Examples diluting solutions

When an electrolyte which is without action on vanadium at ordinary temperatures (for example, dilute solutions of mineral acids, of oxalic acid, or of potassium halides) is electrolysed with a vanadium anode, a complex tetravalent vanadium ion is produced. Similarly, electrolysis at 100° C. and in molten chlorides of sodium or zinc gives rise to complex tetravalent vanadium ions. The E.M.F. in each case is found to be independent of the nature of the electrolyte. When, however, solutions of caustic soda or of caustic potash are employed, the vanadium dissolves as a pentavalent ion, irrespective of variations... 

The precipitation process, the reverse of solid dissolution, is dictated by solution thermodynamics. The solution reaches saturation state when the dissolution rate equals the precipitation rate. Nucleation starts when the solution concentration exceeds the saturation concentration. The solution concentration affects the crystallite size of the precipitated catalyst. For example, diluted solution is beneficial to crystal growth due to slow nucleation and the presence of a few nuclei. In contrast, submicrometer- or even nano-sized amorphous gel or sol can be formed starting with a more concentrated solution. 

Oxidizing solutions (for example diluted solutions of NH4CIO4) have been used for preparing well-defined small particles of chromium dioxide and for stabilizing thermally unstable oxidation states, such as Hg. ... 

Polar solvents such as ethers and amines react with organometallic initiators, as well as propagating polystyryl and polydienyl carbanions, to decrease the concentration of active centers [3, 44, 45]. The rate of reaction with ethers decreases in the order Li > Na > K. For example, dilute solutions of poly(styryl)lithium in THF at room temperature decompose at the rate of a few percent each minute. Alkyllithium initiators also react relatively rapidly with ethers the order of reactivity of organolithium compounds with ethers is tertiary RLi > secondary RLi > primary RLi... 

If the diffusion Deborah number is small (small moleeular relaxation time or large diffusion time) moleeular relaxation is mueh faster than diffusive transport (in fact, it is almost instantaneous). In this case the diffusion process is similar to simple liquids. For example, diluted solutions and polymer solutions above glass transition temperature fall in fliis category. 

Self-assembled monolayers (SAMs) are molecular layers tliat fonn spontaneously upon adsorjDtion by immersing a substrate into a dilute solution of tire surface-active material in an organic solvent [115]. This is probably tire most comprehensive definition and includes compounds tliat adsorb spontaneously but are neither specifically bonded to tire substrate nor have intennolecular interactions which force tire molecules to organize tliemselves in tire sense tliat a defined orientation is adopted. Some polymers, for example, belong to tliis class. They might be attached to tire substrate via weak van der Waals interactions only. 

The oxidising properties of the aqueous solutions of chloric(VII) acid change dramatically with temperature and the concentration of the acid. Cold dilute solutions have very weak oxidising properties and these solutions will react, for example, with metals, producing hydrogen without reduction of the chlorate(VII) ion occurring ... 

RCH(OH)=CHCOR or -keto esters RCH(OH)=CHCOOR ) dissolve in dilute sodium hydroxide solution, i.e., contain an acidic group of sufficient strength to react with the alkah. Carboxyhc acids and sulphonic acids are soluble in dilute solutions of sodium bicarbonate some negatively-substituted phenols, for example, picric acid, 2 4 6-tribromo-phenol and 2 4-dinitrophenol, are strongly acidic and also dissolve in dilute sodium bicarbonate solution. 

Separations based upon differences in the chemical properties of the components. Thus a mixture of toluene and anihne may be separated by extraction with dilute hydrochloric acid the aniline passes into the aqueous layer in the form of the salt, anihne hydrochloride, and may be recovered by neutralisation. Similarly, a mixture of phenol and toluene may be separated by treatment with dilute sodium hydroxide. The above examples are, of comse, simple apphcations of the fact that the various components fah into different solubihty groups (compare Section XI,5). Another example is the separation of a mixture of di-n-butyl ether and chlorobenzene concentrated sulphuric acid dissolves only the w-butyl other and it may be recovered from solution by dilution with water. With some classes of compounds, e.g., unsaturated compounds, concentrated sulphuric acid leads to polymerisation, sulphona-tion, etc., so that the original component cannot be recovered unchanged this solvent, therefore, possesses hmited apphcation. Phenols may be separated from acids (for example, o-cresol from benzoic acid) by a dilute solution of sodium bicarbonate the weakly acidic phenols (and also enols) are not converted into salts by this reagent and may be removed by ether extraction or by other means the acids pass into solution as the sodium salts and may be recovered after acidification. Aldehydes, e.g., benzaldehyde, may be separated from liquid hydrocarbons and other neutral, water-insoluble hquid compounds by shaking with a solution of sodium bisulphite the aldehyde forms a sohd bisulphite compound, which may be filtered off and decomposed with dilute acid or with sodium bicarbonate solution in order to recover the aldehyde. 

The thiazolium ring, as most heterocycloammoniums, is a Lewis acid conferring to the carbon atom in the 2-position the carbocationic property of adding the free pair of a base either organic or mineral that may be the molecule of solvent as ROH (Scheme 11). For many nuclei of suitable acidity, these equilibria can be observed in dilute solution by means of absorption spectra when species A and C possess different characteristics (24). For example, benzothiazolium and benzoxazolium in methanol and ethanol give at 10 mole liter 8 and 54% of the alkoxy derivatives for the former and 29 and 90% for the latter respectively. 

Ion-exchange columns can be substituted into the general HPLC instrument shown in Eigure 12.26. The most common detector measures the conductivity of the mobile phase as it elutes from the column. The high concentration of electrolyte in the mobile phase is a problem, however, because the mobile-phase ions dominate the conductivity, for example, if a dilute solution of HCl is used as the mobile phase, the presence of large concentrations of H3O+ and Ck produces a background conductivity that may prevent the detection of analytes eluting from the column. 

To minimize the mobile phase s contribution to conductivity, an ion-suppressor column is placed between the analytical column and the detector. This column selectively removes mobile-phase electrolyte ions without removing solute ions, for example, in cation ion-exchange chromatography using a dilute solution of HCl as... 

Manganate(VI) formed in the initial oxidation process must first be dissolved in a dilute solution of potassium hydroxide. The concentrations depend on the type of electrolytic cell employed. For example, the continuous Cams cell uses 120 150 g/L KOH and 50 60 g/L K MnO the batch-operated Bitterfeld cell starts out with KOH concentrations of 150 160 g/L KOH and 200 220 g/L K MnO. These concentration parameters minimize the disproportionation of the K MnO and control the solubiUty of the KMnO formed in the course of electrolysis. 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

Sulfates having alkyl groups from methyl to pentyl have been examined. With methyl as an example, the hydrolysis rate of dimethyl sulfate iacreases with the concentration of the sulfate. Typical rates ia neutral water are first order and are 1.66 x lO " at 25°C and 6.14 x lO " at 35°C (46,47). Rates with alkaH or acid depend on conditions (42,48). Rates for the monomethyl sulfate [512-42-5] are much slower, and are nearly second order ia base. Values of the rate constant ia dilute solution are 6.5 X 10 L/(mol-s) at 100°C and 4.64 X 10 L/(mol-s) at 138°C (44). At 138°C, first-order solvolysis is ca 2% of the total. Hydrolysis of the monoester is markedly promoted by increasing acid strength and it is first order. The rate at 80°C is 3.65 x lO " ... 

The production of many high value chemicals requires maximizing separation from a relatively dilute solution. It is common in such instances to use a combination of methods to reduce solute solubiHty in the feed solution. Figure 5, for example, illustrates that the addition of methanol to a saturated aqueous solution of L-serine can reduce solubiHty by more than an order of magnitude. 

Feed Composition. Feed composition has a substantial effect on the economics of a distillation. Distillations tend to become uneconomical as the feed becomes dilute. There are two types of dilute feed cases, one in which the valuable recovered component is a low boiler and the second when it is a high boiler. When the recovered component is the low boiler, the absolute distillate rate is low but the reflux ratio and the number of plates is high. An example is the recovery of methanol from a dilute solution in water. When the valuable recovered component is a high boiler, the distillate rate, the reflux relative to the high boiler, and the number of plates all are high. An example for this case is the recovery of acetic acid from a dilute solution in water. For the general case of dilute feeds, alternative recovery methods are usually more economical than distillation. 

In these equations, the first term is a correction for finite liqiiid-phase concentrations, and the integral term represents the numbers of transfer units required for dilute solutions. It would be very unusual in practice to find an example in which the first (logarithmic) term is of any significance in a stripper design. 

Membrane Efficiency The permselectivity of an ion-exchange membrane is the ratio of the transport of electric charge through the membrane by specific ions to the total transport of electrons. Membranes are not strictly semipermeable, for coions are not completely excluded, particularly at higher feed concentrations. For example, the Donnan eqmlibrium for a univalent salt in dilute solution is ... 

Maak (1961) has obtained the equation governing the oxidation rate of a metal to form both an external oxide and an internally oxidized dilute solute, as for example in Cu-Be alloys, coiTesponding to tire equation given earlier... 

Examples of this procedure for dilute solutions of copper, silicon and aluminium shows the widely different behaviour of these elements. The vapour pressures of the pure metals are 1.14 x 10, 8.63 x 10 and 1.51 x 10 amios at 1873 K, and the activity coefficients in solution in liquid iron are 8.0, 7 X 10 and 3 X 10 respectively. There are therefore two elements of relatively high and similar vapour pressures, Cu and Al, and two elements of approximately equal activity coefficients but widely differing vapour pressures. Si and Al. The right-hand side of the depletion equation has the values 1.89, 1.88 X 10- , and 1.44 X 10 respectively, and we may conclude that there will be depletion of copper only, widr insignificant evaporation of silicon and aluminium. The data for the boundaty layer were taken as 5 x lO cm s for the diffusion coefficient, and 10 cm for the boundary layer thickness in liquid iron. 

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