Activity molality and

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. 

Molality and Activities on the Molality Scale. In order to give a numerical value to the concentration of a solution, it is customary to... 

So far we have considered only symmetrical 1 1 electrolytes such as HC1, K.CI, or MgS04. For unsymmetrical electrolytes, the limiting law takes a different form, and different relationships between activity, molality and activity coefficient are obtained. For example, for the 2 1 electrolyte, Na SO,, the dissociation reaction is... 

For the concentrations of dissolved species encountered in flue gas scrubbing applications, the equilibria must be formulated in terms of activities rather than molalities. The activities, molalities, and activity coefficients are related by... 

PHREEQE can calculate pH, redox potential, concentration of elements, molalities and activities of aqueous species, and mineral or gas mass transfer as a function of reaction progress. The program is capable of simulating reactions due to mixing, titrating, net irreversible reaction, temperature changes, and mineral- or gas- phase equilibration. 

We recognize that we cannot determine experimentally the thermodynamic properties of a single type of ion in solution, because both positive and negative ions must be present to satisfy the condition of electrical neutrality. However, we can use equations based on those previously derived, and express the chemical potential of a single type of ion in terms of the concentration variables at a given temperature and pressure. We follow convention here and use molalities and activity coefficients. Then we have... 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

It is useful to review the problems when we express the chemical potential of the solute in terms of its molality and activity coefficient as well as by Equation (8.181). When we do so, we obtain... 

If we had expressed the chemical potential of the third component in terms of its molality and activity coefficient rather than the mole fraction and excess chemical potential, Equation (10.258) would be expressed as... 

The determination of the value of SB may be illustrated by the use of Equation (12.42). We choose the standard state of silver and silver chloride to be the solid state at the experimental temperature and pressure, so that the activities are unity. We also express the activities of the hydrogen and chloride ions in terms of their molalities and activity coefficients. Equation (12.41) then becomes... 

The value of K can be calculated provided that we know the molalities and activity coefficients of the species which are indicated. The molality of HA is (mt - mH,) and that of A is (m2 + mH+). When K is sufficiently small,... 

This is a good time to bring in a concept that you probably have not encountered before activity. Activity is the effective concentration of a solute, and activity is always less than molality. You need to become increasingly concerned about the difference between molality and activity when the concentration rises above 0.1 molal, especially if you are dealing with ionic solutes. In the previous example, we assumed that sodium chloride dissolves in water to give completely separated ions that have no interactions with each other. Is this reasonable ... 

Dissociation Constants of Bases.—The dissociation constants of bases can be determined, in principle, by methods which are essentially similar to those employed for acids. Replacing activities in equation (8) by the product of molalities and activity coefficients, it is seen that for a base... 

We now have activity, molality and activity coefficient, defined in terms of the geometric mean of the ionic values, with, as usual ... 

The formation of ion pairs such as CaHCOj and the others considered in equation (19.36) reduces the concentration of free (unassociated) anions such as HCOJ , Cl, and SO4 . The concentrations of all free anions are therefore reduced at this stage by the amount of each tied up in ion pairs and complexes. This changes the ionic strength as well, so new estimates of the activity coefficients must also be made at this point. The calculation of free cation and ion pair concentrations is then repeated with these new estimates of anion molalities and activity coefficients. The iteration is continued until the mass balances for all cations and acid anions (such as equations (19.32) and (19.36) agree satisfactorily vk ith measured quantities. 

In addition one can obtain the molalities and activities of all of the species in accordance with the aqueous phase model and in eqnilibrium with the solid phase or the other phases involved (solid, organic or ion exchanger). 

That is, the activity of the weak acid in binary solution is equal to the activity of the weak acid in the ternary solution. This relationship may also be expressed in terms of the molalities and activity coefficients ... 

FORHAT(7x, Liquid Phase Molalities and Activity Coefficients //... 

Determine the mean ionic molality and activity for a 0.200-molal solution of Cr(N03)3 if its mean activity coefficient y+ is 0.285. 

Assume ua = l,fY = 1 (for example, NaCl). Rewriting the activities in terms of molalities and activity coefficients, we obtain... 

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