Weak electrolyte.

Weak electrolytes arc only partly dissociated into ions and their thermodynamic properties in solutions are influenced by electrostatic attractive forces to a much lesser degree, owing to a smaller ionic concentration, than in the ease of strong electrolytes. As hero it is a case of equilibrium between the dissociated and un dissociated parts of the electrolyte, the law of mass action can be applied to the reaction of dissociation. 

The problem of equilibrium in the solution of a weak electrolyte, from the point of view of thermodynamics, can be solved as follows let us assume that e. g. the uni-univalent electrolyte A B is dissociated in the solution according to the equation  

If 1 mol of the electrolyte AB Incomes split to a gram-ions A and a gram-ions B, with the remainder (1— a.) of the oompound AB undissociated, the so called total mean molal free energy Q of the dissolved electrolyte is expressed by the sum total of products of the potentials of all components of the electrolyte and the corresponding number of their moles or gram-ions, thus  

From physico-chemical laws it is obvious that the condition of equilibrium 

The result reached is in agreement with the equations (V-4) and (V-7), according to which the difference between the free energy of products and that of reactants at equilibrium equals zero  

In this section, we discuss the thermodynamic treatment of weak-electrolyte solutions. In weak-electrolyte solutions, both undissociated molecules and ions exist. Thus, it may seem possible to describe the properties of these solutions by using the conventions developed either for nonelectrolyte or for electrolyte solutions. Our discussion will center around the usefulness of these conventions and the regions of concentration in which one may be more applicable than the other. For simplicity, our discussion will be restricted to the case of a weak electrolyte with the formula HA. 

Application of the expression for the chemical potential of a strong electrolyte given by Eq. (12-10) to the system consisting of weak-electrolyte solute HA in a solvent yields the result 

Equation (12-33) is suitable for strong electrolytes but leads to difficulties in the treatment of weak electrolytes. Measurements of //ha by the usual experimental methods show that, as Wha increases, y in Eq. (12-31) becomes a rapidly varying function of composition, deviating widely from unity. We therefore rearrange Eq. (12-31) to obtain 

Application of the conventions used for nonelectrolytes to the weak electrolyte HA yields an expression for the chemical potential of HA in the form 

According to the theory of Arrhenius, the variations of A with concentration are due to shifts in equilibrium between undissociated and dissociated species. This idea was expressed quantitatively by the Russian-German physical chemist Friedrich Wilhelm Ostwald (1853-1932) in terms of a dilution law. Consider an electrolyte AB which exists in solution partly as the undissociated species AB and partly as the ions A and B  

Suppose that n mol of the electrolyte are present in V dm, and that the fraction dissociated is a. The fraction not dissociated is 1 — a. The amounts of the three species present at equilibrium, and the corresponding concentrations, are therefore 

Therefore, for a given number of moles the degree of dissociation a must vary with the volume V as 

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We discuss classical non-ideal liquids before treating solids. The strongly interacting fluid systems of interest are hard spheres characterized by their harsh repulsions, atoms and molecules with dispersion interactions responsible for the liquid-vapour transitions of the rare gases, ionic systems including strong and weak electrolytes, simple and not quite so simple polar fluids like water. The solid phase systems discussed are ferroniagnets and alloys. 

The MS approximation for the RPM, i.e. charged hard spheres of the same size in a conthuium dielectric, was solved by Waisman and Lebowitz [46] using Laplace transfomis. The solutions can also be obtained [47] by an extension of Baxter s method to solve the PY approximation for hard spheres and sticky hard spheres. The method can be fiirtlier extended to solve the MS approximation for unsynnnetrical electrolytes (with hard cores of unequal size) and weak electrolytes, in which chemical bonding is municked by a delta fiinction interaction. We discuss the solution to the MS approximation for the syimnetrically charged RPM electrolyte. 

In a weak electrolyte (e.g. an aqueous solution of acetic acid) the solute molecules AB are incompletely dissociated into ions and according to the familiar chemical equation... 

Weak electrolytes in which dimerization (as opposed to ion pairing) is the result of chemical bonding between oppositely charged ions have been studied using a sticky electrolyte model (SEM). In this model, a delta fiinction interaction is introduced in the Mayer/-fiinction for the oppositely charged ions at a distance L = a, where a is the hard sphere diameter. The delta fiinction mimics bonding and tire Mayer /-function... 

The PY approximation for die binding leads to negative results for X the HNC approximation for this is satisfactory. Figure A2.3.18 shows the excess energy as a fiinction of the weak electrolyte concentration for the RPM and SEM for a 2-2 electrolyte. 

Zhu J and Rasaiah J C 1989 Solvent effects in weak electrolytes II. Dipolar hard sphere solvent an the sticky electrolyte model with L = a J. Chem. Phys. 91 505... 

Ionic conductors arise whenever there are mobile ions present. In electrolyte solutions, such ions are nonually fonued by the dissolution of an ionic solid. Provided the dissolution leads to the complete separation of the ionic components to fonu essentially independent anions and cations, the electrolyte is tenued strong. By contrast, weak electrolytes, such as organic carboxylic acids, are present mainly in the undissociated fonu in solution, with the total ionic concentration orders of magnitude lower than the fonual concentration of the solute. Ionic conductivity will be treated in some detail below, but we initially concentrate on the equilibrium stmcture of liquids and ionic solutions. 

The nitrato compound is a weak electrolyte in acetonitrile solution. 

Ion Exdiange—Stoichiometry In most apphcations, except for some weak-electrolyte and some concentrated-solution cases, the following summations apply ... 

Substances with only a slight tendency to dissociate to form ions in solution are called weak electrolytes. Acetic acid, CH3COOH, is a good example ... 

Acid Dissociation Constants and piC, Values for Some Weak Electrolyt (at 25°C) es... 

The Henderson-Hasselbalch equation provides a general solution to the quantitative treatment of acid-base equilibria in biological systems. Table 2.4 gives the acid dissociation constants and values for some weak electrolytes of biochemical interest. 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

FIGURE 2.13 The titration curves of several weak electrolytes acetic acid, Imidazole, and ammonlnm. Note that the shape of these different curves Is Identical. Only their position along the pH scale Is displaced. In accordance with their respective affinities for ions, as reflected In their differing values. 

A biologically important point is revealed by the basic shape of the titration curves of weak electrolytes in the region of the pK, pH remains relatively unaffected as increments of OH (or H ) are added. The weak acid and its conjugate base are acting as a buffer. 

Table 21.11 Ionisation constants of water and weak electrolytes and variation with temperature...

B. Ionisation constants of weak electrolytes and their temperature variation ... 

Complete and Incomplete Ionic Dissociation. In the foregoing chapter mention has been made of electrolytes that are completely dissociated in solution, and of weak electrolytes where free ions are accompanied by a certain proportion of neutral molecules. In the nineteenth century it was thought that aqueous solutions of even the strongest electrolytes contained a small proportion of neutral molecules. Opinion as to the relation between strong and weak electrolytes has passed through certain vicissitudes and we shall describe later how this problem has been resolved. 

The conductivity of a solution containing such molecular ions may be small compared with the value that would result from complete dissociation into atomic ions. In this way, in the absence of neutral molecules, we can have a weak electrolyte. The association constant for (29) has a value that is, of course, the reciprocal of the dissociation constant for the molecular ion (PbCl)+ the logarithms of the two equilibrium constants have the same numerical value, but opposite sign. 

Incomplete Dissociation into Free Ions. As is well known, there are many substances which behave as a strong electrolyte when dissolved in one solvent, but as a weak electrolyte when dissolved in another solvent. In any solvent the Debye-IIiickel-Onsager theory predicts how the ions of a solute should behave in an applied electric field, if the solute is completely dissociated into free ions. When we wish to survey the electrical conductivity of those solutes which (in certain solvents) behave as weak electrolytes, we have to ask, in each case, the question posed in Sec. 20 in this solution is it true that, at any moment, every ion responds to the applied electric field in the way predicted by the Debye-Hiickel theory, or does a certain fraction of the solute fail to respond to the field in this way In cases where it is true that, at any moment, a certain fraction of the solute fails to contribute to the conductivity, we have to ask the further question is this failure due to the presence of short-range forces of attraction, or can it be due merely to the presence of strong electrostatic forces ... 

Q 31. Proton Transfers in Solution. We must turn now to another aspect of the problem—the familiar fact that the most important weak electrolytes are those involving proton transfers, namely, the familiar... 

Then there are weak electrolytes, which dissolve mostly as molecules with a few ions. 

As we have pointed out, strong acids and bases are completely ionized in water. As a result, compounds such as HC1 and NaOH are strong electrolytes like NaCl. In contrast, molecular weak acids and weak bases are poor conductors because their water solutions contain relatively few ions. Hydrofluoric acid and ammonia are commonly described as weak electrolytes. 

The following figures represent species before and after they are dissolved in water. Classify each species as weak electrolyte, strong electrolyte, or nonelectrolyte. You may assume that species that dissociate during solution break up as ions. 

Freezing point lowering (or other colligative properties) can be used to determine the extent of dissociation of a weak electrolyte in water. The procedure followed is illustrated in Example 10.11. 

Weak electrolyte A species that, in water solution, forms an equilibrium mixture of molecules and ions, 82,... 

The conductivity of a 0.1 M acetic acid solution is much lower, however, than that of a 0.1 M hydrogen chloride solution. This and other experiments show that only a small fraction of the dissolved acetic acid, CH3COOH, has formed ions. Such a substance that dissolves and dissociates to ions only to a limited extent is called a weak electrolyte. 

Fig. 11-1. A strong electrolyte solution conducts better than a weak electrolyte solution.

Careful measurements show that water is, itself, a weak electrolyte. We shall consider it first. 

Now we can explain the low conductivity of pure water. Though water dissociates into ions, H+(aq) and OH (aq), it does so only to a very slight extent. At equilibrium, the ion concentia-tions are only IQ-7 M. Water is a weak electrolyte. 

Earlier in this chapter, strong and weak electrolytes were distinguished in terms of the degree to which the dissolved material forms ions. As a particular case, such distinctions can be made in terms of acids, furnishing a quantitative basis for defining the strength of an acid. 

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