Molal enthalpy

The quantity Hi(v°) is the partial molal enthalpy (molal volume) of component / in the hypothetical infinitely dilute state. Thus the heat of solution from the pure liquids at constant pressure is... 

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... 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

In general, values and molal enthalpies in these MESH equations are complex imphcit functions of stage temperature, stage pressure, and equilibrium mole fractions ... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

To show how we can calculate relative apparent molar enthalpies from enthalpies of dilution, consider as an example, a process in which we start with a HC1 solution of molality m = 18.50 mol-kg-1 and dilute it to a concentration of m = 11.10 mol-kg-1. The initial solution contains 3 moles of H20 per mole of HC1 (A = 3) while the final solution has A = 5. The enthalpy change for that process is measured. Then the m = 11.10 mol-kg-1 solution is diluted to one with m = 4.63 mol-kg-1 and its enthalpy of dilution measured. The series continues as illustrated below,... 

If a2/ax = gim2lgxmx m2/mx (a = activity, g = molal activity coefficient, m = molality) if Henry s law is obeyed and a = gm, mh and m2 are the molal solubilities of the polymorphs, and if the standard molar enthalpies and standard molar entropies of solution are, respectively,... 

Robinson and Baker,18 and Wai and Yates 19 below 71 wt% they can be converted to other temperatures using partial molal enthalpies calculated from the relative enthalpies given by Bidinosti and Biermann.47 Similar values for HC1 in Tables 7 and 8 are obtained from Randall and Young48 and Akerlof and Teare,49 quoted by Bunnett,50 and can be converted to other temperatures using coefficients supplied by Liu and Gren.51 The author uses computer programs, written in Microsoft Basic for the Macintosh, that compute these quantities and others. 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

We have been actively developing two types of calorimeters which will operate at elevated temperatures and pressures. One type is a heat of mixing calorimeter to measure enthalpies of dilution in order to obtain differences in partial molal enthalpy... 

Figure 3. Apparent molal enthalpy of aqueous NaCl as a function of molality...

Solute. The standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4). In both cases, the standard state is obtained by extrapolation from the Henry s-Iaw line that describes behavior at infinite dilution. Thus, the partial molar enthalpy of the standard state is not that of the actual pure solute or the actual 1 -molal solution. 

We have pointed out that a concentration m2(o of the solute in the real solution may have an activity of 1, which is equal to the activity of the hypothetical 1-molal standard state. Also, Hm2, the partial molar enthalpy of the solute in the standard state, equals the partial molar enthalpy of the solute at infinite dilution. We might inquire whether the partial molar entropy of the solute in the standard state corresponds to the partial molar entropy in either of these two solutions. 

Relative partial molar enthalpies can also be obtained from measurements of enthalpies of dilution. Humphrey et al. [4] have used enthalpy of dilution measurements to calculate relative partial molar enthalpies in aqueous solutions of amino acids. Their data for AH n of aqueous solutions of serine are shown in Table 18.2, where mj is the initial molality of the solution, rrif is the molality after addition of a small amount of solvent, and is equal to the measured AH divided by ti2, which is the number of moles of solute in the solutions. 

TABLE 18.10. Enthalpies of Dilution and Initial and Einal Molalities for Aqueous Solutions of Glycyl-L-Valine at 298.15 K... 

The data required to carry out such a calculation are the enthalpies of dilution as a function of molality at each temperature of interest. The integration would have to be carried out numerically. Enthalpy data for aqueous calcium chloride have been reported by Simonson, et al. [5]. 

Equilibrium constants are also dependent on temperature and pressure. The temperature functionality can be predicted from a reaction s enthalpy and entropy changes. The effect of pressure can be significant when comparing speciation at the sea surface to that in the deep sea. Empirical equations are used to adapt equilibrium constants measured at 1 atm for high-pressure conditions. Equilibrium constants can be formulated from solute concentrations in units of molarity, molality, or even moles per kilogram of seawater. 

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