Thermodynamic Equilibrium Measurements

A thermodynamic equilibrium solubihty assay does not mean a traditional low-throughput assay unchanged in design from decades ago. An accurate thermody- 

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Thermodynamic equilibrium measurements of solid-solution solubilities would be the ideal method for obtaining solid-solution excess-free-energies. Unfortunately, thermodynamic equilibrium states commonly can not be obtained in the laboratory, as solid-solution recrystallisation experiments have indicated (4). SSAS systems with highly soluble solid-solutions capable of rapid recrystallisation, such as the K(Cl,Br) - H O system, are a significant exception to this rule (Glynn and Reardon, Am. L Sci. in press). 

Much efibrt has gone into determining these quantities since they are fundamental to ionic reactivity. Examples include thermodynamic equilibrium measurements for all quantities and photoelectron studies for determination of EAs and IPs. The most up-to-date tabulation on ion thermochemistry is the NIST Chemistry WebBook (webbook.nist.gov/chemistry) [123]. 

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

Besides shear-induced phase transitions, Uquid-gas equilibria in confined phases have been extensively studied in recent years, both experimentally [149-155] and theoretically [156-163]. For example, using a volumetric technique, Thommes et al. [149,150] have measured the excess coverage T of SF in controlled pore glasses (CPG) as a function of T along subcritical isochoric paths in bulk SF. The experimental apparatus, fully described in Ref. 149, consists of a reference cell filled with pure SF and a sorption cell containing the adsorbent in thermodynamic equilibrium with bulk SF gas at a given initial temperature T,- of the fluid in both cells. The pressure P in the reference cell and the pressure difference AP between sorption and reference cell are measured. The density of (pure) SF at T, is calculated from P via an equation of state. 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

Thermal desorption spectra, 171 Thermodynamic equilibrium, phase transitions at, 219 Thermodynamic phase formation, passivation potential and, 218 Time resolved measurements in the microwave frequency range, 447 photo electrodes and 493 Tin... 

It should be pointed out that a finite residual entropy calculated for a substance from experimental data obtained at temperatures extending down to a certain temperature, with extrapolation below that point, may arise either from failure of the experimenter to obtain thermodynamic equilibrium in his calorimetric measurements or from error in the extrapolation. Measurements made under ideal conditions and extended to sufficiently... 

Monolayers of distearoylphosphatidylcholine spread on the water-1,2-dichloro-ethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result... 

The EMF of a galvanic cell is a thermodynamic equilibrium quatity. Thus, the potential of a cell must be measured under equilibrium conditions, i.e. without current flow. The measured EMF must be compensated by a known external potential difference. The measurement of the EMF of a cell is thus based on determination of a potential difference that exactly compensates the measured potential difference so that no current passes. This is easily achieved by the Poggendorf compensation method (see Fig. 3.13). 

Rate measurements on these particles indicate that at 85 °C the rate is equal to 1.11 x 10 2 moles/ksec-g catalyst, when the conversion achieved is only 3.9%. From thermodynamic equilibrium data contained within the article, it is estimated that under these conditions, the isobutylene concentration in the reactor at the exterior surface of the resin may be taken as (0.961)(1.72 x 10"5) moles/cm3. 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

Tice changes of more than 0.6 °C between two measurements after 2 h of MD until 8 h of MD. (Note In the first 2 h the thermodynamic equilibrium is not reached and after 8 h MD comes to the end at which TKC decreases anyway.)... 

The liquid temperature (Tl) corresponding to Xl is measured for practical purposes in two apparatuses known as either the closed or open cup flashpoint test, e.g. ASTM D56 and D1310. These are illustrated in Figure 6.3. The surface concentration (Xs) will be shown to be a unique function of temperature for a pure liquid fuel. This temperature is known as the saturation temperature, denoting the state of thermodynamic equilibrium... 

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