Unitary quantities

Ideal and Nonrideal Solutions. Treatment of Solutions by Statistical Mechanics. A Solution Containing Diatomic Solute Particles. A Solution Containing Polyatomic Solute Particles. An Interstitial Solution. Review of Solutions in General. Quantities De-pendent on, and Quantities Independent of, the Composition of the Solution. Unitary Quantities and Cratic Quantities. Molality and Activities on the Molality Scale. 

If in a dilute solution we carry out q proton transfers according to (28), there will be a change in the cratic term, and at the same time the free energy will receive the contribution qj, that is to say, q units each equal to J Since each of the quantities qD, qL, qY, and qj consists of q equal units, we may call them unitary quantities, in contrast to the cratic term, which is a communal quantity, depending as it does on the amount of solvent as well as the amount of solute present. 

The numerical calculations for AgCl and Agl were given here as an example of the way in which one may obtain unitary quantities, by... 

If, in the same way, we use (72) to define for the other processes the characteristic units J, L, and Y, similar remarks can be made with regard to J and J, with regard to L and L, and likewise with regard to Y and Y. By equation (72) a precise definition has been given to the characteristic unit of any process and we must hope that in the future the study of ionic solutions will eventually provide a complete interpretation of these quantities. At the present time we are very far from this goal. At any rate the total unitary quantity for each process must be isolated and evaluated before it can be interpreted. In the remaining chapters of this book we shall have occasion to mention only the quantities D, L, Y, J, and U, defined in accordance with (72) and (73). If, however, anyone should wish to give a precise definition to a quantity that includes less than the whole of the unitary term, the symbols in bold-faced type remain available for this purpose. 

It is a result of this relation that in any process whatever the heat of reaction per mole at extreme dilution, usually denoted by A//0, is a unitary quantity, not depending on the amount of solvent present. According to the Gibbs-IIelmholtz relation1 we have... 

Turning now to the non-ideal solution, we may answer question (1) by saying that the value of (163) will vary with concentration only insofar as the solution differs from an ideal solution and we can proceed to ask a third question how would the value of (163) vary with concentration for an ionic solution in the extremely dilute range We must answer that in a series of extremely dilute solutions the value of (163) would be constant within the experimental error it is, in fact, a unitary quantity, characteristic of the solute dissolving in the given solvent. As in See. 55, this constant value adopted by (163) in extremely dilute solutions may conveniently be written as the limiting value as x tends to zero thus... 

We shall discuss now in greater detail the process depicted in Fig. 11, where ions are taken from the surface of a solid into a solvent. In Sec. 52 we defined a unitary quantity L, which will play a role similar to that played by D and J. The equilibrium between a solid and its saturated solution is an examplo of the equilibria considered in Sec. 51. If a few additional pairs of ions are taken into this solution, the value of dF/dn is zero. We now say that this zero value can come about only when the communal part and the unitary part have values that are equal and opposite. A saturated solution is, in fact, the solution that provides these equal and opposite values. The communal term ill the free energy differs from the cratic term by the value that d has in the saturated solution. When this value is known, AF° and L can be evaluated. Let m.ai, y. t, and x,ai refer to the concentration of the saturated solution. Then, writing AF = 0 in (108), we obtain for the standard free energy... 

The pentaerythritol was introduced into the acid in finely divided and well-dispersed particles and not in large unitary quantities. The entire 92 parts of pentaerythritol tetranitrate was introduced in 35 to 40 minutes. The pentaerythritol thus obtained was separated from the spent acid by filtering or drowning in water. To recover the spent acid the charge was passed onto a nutsch and filtered. The crude product was washed with water, then with a weak water-soluble alkali solution, such as sodium carbonate for example, and subsequently with water in order to remove the acid. 

The thermodynamics of solute-solvent interactions is most conveniently described in terms of unitary quantities. The unitary free energy and unitary entropy changes accompanying some process (such as the transfer of hydrocarbon from nonpolar solvent to water or the transfer of hydrocarbon from pure hydrocarbon to water) are the standard free-energy and entropy changes corrected for any translational entropy terms (the cratic entropy) that are not intrinsic to the interaction under consideration. The cratic entropy is simply the entropy of mixing the solute and solvent into an ideal solution. With the cratic contribution removed, the unitary free energy and entropy contain only contributions to the thermodynamics of the process that come from the interaction of the individual solute molecules with the solvent. 

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