Solubility exponential curve

Fig. 1.11. Determining the solubility (A) and hypersolubility (B) exponential curves of potassium bitartrate in a wine. Defining the hyper-saturation and instability fields according to the KTH content (Maujean et al, 1985). DS = saturation field 1, dissolved KTH 2, supersaturated, surfused KTH 3, crystallized KTH rcs , spontaneous crystallization temperature when 1.1 g/1 KTH is added rsat , saturation temperature of a wine in which 1.1 g/1 KTH have been dissolved...

Once the solubility (A) and hypersolubility (B) exponential curves have been defined, it is possible to determine the state of a wine at a known temperature with considerable accuracy. Indeed, any wine with a KTH concentration, or conductivity, above that defined by the intersection of the vertical line drawn npwards from the temper-atnre of the wine and the exponential solubility curve (A) is in a supersaturated state so, theoretically, there is a probability of spontaneous crystallization. The crystallization phenomenon will, in fact, be observed at the intersection of the same vertical line and the exponential hypersolubility curve (B). It appears, therefore, that supersaturation is necessary, but not sufficient, for primary nucleation phenomena and spontaneous crystallization to occur in a wine. 

A common feature of the solubihty curves, as outlined in Fig. 16, is the exponential increase with the pressure due to the increasing density of CO2. From the solubility measurements [125], it can be concluded that the modification of phosphines by fluorous substituents is not necessarily required to reach sufficient solubilities of the corresponding metal complexes in SCCO2. In particular, alkyl substitution on phosphorus promotes complex solubility. Additional aryl groups, e.g., in lb and 4b, cause a reduced solubility of the corresponding complexes. Moreover, trans-Co2(CO)6 (PC6H5)3 2 (7b) is completely insoluble in SCCO2. 

Solubility values based on a plateau in the dissolution rate curve, when dissolution of the metastable form is essentially complete and the system reaches a pseudoequilibrium state befori conversion to the stable solid state, are reasonably accurate. Those based on peaks in these curves obtained by Ltting exponential functions to estimate the plateau that might be reached in the absenc< of conversion should only be considered estimates ofthe metastable form solubility. The quantitative gain in these systems may be estimated more accurately by comparing initial dissolution rates for the two forms. In most cases, amorphous form solubilities must be estimated by these techniques due to their rapid crystallization when in contact with solvents. 

A second reason for staging continuous crystallizers is to control the process stream concentration-temperature profile for products with a steep solubility curve (i.e., exponential increase in solubility with temperature). Even though the volumetric flow rates would permit a single crystallizer of reasonable size, staged temperature for adiabatic cooling crystallization requires multiple vessels to prevent the local concentration at the hot concentrated feed entrance from exceeding its supersaturation limit when it is diluted and mixed with the circulating bulk. 

Subsequent to the addition of 4 g/1 of KTH, the wine (Figure 1.14a) showed a linear variation in conductivity at low temperatures that could almost be superimposed on that of the wine without crystals until a temperature Tsat, where the conductivity left the straight line and followed the exponential solubility curve. 

Ta then the KTH started to dissolve and the conductivity followed the exponential solubility curve. At temperature Tg, the exponential solubility curve crossed the straight line showing the conductivity of the wine alone. This intersection corresponds to the wine s true saturation temperature. The temperature Ta corresponds to that of the same wine after a contact , leading... 

The equations for the solubility (A) and hypersolubility (B) curves (Section 1.5.1, Figure 1.11) were established for this purpose by measuring electrical conductivity. They follow an exponential law of the following type C = a e ", where C is the conductivity, t is the temperature and a and b are constants. 

The envelope covering this set of spontaneous crystallization temperatures (Tcs,) defines the exponential hypersolubility curve (B). The exponential solubility and hypersolubility curves. 

Novotnd et al. [261] studied a set of eight historical anthroquinone and naphthoquinone dyes (carminic acid, laccaic acid A and B, lawsone, juglone, alizarin, lapachol, emodin). They were well resolved in 12 min on a C]g column (A — 270 nm) using a 15-min exponential gradient from 40/60 -y 95/5 methanol/ water (0.1 M citrate pH 2.5). Separately, alizarin and purpurin were resolved on a C]g column (A = 245 ran) using a 72/25 methanol water (0.2 M acetate pH 4.3) mobile phase. Detection limits of 0.6-12 ng injected (analyte dependent) were reported. Linear curves up to the solubility limit of l mM were also used. 

FIGURE 5 7.5 Fixed time inhibition. DFP 30-min fixed-time inhibition curve of soluble peripheral nerve PV esterase activity (PVase). The curve was fitted to the best model according to the F test (two exponential and a resistant component). Each point represents the mean of three replicates (SD <5%). 

Non-aqueous or partially aqueous systems are also preferred for precipitation titrations in order to lower the solubility of the resulting precipitate. Lower detection limits and more easily evaluated titration curves are thus obtained. The electrodes described here usually have electrical resistances less than 1 MOhm. This allows them to be used in cooled solutions (this resistance often has an exponential temperature dependence), which sometimes also lowers the solubility by a factor of 2 or 3 and thus extends the detection limit. 

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