Weak incompletely dissociated electrolytes

Experimental use of Equations (4.5) and (4.7) from the Arrhenius theory do make possible the determination of dissociation constants even though both equations are based upon erroneous assumptions. Ions, even in dilute solution, do not behave as ideal solutes and their conductances are functions of concentration. The reasons that equilibrium constants determined by the Arrhenius equations are fairly good are that, firstly, interactions between ions are less numerous than for a strong electrolyte and secondly, and more important, corrections to a by the use of the Onsager equation and introduction of 

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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... 

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 ... 

Interionic forces are relatively less important for weak electrolytes because the concentrations of ions are relatively rather low as a result of incomplete dissociation. Thus, in agreement with the classical (Arrhenius) theory of weak electrolytes, the concentration dependence of the molar conductivity can be attributed approximately to the dependence of the degree of dissociation a on the concentration. If the degree of dissociation... 

If a solute of the general formula AX (A is the chiral ion and X is an achiral ion) dissociates completely into ions once dissolved, then the solubility of the racemic conglomerate, SR, is equal to n%V2-SA (where SA is concentration of A in a solution saturated with AX ). If the solute is of the type AX, then 5 = V2-5a. The subscript n refers to the achiral ion and may be fractional, and so A2X must be represented by AXi/. If dissociation of AX is incomplete, SA lies between n i/2-SA and 2SA. For weakly dissociated electrolytes (such as carboxylic acids), SR is approximately 2SA. 

Where both the acid and the base are strong electrolytes, the neutralization point will be at pH = 7 and the end point break will be distinct unless the solutions are very dilute (< 10" 3 mol dm"3). The composition of the titrand at any point in the titration may W computed from the total amount of acid and base present. However, when one of the reactants is a weak acid or base the picture is less clear. The incomplete dissociation of the acid or base and the hydrolysis of the salt produced in the reaction must be taken into account when.calculations of end points and solution composition are made. These points have been considered in chapter 3 and are used in the indicator selection procedure outlined in the preceding section of this chapter. 

In addition to the reason for incomplete dissociation just considered, there are some cases, e.g., weak acids and many salts of the transition and other metals, in which the electrolyte is not wholly ionized. These substances exist to some extent in the form of un-ionized molecules a weak acid, such as acetic acid, provides an excellent illustration of this type of behavior. The solution contains un-ionized, covalent molecules, quite apart from the possibility of ion-pairs. With sodium chlorides, and similar electrolytes, on the other hand, there are probably no actual covalent molecules of sodium chloride in solution, although there may be ion-pairs in which the ions are held together by forces of electrostatic attraction. 

Weak electrolytes Solutes that are incompletely dissociated into ions in a particular solvent. 

The 1957 Fuoss-Onsager equation can be adapted to take account of association of ions to form ion pairs and to account for incomplete dissociation of weak electrolytes. Chemically these are two different types of situation, but physically they are the same, viz. some of the ions are removed from solution by formation of ion pairs, or by formation of undissociated molecular species. The physical manifestation is that not all of the solute will be able to conduct the current, and so the observed conductance will be lower than that predicted by the... 

Aqueous solutions of cadmium halides appear, superficially, to be incompletely dissociated, that is, to be weak electrolytes. Although there are significant amounts of the undissociated halides, CdX2, and polymeric species10 present in moderately concentrated solutions, there are other species also present as shown in Table 18-6. Thus the solutions are best regarded as systems containing all possible species in equilibrium rather than simply as solutions of a weak electrolyte. 

This last condition is fulfilled when the ionic concentrations are very low, as they are in fact in dilute solutions of weak electrolytes. The dissociation constants of substances such as weak organic acids can be determined by a combination of the formulae of Ostwald and Arrhenius, but the procedure is quite inadmissible for salts. Here the degree of dissociation is large. In fact the value of a is often indistinguishable from unity, and the mutual influences of the ions are considerable. They are calculable in principle by methods due to Debye and Hiickel, and operate differently on different properties. The procedure outlined on p. 276 allows the calculation of the activity coefiicients. In general the thermodynamic properties of the salt in solution correspond to those of a system with apparently incomplete dissociation, not because the concentrations of the ions are reduced by molecule formation but because the activity coefficients are lowered by mutual ionic influences. 

The so-called weak electrolytes did not follow Kohlrausch s law. This could be partially explained by incomplete dissociation. The dissociation equilibrium of a salt CA (C cation, A anion) in a diluted electrolyte, where activities a can be approximately substimted by concentrations c, is described by the equation... 

Electrolyte models. Assuming dissociation of the donor salt in the glass matrix, there is either a complete dissociation (strong electrolyte, Anderson-Stuart modeF°) or incomplete dissociation (weak electrolyte, Ravaine-Souqueti model) and the cations usually move in the matrix. 

At large applied voltages (i.e., in strong electric field of about lO -lO V/cm), the velocity of ions is too large to allow perfect establishment of the cloud of solvent molecules around the ions. The actually observed conductance is larger than expected the effect is called electrophoretic or (first) Wien effect. In solutions of weak electrolytes (i.e., incompletely dissociated ones), the large strength of the electric field may cause artificially enhanced dissociation this also results in increased conductance. It is called dissociation... 

We next treat an incompletely dissociated solution due to, for example, the formation of solvation shells because of ion-pairs. Let 1 mole of this weak electrolyte MA be dissolved into v+ mole of cations with a charge z+ and v mole of anions with a charge z under the dissociation constant K, and suppose that the solution reaches a dissociation equilibrium. Then we have... 

The forces binding the atoms A and B together in AB are chemical in nature and must be introduced, at least approximately, in the Hamiltonian. Then it should be possible to apply the same theoretical methods (e.g., HNC and MS approximations) used to study strong electrolytes to investigate incomplete dissociation in weak electrolytes as well. The binding between A and B is quite distinct from the ion pair formation observed for higher valence electrolytes (Fig. 9). In these cases no alterations in the Hamiltonian models already discussed were required to account qualitatively for the experimental observations. 

In the case of ionic solutions, a factor called the Van t Hoff factor, due to the dissociation of the electrolyte, comes into play in the sum of the molar fractions of the solutes. Thus, the situation is complex for weak electrolytes with incomplete dissociation, for which the dissociation coefficient is unknown. In order to resolve this impasse, it is possible to perform measurements using both ebullioscopy and cryometry at once. 

Introduction to conductance of electrolytes. Because a compound or mixture of compounds is electrically neutral, a solution made by dissolving a compound or mixture in any solvent must be neutral also. This means that the total positive charge must equal the total negative charge. This statement is known as the law of electroneutrality for electrolyte solutions. When a substance dissociates into ions in solution and the dissociation is essentially complete, the substance is called a strong electrolyte. Incomplete dissociation is found for weak electrolytes. 

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. 

A study of the concentration dependence of the molar conductivity, carried out by a number of authors, primarily F. W. G. Kohlrausch and W. Ostwald, revealed that these dependences are of two types (see Fig. 2.5) and thus, apparently, there are two types of electrolytes. Those that are fully dissociated so that their molecules are not present in the solution are called strong electrolytes, while those that dissociate incompletely are weak electrolytes. Ions as well as molecules are present in solution of a weak electrolyte at finite dilution. However, this distinction is not very accurate as, at higher concentration, the strong electrolytes associate forming ion pairs (see Section 1.2.4). 

PK. A measurement of the complete ness of an incomplete chemical reaction. It is defined as the negative logarithm ito the base 101 of the equilibrium constant K for the reaction in question. The pA is most frequently used to express the extent of dissociation or the strength of weak acids, particularly fatty adds, amino adds, and also complex ions, or similar substances. The weaker an electrolyte, the larger its pA. Thus, at 25°C for sulfuric add (strong acid), pK is about -3,0 acetic acid (weak acid), pK = 4.76 bone acid (very weak acid), pA = 9.24. In a solution of a weak acid, if the concentration of undissociated acid is equal to the concentration of the anion of the acid, the pAr will be equal to the pH. 

Ostwald s dilution law — A weak - electrolyte is dissociated incompletely upon dissolution in a solvent. The chemical equilibrium of dissociation of a weak acid HA into protons and acid anions is described by ... 

We use the hydrolysis of A into P and Q as an illustration. Examples are the hydrolysis of benzylpenicillin (pen G) or the enantioselective hydrolysis of L-acetyl amino acids in a DL-mixture, which yields an enantiomerically pure L-amino acid as well as the unhydrolysed D-acetyl amino acid. In concentrated solutions these hydrolysis reactions are incomplete due to the reaction equilibrium. It is evident that for an accurate analysis of weak electrolyte systems, the association-dissociation reactions and the related phase behaviour of the reacting species must be accounted for precisely in the model [42,43]. We have simplified this example to neutral species A, P and Q. The distribution coefficients are Kq = 0.5 and Kp = K = 2. The equilibrium constant for the reaction K =XpXQ/Xj = 0.01, where X is a measure for concentration (mass or mole fractions) compatible with the partition coefficients. The mole fraction of A in the feed (z ) was 0.1, which corresponds to a very high aqueous feed concentration of approximately 5 M. We have simulated the hydrolysis conversion in the fractionating reactor with 50-100 equilibrium stages. A further increase in the number of stages did not improve the conversion or selectivity to a significant extent. Depending on the initial estimate, the calculation requires typically less than five iterations. 

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