Solute stoichiometric molality

The Pseudo-Phase Model Consider a process in which surfactant is added to water that is acting as a solvent. Initially the surfactant dissolves as monomer species, either as molecules for a non-ionic surfactant or as monomeric ions for an ionic surfactant. When the concentration of surfactant reaches the CMC, a micelle separates from solution. In the pseudo-phase model,20 the assumption is made that this micelle is a separate pure phase that is in equilibrium with the dissolved monomeric surfactant. To maintain equilibrium, continued addition of surfactant causes the micellar phase to grow, with the concentration of the monomer staying constant at the CMC value. This relationship is shown in Figure 18.14 in which we plot m, the stoichiometric molality,y against mj, the molality of the monomer in the solution. Below the CMC, m = m2, while above the CMC, m2 = CMC and the fraction a of the surfactant present as monomer... 

Figure 18.14 Comparison of the stoichiometric molality m and the molality of the monomer m2 in a surfactant solution, according to the pseudo-phase model.

Since E is known, and the e.m.f. of the cell (E) can be measured with various concentrations of acid, sodium salt and sodium chloride, i.e., for various values of mi, rrh and m3 in the cell depicted above, it is possible to evaluate the left-hand side of equation (14) or (15). In dilute solution, the sodium chloride may be assumed to be completely dissociated so that the molality of the chloride ion can be taken as equal to that of the sodium chloride, i.e., mcr is equal to m3. The acid HA will be partly in the undissociated form and partly dissociated into hydrogen and A ions the stoichiometric molality of HA is mi, and if nin is the molality of the hydrogen ions resulting from dissociation, the molality of undissociated HA molecules, i.e., maA in equation (15), is equal to mi — mn. Finally, it is required to knowm rriA- the A ions are produced by the dissociation of NaA, which may be assumed to be complete, and also by the small dissociation of the acid HA it follows, therefore, that mA is equal to m2 -f Since mu, the hydrogen ion concen-... 

If the stoichiometric molality of II2A is m in a given solution and that of the salt NaHA, assumed to be completely dissociated into HA"" ions, is m2, then... 

These are examples of geometric means. For a 1-3 electrolyte such as CrCls, m is equal to 21) / m2 = 2.2795m2, where m2 is the stoichiometric molality of the solute (the molality that would occur if no dissociation occurred). The chemical potential of the neutral electrolyte solute is given by... 

At 25 C a solution of acetic acid with a stoichiometric molality of 0.100molkg is approximately 1.32% ionized. Assuming that this percentage ionization apphes at the freezing temperature, find the freezing temperature of this solution. 

Here y+ is the mean molal activity coefficient, and m c is the total (stoichiometric) molal concentration of HCl in solution. " Combining Eqs. (6)-(9), and assuming yhci = 1, we obtain,... 

Fig. 8.5. Water activity aw versus stoichiometric ionic strength 7s of NaCl solutions at 25 °C and 300 °C, according to the activity model of Helgeson (1969). Dashed line shows 3 molal limit to the model parameterization values to right of this line are extrapolations of the original data.

Originally, the stoichiometric stability constants 6 for the lead and the cadmium complexes with chloride had been determined in NaCl-NaC104 solutions and it had been assumed that the NaCl was completely dissociated. The nominal ionic strength was one molal. The constants were later corrected by replacing the actual free chlorides for the total chlorides in the calculation of... 

Molality and molarity are each very useful concentration units, but it is very unfortunate that they sound so similar, are abbreviated so similarly, and have such a subtle but crucial difference in their definitions. Because solutions in the laboratory are usually measured by volume, molarity is very convenient to employ for stoichiometric calculations. However, since molarity is defined as moles of solute per liter of solution, molarity depends on the temperature of the solution. Most things expand when heated, so molar concentration will decrease as the temperature increases. Molality, on the other hand, finds application in physical chemistry, where it is often necessary to consider the quantities of solute and solvent separately, rather than as a mixture. Also, mass does not depend on temperature, so molality is not temperature dependent. However, molality is much less convenient in analysis, because quantities of a solution measured out by volume or mass in the laboratory include both the solute and the solvent. If you need a certain amount of solute, you measure the amount of solution directly, not the amount of solvent. So, when doing stoichiometry, molality requires an additional calculation to take this into account. 

It must be emphasized that such stoichiometric stability constants are dependent, inter alia, upon the ionic strength of the solution, and, in reporting experimental results, the ionic strength of the experimental solutions should always be specified. Further, the numerical value of a stoichiometric constant will depend upon the units used, viz. mole fractions, molar, molal, millimole, and so on, and which is used should always be made clear. 

Activities in Concentrated Solutions.—For relatively concentrated solutions it is necessary to use the complete Hiickel equation (62) by choosing suitable values for the two adjustable parameters a and it has been found possible to represent the variation of activity coefficients with concentration of several electrolytes from 0.001 to 1 molal, and sometimes up to 3 molal. The values of C seem to lie approximately between 0.05 and 0.15 in aqueous solution. At the higher concentrations it is necessary to make allowance for the difference between the rational and stoichiometric activity coefficients the latter, which is the experimentally determined quantity, is represented by an extension of equation (62) thus (cf. p. 135),... 

In the experimental determination of activity coefficients of strong electrolytes, by the methods described below, the molalities, etc., of the ions are taken as the stoichiometric values, that is, the total possible molality, etc., disregarding incomplete dissociation, For example, in the last problem, the molalities of the sodium and sulfate ions in the 0.5 molal solution of sodium sulfate were taken as exactly 1.0 and 0.5, respectively, without allowing for the possibility that the salt may be only partially dissociated at the specified concentration. The activity coefficients obtained in this manner are called stoichiometric activity coefficients they allow for all variations from the postulated ideal behavior, including that due to incomplete dissociation. If the treatment is based on the actiuil ionic molalities, etc., in the given solution, as in the Debye-Httckel theory (Chapter XVII), there is obtained the true (or actual) activity coefficient. TTie ratio... 

The activity of each ionic species may be represented as the product of its molality and its (stoichiometric) activity coefficient hence is equal to my. and oci to 2my, where m is the molality of the zinc chloride solution in the cell. By equation (39.9), 7+7I is equal to y , where y is the mean ionic activity coefficient hence equation (45.16) becomes... 

Gas laws, including the ideal gas law, Dalton s law, and Graham s law Stoichiometric relations using the concept of the mole titration calculations Mole fractions molar and molal solutions... 

X Vg is the sum of the stoichiometric coefficients of the reaction, cf. Eq.(II.54) and the values of g are the factors for the conversion of molarity to molality as tabulated in Table II-5 for several electrolyte media at 298.15 K. In the case of very dilute solutions, these factors are approximately equal to the reciprocal of the density of the pure solvent. Then, if the solvent is water, molarity and molality may be used interchangeably, and A",. The differences between the values in Table 11-5 and the values listed in the uranium NEA-TDB review [92GRE/FUG] (p.23) are found at the highest concentrations, and are no larger than + 0.003 dm -kgreflecting the accuracy expected in this type of conversion. The uncertainty introduced by the use of Eq. (11.38) in the values of log will be no larger than + 0.001 X Vg. ... 

Chloroacetic acid, a monoprotic acid, has a K of 1.40 x 10 Compute the freezing point of a O.IOM solution of this acid. Assume that the stoichiometric molar concentration and molality are the same in this case. 

In practice the potentials of a series of cells of type (1) are measured in which the molalities of the acid, its salt, and of sodium chloride are known. In the more dilute solutions however there is an appreciable change of the molalities from the stoichiometric values due to the reaction represented by equation (3) but a correction can be made for this effect using a preliminary value of the ionization constant in evaluating the third term on the left-hand side of equation (8) and in computing the ionic strength, 0), which is used as described below. The method may thus involve a series of approximations, but a single approximation is usually sufficient. 

The first right-hand expression is written in activities, and this quotient gives the intrinsic dissociation constant. The second right-hand expression is made up of two factors, a quotient of (molar or molal) concentrations that may be called the stoichiometric dissociation constant, and a quotient of activity coefficients. All dissociation constants, association constants K = 1 /ATD), and solubility products in reference books are intrinsic constants. They apply to concentrations only if the solution is extremely dilute for all ionic species. In other cases, one has to know the activity coefficients. y0, i.e., y for a nonionic species, will mostly be close to unity, but y+ and y will generally be < 1, the more so for a higher ion concentration. One may define the free... 

Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model ( may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data (]) However, a complete data set for all the ion-interaction parameters is not yet available for this model to be used in complex geochemical solutions. 

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