Dilute solution definition

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 last definition has widespread use in the volumetric analysis of solutions. If a fixed amount of reagent is present in a solution, it can be diluted to any desired normality by application of the general dilution formula V,N, = V N. Here, subscripts 1 and 2 refer to the initial solution and the final (diluted) solution, respectively V denotes the solution volume (in milliliters) and N the solution normality. The product VjN, expresses the amount of the reagent in gram-milliequivalents present in a volume V, ml of a solution of normality N,. Numerically, it represents the volume of a one normal (IN) solution chemically equivalent to the original solution of volume V, and of normality N,. The same equation V N, = V N is also applicable in a different context, in problems involving acid-base neutralization, oxidation-reduction, precipitation, or other types of titration reactions. The justification for this formula relies on the fact that substances always react in titrations, in chemically equivalent amounts. 

It is not only in the field of kinetic relations that discrepancies exist. When the catalyst is a protonic acid and the reaction is carried out in dilute solution, the mechanisms describing the contribution of the catalyst are relatively well-known. But in most other cases and particularly when the catalyst is a metal derivative (see Chap. 4) none of the proposed mechanisms can be considered as definitive. 

In the limit of infinitely dilute solutions, where equation (6.112) holds, m2 —f2/k2. If we maintain this ratio as our definition of activity, a2. then a2 = m2 in these solutions. For solutions which are not in the limiting region, we writecc... 

The changeover to thermodynamic activities is equivalent to a change of variables in mathematical equations. The relation between parameters and a. is unambiguous only when a definite value has been selected for the constant p. For solutes this constant is selected so that in highly dilute solutions where the system p approaches an ideal state, the activity will coincide with the concenttation (lim... 

The pH value obtained in this way is accompanied by an error resulting from the approximation used for the calculation of ycr. Although this error may be small in dilute solutions, the pH values obtained in this manner are not exactly equal to the values corresponding to the absolute definition of... 

In equation (2), by convention (since it is in large excess when HA is in dilute solution) the concentration of water, Ch2o, is left out of the definition. This leads to problems. For instance, when hydronium ion itself is the acid, for consistency equation (3) must be written ... 

It will be obvious from the description of Lewis s and Donnan and Barker s experiments that equilibrium is assumed to establish itself during the time of contact between the mercury or air surface and the liquid in fact this point was checked by increasing the time and showing that the result was not affected, i.e., that no further quantity of the solute was removed from solution. Experiments to decide this question had, however, been made at an earlier date by Wilhelm Ostwald. The strict definition of an equilibrium requires that it should be independent of the mass of the phases in contact thus, a soluble substance and its concentrated solution are in equilibrium at a given temperature and pressure, and this obviously remains unaffected by altering the quantity of either solid substance or solution. Ostwald placed a quantity of charcoal in a given volume of dilute hydrochloric acid and determined the decrease in concentration after a short time. If, then, a part of either the charcoal or the dilute solution was... 

H (MPa) (Eq. (13)) and HA (MPa m3 mor1) (Eq. (14)) are often referred to as Henry s constant , but they are in fact definitions which can be used for any composition of the phases. They reduce to Henry s law for an ideal gas phase (low pressure) and for infinitely dilute solution, and are Henry s constant as they are the limit when C qL (or xA) goes to zero. When both phases behave ideally, H depends on temperature only for a dilute dissolving gas, H depends also on pressure when the gas phase deviates from a perfect gas finally, for a non-ideal solution (gas or liquid), H depends on the composition. This clearly shows that H is not a classical thermodynamic constant and it should be called Henry s coefficient . 

Of these different definitions, the most important usually are g dm 3, molarity, mole fraction, and percentage (or ppm, for dilute solutions). It is often... 

However, let note, that the assumption about independence of the osmotic pressure of semi-diluted solutions on the length of a chain is not physically definitely well-founded per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory-Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. 

In semi dilute (c>c, [B] = 0.3-0.5 mole.l- ) or dilute (c< c, [B] = 10-2 mole.l- -) solution, Kp is significantly greater for copolymers than for the model compounds whatever the solvent is. For semi-dilute solution in a given solvent, the complex influences of composition, unit distribution and tacticity do not result in definite trends on K, values, as illustrated in table 6 by some representative Kj data related to keto-2-picolyl structures at 25°C. 

In dilute solution, the dependance of LnRj on solvent polarity for copolymers is definitely measurable, but it is significantly reduced with respect to that of the model compounds, by a factor of about 3 for a predominantly syndiotactic chain bearing keto-2-picolyl functions in the form of isolated units (DSm = 0.129,... 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

If followed in experimenrtally accessible dilute solutions, Henry s law would be manifested as a horizontal asymptote in a plot such as Figure 19.3 as the square of the molality ratio goes to zero. We do not observe such an asymptote. Thus, the modified form of Henry s law is not followed over the concentration range that has been examined. However, the ratio of activity to the square of the molality ratio does extrapolate to 1, so that the data does satisfy the definition of activity [Equations (16.1) and (16.2)]. Thus, the activity clearly becomes equal to the square of the molality ratio in the limit of infinite dilution. Henry s law is a limiting law, which is valid precisely at infinite dilution, as expressed in Equation (16.19). No reliable extrapolation of the curve in Figure 19.2 exists to a hypothetical unit molality ratio standard state, but as we have a finite limiting slope at = 0, we can use... 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

Kohlrausch law phys chem 1. The law that every ion contributes a definite amount to the equivalent conductance of an electrolyte in the limit of infinite dilution, regardless of the presence of other ions. 2. The law that the equivalent conductance of a very dilute solution of a strong electrolyte is a linear function of the concentration. kol,raush, l6 ... 

The activity of an electrolyte or ion is defined for use in determining true (actual as opposed to theoretical) equihbrium constants. By definition, the activities are equal to the concentrations in very dilute solutions, and the difference between activities and concentration in more concentrated solutions depends on interaction between all the components of the solution, causing the ions to behave differently than they would at a high degree of dilution. 

In some exceptional cases, however, can be given a definite meaning. This is so in the case of adsorption from dilute solutions [13,21]. Incidentally, these are the conditions usually encountered in preparative chromatography. Let us assume the compound numbered 1 to be the preferentially adsorbed. If its equilibrium concentration (x,) is negligibly small, from Equation 10.36 one obtains... 

For solutions of ions, departures from ideality can be large even in quite dilute solutions because of the strong electrostatic attractions or repulsions between the ions. Furthermore, the simple definition of activity coefficient given in Eq. 2.3 fails for electrolytes because we can never measure the activity of, say, a cation Mm+ without anions Xx being present at the same time instead, we usually define a mean ionic activity a and coefficient /y as... 

The automotive engineers were also busy. In 1931 Lovell, Campbell, and Boyd (23) published data on an extended series of pure paraffin and olefin hydrocarbons in fairly dilute solution in gasoline. These data showed a number of definite relations between the molecular structure of the pure hydrocarbon and the tendency of the fuel to knock. The... 

On the other hand, the dilute solution of poly(p-benzyl-L-aspartate) in chloroform or dichloromethane gives a weak but existant CD band centered at 252 nm. A large positive CD band at 222 nm means that poly(p-benzyl-L-aspartate) (PBLA) exists in the left-handed a-helical form. Poly(y-p-nitrobenzyl-L-glutamate) also shows a definite negative CD band around 275 nm, even if the concentration of the polymer... 

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