] at 25 ⁰C -Data confirms stated hypothesis that as temperature increases, the equilibrium shifts toward [L]

- Experimental values are fairly close to literature,

which bodes well for the rest of the analysis

%error [Z] = 1.42 %,

%error K = 4.61 %

Thermodynamics Quantities

Thermodynamic: Finding ∆G⁰, ∆H⁰, & ∆S⁰

-Claurisius-Clapeyron Relationship

-Gibbs–Helmholtz Equation & Summarized Thermodynamics

ln(K)= [(∆S°)/R] - [(∆H°)/RT]

Plotting ln(K) vs 1/T will give us the following linear equation:

y = 861.25x - 2.0791

where m= (-∆H⁰)/R (m = 861.25)

b= (∆S°)/R (b = -2.0791)

Thus, ΔH°= -7.16 x10^3 J/mol

ΔS°= -17.3 J/K•mol

Entropy ( ΔS°):

-Entropy is a measure of how chaotic the system

-Since the solvent is polar and stabilizes the [Z] form, then the entropy

for reaction would probably be negative as the disorder is decreasing

-As the totals moles of the solution or phases are not changing,

entropy should very small

∆G° = —RT ln K

ΔG(25⁰C)= -2.05x10^3 J/mol

Gibbs Free Energy ( ΔG°):

- Negative Free energy means that the reaction is spontaneous

-The reaction occurs readily at room temperature because of the protic solvent and its stabilizing effect on the [Z] form

-When temperature increases and the solvent loses its H-donating capacity, the reaction occurs much less readily

Enthalpy ( ΔH°):

- Negative enthalpy means the system releases heat to the surroundings

-The reaction is Exothermic ( [L] <=> [Z] + Heat )

-Increasing the temperature results in the reverse reaction towards [L] form

This was verified experimentally and agreed with the hypothesis

Experimental Errors

Potential Errors

-The same temperature value sometimes showed multiple absorbency values. Recording the wrong temperature could cause error.

-Miscalibration of the analytical balance used. This experiment utilized s very small concentration, thus even the slightest instrumental error could have impacted final results.

-The volatility of ethanol could also have impacted the final concentration, as heating the cuvette over 60.0 ⁰C or exposing the solvent could have caused some of the solvent to evaporate from the solution which would have thrown off the equilibrium.

*Special Note: Malfunction of the LabQuest2 forced us to leave the Rhodamine B in a hood until the following week. Lack of light protection for the solution might have impacted its thermo-optical capacity.

This could have potentialy increased our error

Conclusion

At equilibrium, the chemical dye Rhodamine B is present as a mixture of its Lactone form and its Zwitterion form.

This experiment tested our knowledge of:

Beer’s Law

Protic solvent association

Fundamentals of reaction equilibria

Gibbs–Helmholtz equation

Clausius-Clayperon relationship

The experiment was deemed quite successful, as the experimental data of absorbance at a given temperature followed le Châtelier’s principle:

Increase in temperature in an exothermic process (ΔH°= -7.16x103 J/mol) shifted the equilibrium towards the reactants (Lactonic form)

The relatively low percent error obtained for both experimental values of

[Z] (%error[Z] = 1.42 %) and K (%errorK = 4.61 %) also hint at accurate results

References

References

1.Department of Chemistry and Biochemistry. CHEM 336: Physical Chemistry I Laboratory Manual. George Mason University: Fairfax, VA, 2018.

2. Taylor and Francis Group. (2018) Chemical Information Classification: Rhodamine B. CRC Handbook of Chemistry and Physics. CRC Press.

3. Hinckley, D. A., and Seybold, P. G. (1987) Thermodynamics of the rhodamine B lactone zwitterion equilibrium: An undergraduate laboratory experiment. J. Chem. Educ. ACS Publications.

4. BRAND GMBH CO KG. (2012) Product Information: Volumetric instruments according to USP tolerances. BLAUBRAND® volumetric instruments with USP certificate. BRAND GMBH CO KG ⋅ Otto-Schott-Straße 25.

5. Jorgensen, W. L., Briggs, J. M., and Contreras, M. L. (1990) Relative partition coefficients for organic solutes from fluid simulations. J. Phys. Chem. ACS Publications.

6. Government of Canada (2017) Volume correction factors-ethanol (ethyl alcohol anhydrous). Measurement Canada. Innovation, Science and Economic Development Canada.

7. Baltisberger, J. (2011) Thermochemistry/Spectroscopy. Chemical Dynamics, Thermochemistry, and Quantum Chemistry. Berea College Publishing.

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