Chemical equilibrium molar solubility

STRATEGY First, we write the chemical equation for the equilibrium and the expression for the solubility product. To evaluate Ksp, we need to know the molarity of each type of ion formed by the salt. We determine the molarities from the molar solubility, the chemical equation for the equilibrium, and the stoichiometric relations between the species. We assume complete dissociation. 

STRATEGY As usual, we begin by writing the chemical equation for the solubility equilibrium and the expression for Ksp. The molar solubility is the molarity of formula units in the saturated solution. Because each formula unit produces a known number of cations and anions in solution, we can express the molarities of the cations and anions in terms of s. Then we express Ksp in terms of s and solve for s. Assume complete dissociation. 

The simplest deLnition of solubility is that the solubilfy, of a substance is the molarity of that substance (counting all its solution species) in a solution that is at chemical equilibrium with an excess of the undissolved substance. This implies that there must also be a uniform temperature throughout the system, becaifiteis typically temperature dependent (Ramette, 1981). 

Older biodiesel processes are essentially batchwise. The oil is submitted to transesterification in a stirred-tank reactor in the presence of a large amount of methanol, and base catalyst, mostly NaOH or KOH. An excess of methanol is necessary chiefly to ensure full solubility of triglyceride and keep the viscosity of the reaction mixture low, but also for shifting the chemical equilibrium. A minimum molar ratio methanoktriglyceride of 6 1 is generally accepted [16, 17, 29], The reaction... 

For part (a), we write the appropriate chemical equations and solubility product expression, designate the equilibrium concentrations, and then substitute into the solubility product expression. For part (b), we recognize that NaF is a soluble ionic compound that is completely dissociated into its ions. MgF2 is a slightly soluble compound. Both compounds produce F ions so this is a common ion effect problem. We write the appropriate chemical equations and solubility product expression, represent the equilibrium concentrations, and substitute into the solubility product expression. For part (c), we compare the molar solubilities by calculating their ratio. 

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

PROBLEM STRATEGY This problem is the reverse of the preceding ones instead of finding K p from the solubility, here you calculate solubility from the K p. You follow the three steps for equilibrium problems, but since the molar solubility is not hnmediately known, you assign it the value x. For Step 1, you obtain the concentration of each ion by multiplying x by the coefficient of the ion in the chemical equation. In Step 2, you obtain AT as a cubic in x. In Step 3, you solve the equilibrium-constant equation... 

Thus, if the partial molar volume of solute in aqueous solution is greater than the molar volume of solid solute, an increase in pressure will increase the chemical potential of solute in solution relative to that in the solid phase solute will then leave the solution phase until a lower, equilibrium solubility is attained. Conversely, if the partial molar volume in the solution is less than that in the solid, the solubility will increase with pressure. 

Physico-chemical properties constitute the most important class of experimental measurements, also playing a fundamental role as - molecular descriptors both for their availability as well as their interpretability. Examples of physico-chemical measurable quantities are refractive indices, molar refractivities, parachors, densities, solubilities, partition coefficients, dipole moments, chemical shifts, retention times, spectroscopic signals, rate constants, equilibrium constants, vapor pressures, boiling and melting points, acid dissociation constants, etc. [Lyman et al, 1982 Reid et al, 1988 Horvath, 1992 Baum, 1998]. 

A solution with constant Th(N03)4 concentration of 0.0251 M was mixed with different concentrations of NaF at (25 + 0.1)°C to obtain molar ratios of F to Th of 1 to 10. The solubility and solid phase characterisations of the resulting precipitates were investigated at pH values ranging from 2.52 to 6.30. The solubility results are presented in a tabular form. The authors did not detect any soluble Th at F Th ratios of > 4.0 and the aqueous Th concentrations at F Th ratios of < 1.5 are veiy similar to the Th added initially. The authors report the presence of colloids at F Th ratios of < 3.8. The authors do not report any thermodynamic data, nor can any thermodynamic data be calculated because of the paucity of data points (only 4 points), lack of evidence for the presence of solid phase, and of equilibrium in this system. However, the authors provide convincing evidence, based on chemical, thermogravimetric, and X-ray diffraction analyses, that the compound that precipitates at higher NaF concentrations is NaThFs-HzO. 

In NMP, the nitroxide deactivator should be sufficiently oil-soluble to remain within the particles and participate in the activation-deactivation equilibrium. In case of favorable partitioning towards the aqueous phase or chemical degradation due to side reactions, an increase in the polymerization rate is observed at the expense of the molar mass distribution, which broadens. In ATRP, the transition metal complexes (mainly copper-based activator and deactivator) should be stable enough in the presence of water and should not interact with the various components of... 

The description of phase equilibria makes use of the partial molar free enthalpies, i, called also chemical potentials. For one-component phase equilibria the same formalism is used, just that the enthalpies, G, can be used directly. The first case treated is the freezing point lowering of component 1 (solvent) due to the presence of a component 2 (solute). It is assumed that there is complete solubility in the liquid phase (solution, s) and no solubility in the crystalline phase (c). The chemical potentials of the solvent in solution, crystals, and in the pure liquid (o) are shown in Fig. 2.26. At equilibrium, ft of component 1 must be equal in both phases as shown by Eq. (1). A similar set of equations can be written for component 2. By subtracting j,i° from both sides of Eq. (1), the more easily discussed mixing (left-hand side, LHS) and crystallization (right-hand side, RHS) are equated as Eq. (2). 

A third illustration of the use of FST for open systems involves the effects of cosolvents or additives on the solubility of a solute in a solvent. If one follows the solute solubility curve, at a fixed temperature and pressure, then the chemical potential of the solute at saturation remains constant as it is in equilibrium with the solid solute. Hence, the effect of an additive on the molar solute solubility can be expressed in terms of derivatives of this curve taken at constant T, p, and P2. Using these constraints in Equation 1.43 and taking the appropriate derivatives, one immediately finds (Smith and Mazo 2008)... 

In the cryoscopic method, the fi eezing temperature of a solution is compared with that of the pure solvent. The polymer must be solvable in the solvent at the fi-eezing temperature and must not react with the solvent either chemically or physically. Difficulties may arise Irom limited solubility and from the formation of solid solutions on fi eezing. Application of cryoscopy to polymer solutions is not widespread in literature despite the simplicity of the required equipment. Cryoscopy was reviewed by Glover, who also discussed technical details and problems in concern with application to polymer solutions. A detailed review on cryometers and cryoscopic measurements for low-molar mass systems was recently made by Doucet. Cryometers are sold commercially, e.g., Knauer. Measurements of thermodynamic data are infrequent. Applications usually determine molar masses. Accurate data require precise temperature measurement and control as well as caution with the initiation of the crystallization process and the subsequent establishment of equilibrium (or steady state) conditions. High purity is required for the solvent and also for the solute. 

The standard molar quantities appearing in Eqs. 12.10.1 and 12.10.2 can be evaluated through a variety of experimental techniques. Reaction calorimetry can be used to evaluate AfH° for a reaction (Sec. 11.5). Calorimetric measurements of heat capacity and phase-transition enthalpies can be used to obtain the value of Sf for a solid or liquid (Sec. 6.2.1). For a gas, spectroscopic measurements can be used to evaluate S° (Sec. 6.2.2). Evaluation of a thermodynanuc equilibrium constant and its temperature derivative, for any of the kinds of equilibria discussed in this chapter (vapor pressure, solubility, chemical reaction, etc.), can provide values of ArG° and AfH° through the relations AfG° = —RTln K and ArH° = -Rd aK/d /T). 

Solubility is defined by the thermodynamic equilibrium of a solute between two phases, which in the context of this chapter are a solid phase and a liquid solution phase.The criterion for equilibrium between coexisting phases is that the temperature, pressure and molar free energies or chemical potentials of each individual species in each phase are equal.For a co-crystal, however, the sum of the molar free energies or chemical potentials of each co-crystal component plays a key role in determining phase equilibria. The molar Gibbs energy of the co-crystal A B in equilibrium with a solution phase is given by ... 

The ionization of an ionic salt, such as NaCl (see Equation 11.10), poses a special problem. The un-ionized chemical species in this equilibrium is not dissolved. This is an example of what is termed a heterogeneous equilibrium (i.e., two or more of the equilibrium participants are present in different phases [solid, liquid, gas, or dissolved]). In this case, we have a solid that is not dissolved while everything else is dissolved. Since the solid is undissolved, it does not make sense to refer to its molar concentration. An interesting and important fact about this undissolved solid is that regardless of how much is present, the concentrations of the dissolved ions are constants (at a given temperature). Thus, while the molar concentrations of the ions are real numbers, the molar concentration of the un-ionized species is a nonsensical term. In this case, a special equilibrium constant is defined which uses only the molar concentrations of the dissolved ions in its definition. This special equilibrium constant is called the solubility product constant (K p), which is defined as the mathematical product of the molar concentrations of the ions raised to the power of their balancing... 

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