Molal units

For applications where the solution temperature changes, chemists prefer to use the molality, units of mol/kg). Molality is defined to be the number of moles of solute divided by the mass of solvent in kilograms. Moles of solute solute... 

Figure 1.86. Variation in chemical compositions (in molal unit) of hydrothermal solution with temperature. Thermochemical data used for the calculations are from Helgeson (1969). Calculation method is given in Shikazono (1978a). Chloride concentration in hydrothermal solution is assumed to be 1 mol/kg H2O. A-B Na concentration in solution in equilibrium with low albite and adularia, C-D K concentration in solution in equilibrium with low albite and adularia, E-F HaSiOa concentration in equilibrium with quartz, G-H Ca + concentration in equilibrium with albite and anorthite (Shikazono, 1978a, 1988b).

Here, we define the total dissolved solids (in mg kg-1) for early releases of the REACT program (GWB 6.0 and previous), so the software can correctly convert our input constraints from mg kg-1 to molal units, as carried internally (i.e., variables nii and m.j). The print command causes the program to list in the output all of the aqueous species, not just those in greatest concentration. Typing go triggers the model to begin calculations and write its results to the output dataset. 

Variable di in Equation 8.2 is the ion size parameter. In practice, this value is determined by fitting the Debye-Huckel equation to experimental data. Variables A and B are functions of temperature, and I is the solution ionic strength. At 25 °C, given I in molal units and taking a, in A, the value of A is 0.5092, and B is 0.3283. 

Since the input constraints are in molar (instead of molal) units, we have specified the dissolved solid content and the fluid density under laboratory conditions, the latter estimated from the correlation of Phillips el al. (1981) for NaCl solutions. The resulting fluid is, as expected, acidic, with a predicted pH of 2.9. Neutral pH... 

Equilibrium constants corrected from molarity to molality units, according to the procedure described in Ref. 2. 

In physical chemistry it is convenient to express concentrations as molalities and to use molality units to express the activity of the components. This is the convention we follow in this section. Accordingly, the standard state for a component consists of a solution in which that component has an activity of 1.0 mole (kg solvent) ... 

Remembering that a+ = y+m + and y2 = 7+7., where y is the mean ionic activity coefficient (appropriate to molality units), enables us to rewrite Equation (85) as... 

A convenient unit of solubility is the mass of solute per unit mass of solvent, or commonly g solute/100 g solvent. Interconversions with molal units and mol fractions are made readily when densities of the solutions are known. 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Molar concentration units were converted into molal units using the partial molar volume of the salt. (W e assume that RNA and other buffer components are present in such low concentrations that the density of the solution is not significantly different than a solution of water and salt alone.) The formula is... 

See Section 2.1 ofEisenberg (1976) for a full discussion of the relation between molal and molar units. Table 21.1 lists partial molar volumes of different salts. The difference between molar and molal units is about 1% for a 0.3 MKC1 solution, and rises to only 3% for 1 MKC1. These percentages are smaller than the error in most measurements of Kohs. 

Upon substitution of Eq. (21.27) into the linkage Eq. (21.26), and including the above approximation that (9himMgCi2/dln< MgCi2) 1, as well as the additional approximation that molarity and molality units are interchangeable, the linkage relation for MgCl2 becomes... 

The predicted values for the various solid phases shown in Table IV were calculated using the hydroxide and carbonate activity printout of the model. These values were used to calculate the equilibrium trace cation activities in the brine. The activity values were then divided by the predicted single ion activity coefficients and thereby converted to the molal concentration scale. These molal units were then converted to molar units, and then into the milligrams per kilogram of solution units reported. 

This is rigorous only if concentrations are expressed in mol kg (i.e., in molal units). The mixed acidity constants K and are the same whether molar or molal concentration units are used. Ajo for calcite is given in molar units. We would correct by considering the density of the seawater at any Tand P, but the correction is much smaller (< 3%) than the uncertainty in the value. 

We saw in Section 3-6 that concentrations of solutions are often expressed as percent by mass of solute or as molarity. Discussion of many physical properties of solutions is often made easier by expressing concentrations either in molality units or as mole fractions (Sections 14-9 to 14-14). 

Mass and energy balances may be written either in terms of mass or moles as long as all quantities are on the same basis. For example, if mass units are used, both the rate and the feed rate must be in mass units. For isothermal reactors molal units are more convenient, and the examples in Chap. 4 are solved using these units. Mass units may be more suitable for energy balances so that some examples in Chap. 5 are treated on a mass basis. In this chapter all the equations are written with the supposition that mass units are employed. Also note that the conversion x refers to the fraction of the reactant feed rate F that is converted, not to the fraction of the total feed rate /J. 

Solution As the conversion is to be based on the acetic acid and there is no acid in the initial charge to the reactor, the proper design equation is Eq. (4-18). Since the rate constants are in molal units, the concentrations will also be expressed in those units. 

Since the total conversion is becoming significant at the end of the second increment, it may be necessary to evaluate F/Cj, in terms of the actual mixture in the reactor instead of assuming that it equals that for the feed. This may be approximated by noting that F,Cp = Z,-To evaluate this summation molal units will be used. The rate of flow of each component at the end of the second increment will be... 

Solution The rate of each reaction (allyl chloride and dichloropropane formation) will be a constant and should be evaluated at the temperature and cornposition of the stream leaving the reactor. The temperature is determined by Eq. (3-6). For adiabatic operation and zero conversion in the feed this becomes, using molal units for F,... 

Since a large part of the NEA-TDB project deals with the thermodynamics of aqueous solutions, the units describing the amount of dissolved substance are used very frequently. For convenience, this review uses M as an abbreviation of mol-dm for molarity, c, and, in Appendices B and C, m as an abbreviation of mol-kg for molality, m. It is often necessary to convert concentration data from molarity to molality and vice versa. This conversion is used for the correction and extrapolation of equilibrium data to zero ionic strength by the specific ion interaction theory, which works in molality units (c/ Appendix B). This conversion is made in the following way. Molality is defined as moles of substance B dissolved in 1 kilogram of pure water. Molarity is defined as Cg moles of substance B dissolved in (/ - c M) kilogram of pure water, where p is the density of the solution in kg-dm and the molar weight of the solute in kg-mof. ... 

It should be noted that equilibrium constants need also to be converted if the concentration scale is changed from molarity to molality or vice versa. For a general equilibrium reaction, 0 = SVgB, the equilibrium constants can be expressed either in molarity or molality units, or, respectively ... 

The correction of log, P (C.17) to = 0 is done using the specific ion interaction equation, cf. TDB-2, which uses molal units ... 

D is the Debye-Huckel term in molal units and / , the ionic strength converted to molal units by using the conversion factors listed in [76BAE/MES] (p.439). The following list gives the details of this calculation. The resulting uncertainties in log p are obtained based on the rules of error propagation as described in Section C.6.2. 

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