Supersaturation molar

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

In this chapter, you learned about solutions. A solution is a homogeneous mixture composed of a solvent and one or more solutes. Solutions may be unsaturated, saturated, or supersaturated. Solution concentration units include percentage, molarity, molality, and mole fraction. The solubility of solids in liquids normally increases with increasing temperature, but the reverse is true of gases dissolving in liquids. The solubility of gases in liquids increases with increasing pressure. 

The possibility that a separate BaC03 phase precipitated in the speed runs (at levels undetectable by x-ray diffraction) also must be noted. Since calcite is approximately three times as soluble as witherite (BaC03), the latter can precipitate from a solution at equilibrium with calcite only if the molar ratio of Ba2 to Ca2 exceeds 1 3. Starting compositions for the speed runs had Ba2 /Ca2 ratios from 3.6 x 10-if to 3.9 x 10 3 and final compositions from 2.6 x 10 3 to 2.3 x 1(T2. To exceed the solubility of witherite during these runs, in which the rapid decarboxylation supersaturates the solution relative to calcite, minimum supersaturations ranging from 14 to 130 with respect to calcite would have been required. Such supersaturations would appear difficult to achieve by decarboxylation, especially in the presence of calcite seed. Viewed in another fashion, the C032 saturation concentration of 0.11 g calcite per 200 ml solution at the start of a run is 9.1 x 10 7M. After decarboxylation to atmospheric levels of C02 and precipitation of calcite... 

There are many ways of expressing the relative amounts of solute(s) and solvent in a solution. The terms saturated, unsaturated, and supersaturated give a qualitative measure, as do the terms dilute and concentrated. The term dilute refers to a solution that has a relatively small amount of solute in comparison to the amount of solvent. Concentrated, on the other hand, refers to a solution that has a relatively large amount of solute in comparison to the solvent. However, these terms are very subjective. If you dissolve 0.1 g of sucrose per liter of water, that solution would probably be considered dilute 100 g of sucrose per liter would probably be considered concentrated. But what about 25 g per liter—dilute or concentrated In order to communicate effectively, chemists use quantitative ways of expressing the concentration of solutions. Several concentration units are useful, including percentage, molarity, and molality. 

Finally, the term A/to can be expressed as a function of the molar fractions C and Coo (he. concentration, or activity, or partial pressure, depending on the system), the concentrations near the growing surface, and around an infinite planar surface of the sohd formed, respectively. The supersaturation parameter S is generally defined as the ratio C/Coo, thus ... 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

Note. V is the molar volume, JVyi is Advogadro s number, is the equilibrium concentration, D is the diffusion coefficient, sub-s surface, hHfiB the heat of fusion, t) is the Damkohler number. Ah is the thermal conductivity, i die area shape factor for surface nuclei , y, is the distance between steps, n is the equilibrium surface concentration, p = 1 - o-JS is one minus the maximum surface supersaturation divided by the solution supersaturation, and p is the density. ihG - pl- fPMpAkBT In S)... 

The high prevalence of oxalate containing renal (tubular) and urinary tract calcifications is related to the low solubility of the oxalate-calcium salt. High urine oxalate excretion increases urine calcium oxalate supersaturation and, therefore the risk of crystal formation in tubular fluid and urine. In human urine, calcium concentration is about ten fold higher than oxalate on molar base. Relatively modest increases in urine oxalate excretion will have significant effects on urine supersaturation [49], especially in patients with hypercalciuria where calcium is even in greater excess of oxalate. Nevertheless, most people do not suffer from renal calcifications [50-54], suggesting that renal protection mechanisms exist. 

In contrast, several quantities are commonly used to measure the supersaturation. Some of these are P, Ln P, (P - 1) and (C - C ), where P = C/C and C is the concentration of the compound (i.e., TAG) in the solution (i.e., vegetable oil in a solution) at a given temperature. To achieve crystallization, C always must be higher than the concentration at saturation at the same temperature (C ). In the case of supersaturation, the units used to calculate C and differ according to the character of the solute, i.e., electrolyte or nonelectrolyte. The most common units used with TAG are molarities, molalities, and molar fractions. 

Silver chloride illustrates that the relative supersaturation concept is imperfect. This compound ordinarily forms as a colloid, yet its molar solubility is not significantly different from that ot other compounds, such as BaS04, which generally form as crystals. 

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