Partial molal

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

COMPUTER PROJECT 3-4 The Partial Molal Volume of ZnCl2... 

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

Find the partial molal volume of ZnCl2 in these solutions at 0.5, 1.0, 1.5 and 2.0 molar concentrations. 

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).]... 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

Entropy of Solution and Partial Molal Entropy. If the heat of solution of a solute is known, and the free energy of solution is known at some low concentration, then the entropy of solution AS at the same concentration can at once be found from the relation... 

In the case of a sparingly soluble substance, if each of the quantities in (64) is divided by Avogadro s constant, we confirm the statement made above— namely, that, if AS at per ion pair is added to the contribution made to the entropy of the crystal by each ion pair, in this way we evaluate the contribution made by one additional ion pair to the entropy of the saturated solution and it is important to grasp that this contribution depends only on the presence of the additional pair of ions in the solution and does not depend on where they have come from. They might have been introduced into the solution from a vacuum, instead of from the surface of a solid. In (64) the quantities on the right-hand side refer to the solution of a crystal, but the quantity (S2 — Si) does not it denotes merely a change in the entropy of a solution due to the presence of additional ions, which may have come from anywhere. When Si denotes the entropy of a sufficiently large amount of solution, (S2 — Si) is the partial molal entropy of the solute in this solution. 

When solid AgCl is in contact with its saturated aqueous solution, we have found that, if additional ion pairs are transferred from the surface of the crystal to the solution, the total change of entropy is equivalent to 52.8 e.u Since the entropy of the solid is 23.0 e.u., we find that the partial molal entropy of AgCl in its saturated aqueous solution at 25°C is... 

Since the saturated solutions of AgT and AgCl are both very dilute, it is of interest to examine their partial molal entropies, to see whether we can make a comparison between the values of the unitary terms. As mentioned above, the heat of precipitation of silver iodide was found by calorimetric measurement to be 1.16 electron-volts per ion pair, or 26,710 cal/mole. Dividing this by the temperature, we find for the entropy of solution of the crystal in the saturated solution the value... 

The entropy of solid Agl is a little larger than that of AgCl, namely, 27.1 e.u., as compared with 23.0 e.u. Using (64) we find for the partial molal entropy of Agl in its saturated solution the value... 

Conventional Partial Molal Ionic Entropies. Correlation between Ionic Entropy and Viscosity. Conventional Partial Molal Entropy of (H30)+ and (OH)-. The Conventional and the Unitary Entropy of Solution. Solutes in Aaueous Solution. Solutes in Methanol Solution. 

Suppose that we arbitrarily set the partial molal entropy of the K+ ion equal to zero. This means that we assign to the Cl- ion the whole of the partial molal entropy of the ion pair (K+ + Cl-) that is to say, we assign to the Cl- ion, not only the unitary term for the Cl- ion, but also the cratic term for both ions, and also the unitary term for the potassium ion. 

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. 

Fto. 54. Viscosity S-coofHoients from Table 24 plotted against partial molal entropies from Table 25 (on scale of 0.0 for H+). 

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The molar entropy of solution of a crystal—the AS0 of (168)—may be regarded as the difference between (1) the molar entropy of the crystal, and (2) the partial molal entropy of the solute in a solution of a certain Concentration. The question arises In a solution of what concentration Now we notice that (168) may be written in the form... 

Accordingly, the conventional partial molal entropies of ions in solution are often said to refer to the ions in a one-molal solution (m = 1) hot in a real one-molal solution, but in a hypothetical ideal one-molal solution, where the contribution from the interionic forces is taken to be zero, and the cratic term replaces the communal term. 

Table 30. The Unitary Partial Molal Entropy in Aqueous Solution...

Taking the values for the Ag+ ion and the Cl" ion from Table 25, and adjusting the cratic term, find the value of the partial molal entropy of silver chlorido in an aqueous solution having a molality equal to 10 8. 

Table 31. Partial Molal Volume of Ion PAins at Infinite Dilution in Water at 25°C and 1 Atmosphere, and tiie Molal Volume in tiie Crystalline Solid, Both in Cm /Mole...

Fig. 57. Ion pairs in aqueous solution at 25°C. Partial molal volume at extreme dilution, plotted against the volume in the crystalline solid, both in cubic centimeters per mole.

Let us now ask how this value could be used as a basis from which to measure the local disturbance of the water structure that will be caused by each ionic field. The electrostriction round each ion may lead to a local increase in the density of the solvent. As an example, let us first consider the following imaginary case let us suppose that in the neighborhood of each ion the density is such that 101 water molecules occupy the volume initially occupied by 100 molecules and that more distant molecules are not appreciably affected. In this case the local increase in density would exactly compensate for the 36.0 cm1 increment in volume per mole of KF. The volume of the solution would be the same as that of the initial pure solvent, and the partial molal volume of KF at infinite dilution would be zero. Moreover, if we had supposed that in the vicinity of each ion 101 molecules occupy rather less than the volume initially occupied by 100 molecules, the partial molal volume of the solute would in this case have a negative value. 

As mentioned in Sec. 90 we may think of this AS0 as being the difference between the molar entropy of solid 1 j2C03 and the partial molal entropies of one (C03) ion and two Lif ions, each in its hypothetical standard aqueous solution. We propose now to compare the AS of the reaction... 

From Table 44 it will be seen that the molar entropy of solid Li2C03 amounts to 21.60 cal/degree. In Sec. 104 it was pointed out that, if the AS0 for the process (192) is added to the entropy of solid Li2C03, the sum will be equal to the partial molal entropies of the COJ" ion and two Li+ ions. For this sum then we obtain... 

Table 45. Conventional Partial Molal Entropies of Ions in Water at 25°C...

Electrostriotion, 188, 190-192 Energy levels, 34, 151-152 Entropy, of crystals, 95, 180, 211, 267 partial molal (see Partial molal entropy) of solution (see Solution)... 

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