Equilibria solution-solid solvent

By the second law of thermodynamics, when a solution is in equilibrium with solid solvent, the solvent vapor pressures of the two must be equal. Therefore, for a solution... 

Another consequence of lowering of vapour pressure is that the freezing point of the solution is lower than that of the pure solvent. The freezing point of a solution is the temperature at which the solution exists in equilibrium with solid solvent. In such an equilibrium, the solvent must have the same vapour pressure in both solid and liquid states. Consequently, the freezing point is the temperature at which the vapour pressure curves of the solvent and solution intersect the sublimation curve of the solid solvent that is, points C and D, respectively, in Fig. 2.8. The freezing point depression is T-To = ATf. An expression for freezing... 

According to equation (3.7.20), under the equilibrium conditions between the solution, solid, solvent, and vapour, the partial pressure over the solution is... 

The equilibrium between solid solvent and solution was considered in Section 13.6. The same equilibrium may be considered from a different point of view. The word solvent as we have seen is ambiguous. Suppose we consider the equilibrium between solute in solution and pure solid solute. In this condition the solution is saturated with respect to the solute. The equilibrium condition is that the fi of the solute must be the same everywhere, that is... 

Undersaturated The same quantities of solute and solvent are mixed, as for the above ease, but the system is then heated for about 20 min above the required temperature (if solubility inereases with temperature) so that most, but not all, of the solid is dissolved. The solution is then eooled and agitated at a given temperature for a long period, to allow the exeess solid to deposit and an apparent equilibrium to be reaehed. 

The freezing-point of a solution is the temperature at which the solution is in equilibrium with ice, the latter term being used in its general significance of frozen, or solid, solvent. 

The addition of solutes decreases the freezing point of a solution. In the solution, solvent molecules collide with crystals of solid solvent less frequently than they do in the pure solvent. Consequently, fewer molecules are captured by the solid phase than escape from the solid to the liquid. Cooling the solution restores dynamic equilibrium because it simultaneously reduces the number of molecules that have sufficient energy to break away from the surface of the solid and increases the number of molecules in the liquid with small enough kinetic energy to be captured by the solid. 

Crystallization involves formation of a solid product from a homogeneous liquid mixture. Often, crystallization is required as the product is in solid form. The reverse process of crystallization is dispersion of a solid in a solvent, termed dissolution. The dispersed solid that goes into solution is the solute. As dissolution proceeds, the concentration of the solute increases. Given enough time at fixed conditions, the solute will eventually dissolve up to a maximum solubility where the rate of dissolution equals the rate of crystallization. Under these conditions, the solution is saturated with solute and is incapable of dissolving further solute under equilibrium conditions. In fact, the distinction between the solute and solvent is arbitrary as either component can be considered to be the solute or... 

Equation 1 implies that solubility is independent of solvent type, and is only a function of the equilibrium temperature and characteristic properties of the solid phase. In real systems the effect of non-ideality in the liquid phase can significantly impact the solubility. This effect can be correlated using an activity coefficient (y) to account for the non-ideal liquid phase interactions between the dissolved solute and solvent molecules. Eq. 1. then becomes [7,8] ... 

This relationship constitutes the basic definition of the activity. If the solution behaves ideally, a, =x, and Equation (18) define Raoult s law. Those four solution properties that we know as the colligative properties are all based on Equation (12) in each, solvent in solution is in equilibrium with pure solvent in another phase and has the same chemical potential in both phases. This can be solvent vapor in equilibrium with solvent in solution (as in vapor pressure lowering and boiling point elevation) or solvent in solution in equilibrium with pure, solid solvent (as in freezing point depression). Equation (12) also applies to osmotic equilibrium as shown in Figure 3.2. 

Figure 16.5. Supersaturation behavior, (a) Schematic plot of the Gibbs energy of a solid solute and solvent mixture at a fixed temperature. The true equilibrium compositions are given by points b and e, the limits of metastability by the inflection points c and d. For a salt-water system, point d virtually coincides with the 100% salt point e, with water contents of the order of 10-6 mol fraction with common salts, (b) Effects of supersaturation and temperature on the linear growth rate of sucrose crystals [data of Smythe (1967) analyzed by Ohara and Reid, 1973],...

Adsorption isotherms are used to quantitatively describe adsorption at the solid/ liquid interface (Hinz, 2001). They represent the distribution of the solute species between the liquid solvent phase and solid sorbent phase at a constant temperature under equilibrium conditions. While adsorbed amounts as a function of equilibrium solute concentration quantify the process, the shape of the isotherm can provide qualitative information on the nature of solute-surface interactions. Giles et al. (1974) distinguished four types of isotherms high affinity (H), Langmuir (L), constant partition (C), and sigmoidal-shaped (S) they are represented schematically in Figure 3.3. 

Considering freezing, equilibrium requires that the chemical potential of the solvent in solution equal that of the (pure) solid solvent ... 

The equilibrium (51.3) (Figure 51.2(b)) which exists after addition of the solute (Figure 51.2(a)) to the pure solvent is between the aqueous solution formed on the dissolution and the solid (solvent) deposited on freezing ... 

Consider now the equilibrium at temperature, T between solid solvent and solvent in a liquid solution... 

On cooling dilute solutions, the solvent usually separates as the solid phase. There are two phases at equilibrium solid solvent and liquid solution with a solute. Assume that the solute does not dissolve in the solid solvent. The thermodynamic approach to this equilibrium is identical to the one for saturated solutions as described in Section 3.1.1. Following the same reasoning as in Section 3.1.1, Equation (3.1) to Equation (3.6) can be applied to the solvent (component 1), and the freezing point of an ideal solution becomes ... 

Equilibrium saturated solution change in composition of the solid phase. Relation between temperature coefficient of solubility and heat of solution—application of the principle of Le Chaielier. Solubility in relation to nature of solute and solvent like dissolves like. ... 

Freezing poirU of solutions. The freezing point of a solution is always lower than that of the pure solvent. This may be seen at once from Fig. 26, which differs from Fig. 25 only by the addition of the vapour pressure curve CNF of the solid solvent. The abscissa of P, the intersection of CP and is the freezing point Tq of the pure solvent, and the abscissa of the corresponding intersection N is the freezing point of the solution, for at these points the solid solvent is in equilibrium with solvent and solution... 

In Zone A, at monomer concentrations below the equilibrium concentration solid polymer dissolves. This is equivalent to the dissolution of a crystalline low molecular wt. compound in a good solvent. In Zone C the solution is super-saturated, it is above the stability limit, spontaneous nucleation occurs and polymer precipitates from the clear solution. There is a Zone B, about 4—8% above the equilibrium concentration of formaldehyde, where super-saturation is insufficient to cause spontaneous precipitation of polyoxymethylene but where seeds or nuclei of polyoxy-m ethylene can grow when added to the clear solution and can increase in weight and molecular weight. This is the desirable range for the preparation of high molecular weight polyoxymethylene in hydroxylic media. 

Pure solid solvent coexists at equilibrium with its characteristic vapor pressure, determined by the temperature (Section 10.4). Solvent in solution likewise coexists with a certain vapor pressure of solvent. If solid solvent and the solvent in solution are to coexist, they must have the same vapor pressure. This means that the freezing temperature of a solution can be identified as the temperature at which the vapor-pressure curve of the pure solid solvent intersects that of the solution (Fig. 11.12). As solute is added to the solution, the vapor pressure of the solvent falls and the freezing point, the temperature at which the first crystals of pure solvent begin to appear, drops. The difference ATf = T/ — Tf is therefore negative, and a freezing-point depression is observed. 

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