The aim of the experiment was to determine the enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) for the Rhodamine β-Lactone Equilibrium. To accomplish this, a manual spectrophotometer was used to determine the maximum absorbance of a sample of Rhodamine β-Lactone. The absorbance of the sample was then measured over a range of temperatures from which the equilibrium constant (K), enthalpy (ΔH), entropy (ΔS) and Gibbs free energy were then calculated.
The xanthene dye Rhodamine β-Lactone can undergo multiple equilibria. “In protic solutions, Rhodamine β-Lactone exists as an equilibrium mixture of a colourless lactone and a coloured zwitterions.”  as shown in appendix 1. The position of the equilibrium depends on solvent hydrogen-bond donating ability and solvent polarisability . The equilibrium also shifts under an increase in temperature to the less polar lactone. This thermochromic transformation allows for the study of the thermodynamic properties of the equilibrium as it progresses.
Refer to Manual for CHEM 2701: Chemical Reactivity Experiment 2: Thermodynamics of the Rhodamine β-Lactone Zwitterion Equilibrium, pages 28-31.
The mass of Rhodamine β-Lactone required to make up the stock solution, specified on page 30 of Manual for CHEM 2701: Chemical Reactivity Experiment 2: Thermodynamics of the Rhodamine β-Lactone Zwitterion Equilibrium, was calculated in the following way: * Using the relationship n=CV, the number of moles were calculated using the listed volumes and concentrations. * The required masses were then calculated using the following relationship: n=mMr. The absorbance at 100% concentration of Rhodamine β-Lactone zwitterion was then calculated using Beer’s Law (A=εbc), in accordance with the manual. The full calculations can be seen in Appendix 3.
It should be noted here that from the above calculation, A100% was found to be above 1, and as a result the stock solution was diluted by a further factor of ten, i.e. 1100→11000, for the calculation of the maximum absorbance. However for remainder of the experiment, a 1100 dilution was used. The maximum absorbance was then determined using a manual spectrophotometer to scan the stock solution across a range of wavelengths (450nm-650nm), figure 1 (Raw data shown in appendix 3), the result of which was confirmed using a UV/Vis spectrophotometer, figure 2 and appendix 4. In order to determine the zwitterion concentration in the sample, a ratio between the absorbance at a given temperature (AT) and the absorbance at 100% concentration of Rhodamine β-Lactone zwitterion (A100%) was calculated, with the change in density of the solution with temperature taken into consideration as can be seen below and further explained in appendix 2. Z=AT×ρ15°cA100%×ρT°c
From this the fraction of lactone was calculated and consequently the equilibrium constant (K) was determined. L=1-Z
This value calculated was for all temperatures and their corresponding absorbances, show in figure 2. The Gibbs free energy (ΔG) for each value of K was then found using the relationship ∆G=-RTlnK, from which a plot of ΔG against temperature was made, figures 3 and 6. The enthalpy (ΔH) and entropy (ΔS) of the equilibrium were then able to be determined by using the relationship lnK=∆S°R-∆H°R1T plotting the lnK against 1T (figures 4 and 7), from which the slope was used to calculate ΔH and the vertical intercept was used to calculate ΔS. The processes used to calculate K, ΔG, ΔH and ΔS were all repeated using the duplicated data, as specified on page 30 of the Manual for CHEM 2701: Chemical Reactivity Experiment 2: Thermodynamics of the Rhodamine β-Lactone Zwitterion Equilibrium. The final results from these calculations (ΔH and ΔS) were then averaged across the two data sets.
Figure 1: Measure of Absorbance of a sample of Rhodamine β-Lactone across a range of...