Moderately dilute solutions

In moderately diluted solutions, i.e. for concentrations fulfilling the condition, c K, ... 

In moderately dilute solution, with a salt concentration e8 and a nonelectrolyte of concentration (the solubility), the following expressions have been experimentally justified ... 

It is suggested by several equations describing the solution behavior of flexible polymers in good solvents that the second and third virial coefficients of the concentration dependence have a common parameter dependence 12-14). This behavior may be attributed to interchain entanglements for some polymers. In contrast, rigid rods can show completely linear concentration dependence in moderately dilute solution. Here the third virial coefficient is either negligibly small, or it is non-existent—in which case no relation exists between the second and third coefficient. Viscometry of some polyisocyanide solutions shows time-dependent transformations, reflected in pronounced changeovers from parabolic to linear concentration dependencies, and it would be of interest to define the transformations, and to detail their physical descriptions. 

In moderately dilute solutions the activity coefficients do depart from unity but to a limited extent. If the reactants and products are all uncharged, of similar... 

The oxidation of secondary alcohols gives good to excellent yields of the corresponding ketones (Eqn. 21.1)28 while primary alcohols are oxidized to the aldehydes at low conversions and the acids at high conversions. 22.28 Secondary alcohols on the second carbon atom (P) of a chain react more rapidly than primary alcohols while secondary alcohols on other carbon atoms of the chain (y) react more slowly. 28-29 The general order for the oxidation of alcohols on a linear carbon chain is P > a > y.28 The difference in activity between the P and Y alcohols has been ascribed to a difference in the transition state restrictions in these oxidations. These reactions are usually run in moderately dilute solutions at temperatures between 50°-70°C. 

In many instances, especially when the solute has a limited solubility in the solvent, as is often the case for solid solutes, particularly electrolytes or where dilute solutions are under consideration, it is more convenient to choose an entirely different standard state. Three such states are used one is based on compositions expressed in mole fractions, but the others are more frequently employed, because the compositions of dilute and moderately dilute solutions are usually stated in terms of molality, i.e., moles per 1000 g. solvent, or in terms of molarity, i.e., moles per liter of solution. ... 

Activity coefficients can, as a rule, be neglected for moderately dilute solutions (say, up to 1-2 M), since they appear in the Nemst equation in logarithmic form. Thus, for example, if the activity coefficient is only 0.8, instead of an assumed value of 1.0, the resulting error in the value of is only (5.7/h) mV. It should be borne in mind, however, that in highly concentrated electrolytes, such as 30% KOH or 85% H3PO4, used in some batteries and tuel cells, such an approximation is no longer valid and may introduce significant errors. 

Hansen (57) pointed out that evaporation of a solvent from a polymer solution faced two barriers when cast on an impermeable substrate resistance to solvent loss at the air-liquid interface and diffusion from within the film to the air interface. Evaporation of neat solvents as well as moderately dilute solutions is limited by resistance at the air interface, but as solvent concentration becomes low (5-10-15%), the rate-controlling step is diffusion through the film. Hansen pointed out that at the point when solvent loss changes to a diffusion-limited process, the concentration of solvent is sufficient to reduce the glass transition temperature, Tg, of the polymer to the film temperature. 

Equating the forces and assuming a moderately dilute solution with the partial molar volume of the solvent replaced by V/ 3 , we obtain... 

This convention is used when dilute or moderately dilute solutions of components 2,. . . , r in component 1 (solvent) are being considered. We shall restrict ourselves to a discussion of binary solutions and use of the second convention [Eq. (3-69)] the reader will find no difficulty in extending the treatment to multicomponent solutions. In the following, we define the quantities integral heat of solution, heat of dilution, and heat of concentration. We present three alternative expressions for these quantities in terms of either the relative partial enthalpies, the integral heat of solution per mole of component 2, or the integral heat per mean mole of solution. 

Making use of Eqs. (6-54) and (7-142), we find that in the moderately dilute solution... 

Perchloric acid solution (HCIO4) white crystalline precipitate of potassium perehlorate KCIO4 from moderately dilute solutions. 

According to Bauer, in the electrolysis of the acetic acid salts of metals possessing a constant valence (K, Na, NH Mg, Ca, Zn, and Al), when cold, moderately dilute solutions and relatively high current densities are employed, gases consisting chiefly of ethane and carbon dioxide are given off at the anode. No inconsiderable quantities of ethylene are formed in the case of calcium, magnesium, and potas-... 

Wool can be dissolved in a moderately dilute solution of caustic soda, and the presence of this latter in soap, even in small quantities, is therefore liable to injure the fibres and make the resultant fabric possess a harsh feel/ and be devoid of lustre. 

The separation of Ti from Nb and Ta is quite difficult. Reactions that are excellent with the individual metals are very poor with a typical mixture. One good method for removing Ti is to boil the precipitated hydrated hydroxides of the Ti, Zr, Hf, Nb, and Ta with a moderately dilute solution of 2-hydroxybenzoate [salicylate, o-C6H4(OH)C02 ] and 2-hydroxybenzoic acid, whereupon all of the Ti is dissolved and the other metals are left in the residue. 

Using values of the ionization product of water K, the dissociations constants of citric acid, Kj, Kj and K3, the corresponding citrate ions sizes and a(Na+)=5.0 A, the distribution of individual species as a function of total concentration of sodium dihydrogen citrate at 25 °C is illustrated in Fig. 3.2. As can be observed, in moderate dilute solutions of sodium dihydrogen citrate, olO" mol dm", the mono-charged H2Cir is dominant anion, HCit is of importance in the 10" mol dm" -10 mol dm concentration range and CiU only for c< 10" mol dm". ... 

The osmotic pressure of a moderately dilute solution can be surprisingly large. Find the osmotic pressure at 25°C of an aqueous solution of sucrose with a molar concentration of 0.200 mol L . ... 

Crystallization from dilute and moderately dilute solutions... 

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