Enthalpies of dilution

Next let us consider a dilution process in which solvent is transferred from a pure solvent phase to a solution phase. The molar differential enthalpy of dilution is the rate of change of H with the advancement dii at constant T and p of the dilution process, where is the amount of solvent transferred  

An integral enthalpy of dilution, A7/(dil), refers to the enthalpy change for transfer of a finite amount of solvent from a pure solvent phase to a solution, T and p being the same before and after the process. The molar integral enthalpy of dilution is the ratio of 

A//(dil) and the amount of solute in the solution. For a dilution process at constant solute amount b in which the molality changes from mg to mg, this book will use the notation A//m(dil, mg mg)  

There is a simple relation between molar integral enthalpies of solution and dilution, as the following derivation demonstrates. Consider the following two ways of preparing a solution of molality mg from pure solvent and solute phases. Both paths are at constant T and p irn, closed system. 

Path 1 The solution forms directly by dissolution of the solute in the solvent. The enthalpy change is nBA//m(sol,mg), where the molality of the solution is indicated in parentheses. 

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Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

In this process, the original solution is diluted by the addition of pure solvent, and hence, the enthalpy change is called an integral enthalpy of dilution. 

The relative apparent molar enthalpy, 4>L, is usually obtained from enthalpy of dilution measurements in which the moles of solute are held constant and additional solvent is added to dilute the starting solution. The process can be represented as... 

The enthalpy change for this process is an integral enthalpy of dilution for which we saw earlier that... 

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,... 

Figure 7.9 (a) Enthalpies of dilution starting with a solution containing 3 moles fEO per 1 mole HC1 (m = 18.50 or w1/2 = 4.30) and (b), relative apparent molar enthalpies (4>L) and relative partial molar enthalpies (L and L >) for the resulting mixtures. 

A thermal stability study was first carried out to determine the following information (1) the solidification temperature as a function of the concentration of the sulfonate (2) the enthalpy of decomposition by DTA (3) the autocatalytic nature of the decomposition by Dewar flask (4) kinetic data for decomposition by Dewar flask (5) the time to maximum rate by ARC, and (6) the heat generation as a function of temperature, also by ARC. In addition, the enthalpy of dilution was determined for various potential water leak rates. These data were useful in defining emergency response times. 

In addition to the activity and osmotic coefficients at room temperature, the first temperature derivatives and the related enthalpy of dilution data were considered for over 100 electrolytes (26, 29). The data for electrolytes at higher temperatures become progressively more sparse. Quite a few solutes have been measured up to about 50°C (and down to 0°C). Also, over this range, the equations using just first temperature derivatives have some validity for rough estimates in other cases. But the effects of the second derivative (or the heat capacity) on activity coefficients at higher temperatures is very substantial. 

In addition, the critical evaluation of enthalpies of dilution and solution, as well as evaluations of heat capacities have been initiated. These evaluations will allow calculations and correlations of activity and osmotic coefficients as a function of temperature and composition. 

The techniques used in the critical evaluation and correlation of thermodynamic properties of aqueous polyvalent electrolytes are described. The Electrolyte Data Center is engaged in the correlation of activity and osmotic coefficients, enthalpies of dilution and solution, heat capacities, and ionic equilibrium constants for aqueous salt solutions. 

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 2. Results of an enthalpy of dilution run on aqueous MgCh at 473 K (thermopile voltage vs. time—maximum 1.23 0.002 Q = 1.129 watts AT...

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 18.2. Enthalpies of Dilution of Aqueous Solutions of Serine [4]... 

The apparent molar enthalpy d>//2 has been used to derive relative partial molar enthalpies from enthalpy of dilution data. The apparent molar enthalpy is dehned as... 

Enthalpy of dilution data can be used to calculate excess enthalpies by a procedure analogous to that we used to calculate relative molar enthalpy from enthalpy of dilution. We can describe the dilution of an aqueous solution of rii moles of water and 2 nioles of solute S with (riif — riu) moles of water by the equation... 

The constants needed to obtain a value of ifl as a function of m can be obtained by fitting the enthalpy of dilution data to Equation (18.67) by a nonlinear least-squares method, (see Section A.l). 

Show that the molar enthalpy of dilution A//dii/ 2 is equal to... 

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

Once activity coefficients have been determined at one temperature by one of the methods mentioned above, calorimetric measurement of enthalpies of dilution can be used to determine activity coefficients at other temperatures. 

Extension of Activity Coefficient Data to Additionai Temperatures with Enthalpy of Dilution Data... 

We see from Section 18.1 that can be calculated from data for enthalpies of dilution fitted to a polynomial such as that in Equation (18.27). The result for from Equation (18.28) is... 

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]. 

The enthalpies of dilution of BE were required to calculate the enthalpies of transfer (19). From these Integral enthalpies of dilution AHj.jj the relative apparent molar enthalpies were derived following the technique of Fortier et al (21). The values of AHjjj corresponding to the Initial and final molalities are given In Table 1 along with the parametric equation for. ... 

Thermochemically, the association is not a major factor since the enthalpies of dilution of Grignard reagents are very small in diethyl ether as well as in THF An explanation... 

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