Solutions dissolving solid rates

In a saturated solution, any solid solute present still continues to dissolve, but the rate at which it dissolves exactly matches the rate at which the solute returns to the solid (Fig. 8.17). In a saturated solution, the dissolved and undissolved solute are in dynamic equilibrium with each other. 

The most common extravascular route is oral. When a solution or a rapidly dissolving solid dosage form is given orally, the absorption process often obeys first-order kinetics. In these cases, absorption can be characterized by evaluating the absorption rate constant, ka, using plasma concentration versus time data. 

One approach to the study of solubility is to evaluate the time dependence of the solubilization process, such as is conducted in the dissolution testing of dosage forms [70], In this work, the amount of drug substance that becomes dissolved per unit time under standard conditions is followed. Within the accepted model for pharmaceutical dissolution, the rate-limiting step is the transport of solute away from the interfacial layer at the dissolving solid into the bulk solution. To measure the intrinsic dissolution rate of a drug, the compound is normally compressed into a special die to a condition of zero porosity. The system is immersed into the solvent reservoir, and the concentration monitored as a function of time. Use of this procedure yields a dissolution rate parameter that is intrinsic to the compound under study and that is considered an important parameter in the preformulation process. A critical evaluation of the intrinsic dissolution methodology and interpretation is available [71]. 

Several factors influence a drug s absorption (table 3.1). Aqueous solutions are more easily absorbed than a lipid solution or solid form. Absorption of drugs in solid form is affected by the rate at which it dissolves. Higher concentrations of a drug are more rapidly absorbed than low concentrations. The amount of blood flow to the site also influences absorption heat and vasodilators increase absorption. 

The major ions have two main escape routes from the ocean (1) incorporation into sediments or pore water and (2) ejection into the atmosphere as seasalt spray. This spray is caused by bursting bubbles that produce small particles, called aerosols, that range in diameter from 0.1 to 1000 pm. The annual production rate of seasalt aerosols is large, on the order of 5 x lO kg/y, but virtually all of it is quickly returned when the spray fells back onto the sea surfece. A small fraction (about 1%) is deposited on the coastal portions of land masses and carried back into the ocean by river runoff. As shown in Table 21.6, seasalts represent a significant fraction of dissolved solids in river runoff, especially for sodium and chloride. Due to the short timescale of this process, seasalt aerosol losses and inputs are considered by geochemists to be a short circuit in the crustal-ocean-atmosphere fectory. The solutes transported by this process are collectively referred to as the cyclic salts. ... 

In nonporous membranes, diffusion occurs as it would in any other nonporous solid. However, the molecular species must first dissolve into the membrane material. This step can oftentimes be slower than the diffusion, such that it is the rate-limiting step in the process. As a result, membranes are not characterized solely in terms of diffusion coefficients, but in terms of how effective they are in promoting or limiting both solubilization and diffusion of certain molecular species or solutes. When the solute dissolves in the membrane material, there is usually a concentration discontinuity at the interface between the membrane and the surrounding medium (see Figure 4.55). The equilibrium ratio of the solute concentration in one medium, c, to the solute concentration in the surrounding medium, C2, is called the partition coefficient, K12, and can be expressed in terms of either side of the membrane. For the water-membrane-water example illustrated in Figure 4.55,... 

A solution at equilibrium that cannot hold any more solute is called a saturated solution. The equilibrium of a solution depends mainly on temperature. The maximum equilibrium amount of solute that can usually dissolve per amount of solvent is the solubility of that solute in that solvent. It is generally expressed as the maximum concentration of a saturated solution. The solubility of one substance dissolving in another is determined by the intermolecular forces between the solvent and solute, temperature, the entropy change that accompanies the solvation, the presence and amount of other substances and sometimes pressure or partial pressure of a solute gas. The rate of solution is a measure of how fast a solute dissolves in a solvent, and it depends on size of the particle, stirring, temperature and the amount of solid already dissolved. 

D Choice A is a restatement of Le Chatelier s Principle. B is a definition of equilibrium. A constant humidity (Choice C) occurs if the rate of vaporization and condensation are equal, indicating equilibrium. No solid is present in an unsaturated solution. If solid is added, all of it dissolves indicating a lack of equilibrium. D would be true for a saturated soution. 

It is necessary to estimate the quantity of each gas in the liquid to accurately determine the productivities and usage rates. The species equilibrium concentration, x, in the liquid is estimated by Henry s Law (Eq. 3). Unfortunately, H, the Henry s Law constant, for a gas in contact with a solution depends on the nature and concentrations of dissolved solids, tending to be less than the value for pure water [71]. For this reason, we can only obtain an upper limit for the dissolved gas quantity. However, the solubility depression for our rather dilute culture medium is low. A 0.5 mole/1 concentration of sodium chloride results in an oxygen solubility depression of 15 % [71]. The total concentration of dissolved solids in our medium was less than half of that (0.22 mole/1), so the gas solubility depression was almost certainly less than 10%. A more serious uncertainty occurs because the culture volume includes cell volume by treating the entire 83 ml as liquid volume (V ), we may tend to overestimate the dissolved gas quantity. 

Changes in sensitivity (signal/concentration) can occur in ICP-MS, depending on the identity and concentration of elements in the sample solution and the solvent. Chemical matrix effects can be due to changes in the analyte transport efficiency from the nebulizer into the plasma or modification of ion generation in the plasma. The severity of this matrix effect depends on the concentration of matrix ions generated in the ICP, not the matrix-to-analyte ratio. Whenever the matrix ion current becomes significant compared to other ion currents, matrix effects are observed [166]. Therefore, sample introduction systems that increase the sample transport rate into the ICP suffer from chemical matrix effects at lower dissolved solid concentrations in the sample. 

Rate of Solubility—The rath of solubility of small particles depends on a great number of variables. Eq (12-2) takes into account free surface energy (a) and particle surface (1 /d). These are purely surface considerations, and are scarcely complete in themselves. The shape of the surface and its physical state must also be specified, that is, its relative freedom from contamination which might influence the speed of reaction. The effect of packing density and the extent of agitation imparted to the particles are also important, particularly with regard to exposure of fresh surfaces and formation of possible gas pockets. The liquid and liquid-solid phases jointly are additional important considerations. The volume of the liquid, its temperature, and the amount of dissolved solid already in solution must enter into all calculations. Nor can we ignore the chemical nature of the substances involved in the... 

The rate at which a solid solute dissolves in water can usually be increased by increasing the temperature of the solution. 

H. J. ENGELL (Max Planck Institute) As already explained by Prof. Hackerman, two limiting mechanisms can be expected for the dissolution of a solid (a) Equilibrium exists at the phase boundary of the solid and the solution, and the transport of the dissolved solid into the interior of the solution is rate determining, (b) The rate determining step of the solution process is the transport through the phase boundary solid-solution then the transport of dissolved particles from the inter phase into the solution can be assumed to be fast enough to be without influence on the overall rate of the dissolution. 

An aqueous solution containing 7.00 wt% sodium carbonate and a gas stream containing 70.0 mole% CO2 and the balance air are fed to the reactor. All of the sodium carbonate and some of the carbon dioxide in the feed react. The gas leaving the reactor, which contains the air and unreacted CO2, is saturated with water vapor at the reactor conditions. A liquid-solid slurry of sodium bicarbonate crystals in a saturated aqueous solution containing 2.4 wt% dissolved sodium bicarbonate and no dissolved CO2 leaves the reactor and is pumped to a filter. The wet filler cake contains 86 wi% sodium bicarbonate crystals and the balance saturated solution, and the filtrate is also saturated solution. The production rate of solid crystals is 500 kg/h. 

For the majority of solids, solubilization is temperature dependent and increases in elevated temperatures as heat is absorbed during solubilizing. The degree to which temperature can influence solubility is dictated by the differential heat of solution, AHs, which represents the rate of heat change of a solution per mole of solute dissolved. The higher the heat of solution, the greater the influence of temperature on solubility, as shown by Eq. (7). 

There was a marked difference in the rate of triplet energy transfer for 24 and 26. In a benzene solution of 24, the carotenoid triplet species had a rise time of ca. 2/is and decayed in ca. lO s. Concomitant with the rise of the carotenoid triplet absorbance at 550 nm, the porphyrin triplet absorbance at 440 nm decayed with a time constant of 2/js. There was no appreciable change in these parameters when 24 was dissolved in a rigid plastic matrix [73]. For 26 the triplet energy transfer was much faster. In 1981, we reported it as faster than 30 ns, which was the limit of our instrumentation [91]. Measurements with greater time resolution were made in 1983, but it remained difficult to separate the carotenoid triplet rise time from the instrument response time [73]. In any case, under conditions ranging from solution to solid plastic to a glass at 10 K, the rise time of triplet carotene in 26 was < 5 ns. 

The important features of the sample preparation procedure were as follows. First, the samples were acidified to dissolve normal urine precipitates and to prevent analyte loss by adsorption on the walls of the sample containers (13). Second, the procedure was kept as simple as possible so that the risk of contamination and/or loss was minimized. Third, dilute, normal, and concentrated series of solutions were used to simulate actual urine samples with a wide range of total dissolved solids. Fourth, because the rate of sample nebulization and the corresponding rate of sample introduction into the plasma can be aflFected by changes in the amount of total dissolved solids, internal reference elements were included in each sample and reference solution. The use of analyte/internal reference element net intensity ratios provided a means of correcting for possible diflFerences in sample introduction rate according to the internal reference principle (14,15). Finally, because all of the sample solutions introduced into the plasma were derived from one composite, the different series were known to have trace element concentrations which were related to each other by known dilution factors (see Table IV). 

Some examples for PAH compounds suggest that decreased solubility and non-aqueous-phase partitioning and sorption processes are restrictive toward microbial degradation. Wodzinski and Bertolini (16) and Wodzinski and Coyle (17) concluded that bacteria utilize naphthalene, biphenyl, and phenanthrene as dissolved solutes, with the rate of biodegradation independent of the total amount of solid-phase hydrocarbon. Stucki and Alexander (18) found that the dissolution rate of phenanthrene may limit the biodegradation rate. 

At a given temperature, the rate of dissolution of a solid increases if large crystals are ground to a powder. Grinding increases the surface area, which in turn increases the number of solute ions or molecules in contact with the solvent. When a solid is placed in water, some of its particles solvate and dissolve. The rate of this process slows as time passes because the surface area of the crystals gets smaller and smaller. At the same time, the number of solute particles in solution increases, so they collide with the solid more... 

Let Xq = initial concentration of the dissolved solid in the solution Xj = solubility of the solid species in a solvent x = concentration of dissolved species at time f = (At)n, where n stands for the number of discrete time steps, (At). For dissolution to occur, we must of course assume that Xq < Xj. The rate law for the concentration of dissolved solid in the solution follows the equation... 

A saturated solution need not be accompanied by excess solid in its container, although if it does, there will be a dynamic equilibrium between the rate of solution and the rate of return. A saturated solution without excess solid can be made by first adding solid to a solvent until no more will dissolve, and then filtering out the excess solid. 

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