Molality procedure

Procedure. Calculate the heats of solution of the two species, KF and KF HOAc, at each of the four given molalities from a knowledge of the heat capacity. Calculate the enthalpy of solution per mole of solute at each concentration. Find... 

Procedure. A study on the partial molal volume of ZnCl2 solutions gave the following data (Alberty, 1987)... 

For preliminary studies of batch rectification of multicomponent mixtures, shortcut methods that assume constant molal overflow and negligible vapor and liquid holdup are useful. The method of Diwekar and Madhaven [Ind. Eng. Chem. Res., 30, 713 (1991)] can be used for constant reflux or constant overhead rate. The method of Sundaram and Evans [Ind. Eng. Chem. Res., 32, 511 (1993)] applies only to the case of constant remix, but is easy to apply. Both methods employ the Fenske-Uuderwood-GiUilaud (FUG) shortcut procedure at successive time steps. Thus, batch rectification is treated as a sequence of continuous, steady-state rectifications. 

A procedure like this has been adopted in the literature, except that it is the value for the hydrogen ion that has been set equal to zero. This involves a slightly more difficult concept for, when a proton is added to water, it converts an H20 molecule into an (HsO)+ ion. The entropy of the original water molecule is replaced by the entropy of the (HsO)+ ion and its co-sphere. When the partial molal entropy of HC1 in aqueous solution has been determined, the whole is assigned to the Cl- ion that is to say, the value for the hydrogen ion is set equal to zero, and the values for all other species of ions are expressed relative to this zero. 

FIGURE 8.26 The steps taken to prepare a solution of a given molality. First (left), the required masses of solute and solvent are measured out. Then (right), the solute is dissolved in the solvent. Compare this procedure with that for preparing a solution of given molarity (see Fig. G.8). 

In order to predict approximate values of the principal susceptibilities K i (= Ki) and K3 ( = K1+AK) of these substances we may adopt the following empirical procedure. The molal susceptibility of H2 is — 4.00X10-6 we accept... 

To see the autocatalytic nature of the reaction, we can compare the simulation to one made assuming a constant amount of catalyst. Taking mMn(OH)(s) to be 4.5 xlO-4 molal, its value when oxidation in the previous run is complete, the procedure is... 

To incorporate nonlinear rate laws into the solution procedure for tracing kinetic reaction paths (Section 16.3), we need to find the derivative of the reaction rate with respect to the molalities m,- of the basis species A,. The derivatives are given by,... 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

System NH -S02 H20 For comparison with calculated data only the experimental results of Johnstone (16) and Boublik et al. (JT 1 ) were used. (Boublik et al. investigated the system NH3-SO2-SO3-H2O only some of their results with very low SO3/SO2 ratios were used for comparison with calculated data). Experimental results by other authors mostly cover very high solute concentrations in the liquid phase (20 molal and more) and are, therefore, not suitable for comparison with the models discussed here. As van Krevelen s method cannot be used for this system, the comparison is limited to the other procedures. Partial pressures of ammonia calculated from the BR-model are generally too large the calculated values exceed the experimental results mostly by a factor larger than 5. The EMNP method generally yields partial pressures which are only about half as large as the measured ones. The calculated partial pressures of SO2 are always too small, for temperatures between 50 and 90 °C the mean deviations a-mount from 20 to 40 per cent for the EMNP-model and from 40 to 70 per cent for the BR-model. 

At 25°C the partial molar volume of urea [CO(NH2)2] solution in water is found by a nonlinear least-squares fitting procedure to be the following function of m2 up to 17-molal concentration (with V in cm mol ), with experimental data from Gucker et al. [10] and the form of the equation from Stokes ... 

In Chapters 16 and 17, we developed procedures for defining standard states for nonelectrolyte solutes and for determining the numeric values of the corresponding activities and activity coefficients from experimental measurements. The activity of the solute is defined by Equation (16.1) and by either Equation (16.3) or Equation (16.4) for the hypothetical unit mole fraction standard state (X2° = 1) or the hypothetical 1-molal standard state (m = 1), respectively. The activity of the solute is obtained from the activity of the solvent by use of the Gibbs-Duhem equation, as in Section 17.5. When the solute activity is plotted against the appropriate composition variable, the portion of the resulting curve in the dilute region in which the solute follows Henry s law is extrapolated to X2 = 1 or (m2/m°) = 1 to find the standard state. 

Of course, (4.9) cannot be used at higher ionic strengths. A more precise procedure is then required, such as the Robinson-Stokes equation for the mean molal activity coefficient [11] (see also [86a], chapter 1)... 

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

The standard emf E° of the cell was determined by means of an extrapolation technique involving a function of the measured emf E (which was measured experimentally), taken to the limit of zero ionic strength /. A linear function of I was observed when the Debye-Hiickel equation (in its extended form) (12) was introduced for the activity coefficient of hydrobromic acid over the experimental range of molalities m. With this type of mathematical treatment, the adjustable parameter became a0, the ion-size parameter, and a slope factor / . This procedure is essentially the same as that used in our earlier determinations (7,10) although no corrections of E° for ion association were taken into account (e = 49.5 at 298.15°K). 

His procedure was used for the calculation of the activity coefficients in the aqueous solution of two electrolytes with a common ion from isopiestic data (3). Kelly, Robinson, and Stokes (4) proposed a treatment of isopiestic data of ternary systems with two electrolytes by a procedure based on the assumption that at all values of molal concentrations, mi,m2, the partial derivatives may be expressed by a sum of two functions in their differential form as follows ... 

The procedure starts with the specified terminal compositions and applies the material and energy balances such as Eqs. (13.64) and (13.65) and equilibrium relations alternately stage by stage. When the compositions from the top and from the bottom agree closely, the correct numbers of stages have been found. Such procedures will be illustrated first with a graphical method based on constant molal overflow. 

A brief description of this procedure is abstracted from the fuller treatment of Henley and Seader (1981). The MESH equations (13.182)-(13.186) in terms of mol fractions are transformed into equations with molal flow rates of individual components in the liquid phase ltJ and vapor phase vif as the primary variables. The relations between the transformed variables are in this list ... 

Our procedure was to follow the changes in concentrations and ionic strength as the water is evaporated, and by correcting ion molalities by activity coefficients, keep track of the ion activity products of the various... 

Similar relationships can be used to obtain the other thermodynamic properties. The reader is referred to the Pitzer and Brewer reference for details. This procedure provides a good method for determining the thermodynamic properties because of the nature of Bm. Figure 18.2 shows a graph of B as a function of molality for several electrolytes. We note that B changes slowly with molality (except at low m where more rapid changes are not as important in the calculation). Thus, it is easy to interpolate in a table of AB values, and an extensive table is not needed to obtain accurate values for the thermodynamic properties. 

Equation 2.41 would be useful if we could estimate the values of the solubility parameters and the partial molal volume of the supercooled liquid solute. Additive procedures, based on functional groups found in the molecule, have been developed to estimate partial molal volumes and solubility parameters (Small, 1951 Hoy, 1970 Konstam and Feairheller, 1970 Fedors, 1974). Another... 

To determine the theoretical decomposition voltage of hydrochloric acid in solution with molal concentration m = l at a pressure of 1 atm. and temperature 25 °C with y i, = 0.811, the same procedure will be used ... 

For species at low concentration in aqueous solution, a different procedure has been widely adopted, because in this case the equality of a, and x, is usually far from correct. The method is based on the use of a fictitious or hypothetical standard state for the solute, taken as the state that would exist if the solute obeyed Henry s law up to a molality m of unity. In this application, Henry s law is expressed as... 

Note that by our procedure r m) is evaluated at the freezing temperature of the solution Tf Tc - 9. The first term on the right is easily found from (3.12.10). The second term is found from a plot of — m-1(l — 6/Am) versus m, and the third term is found from a plot of cfl/m versus 6, taking the area under the resulting curve in both cases. This requires measurements of a series of values corresponding to a set of closely spaced solutions for different molalities mi. r m)(Tf) is now known note that... 

One notes that a knowledge of the mean molal activity of HCi in a solution of molality m and the tabulation of standard emfs enables one to calculate the value for the schematized cell. Normally, however, the procedure is used in reverse i.e., from a measurement of emfs the mean activity coefficients for ions in solution may then be determined. The procedure is now... 

The molalities m (concentration in moles per kilogram of solvent) that are needed for the calculations can be obtained from the molarities M (concentration in moles per liter of solution) obtained from the volumetric procedures by using the equation... 

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