Equilibrium constant electrolyte dissociation

DETERMINATION OF EQUILIBRIUM CONSTANTS FOR DISSOCIATION OF WEAK ELECTROLYTES... 

It is instructive to consider the effect of dissociation on the adsorption of amphipathic substances since many of the compounds that behave according to curve 3 are electrolytes. We consider only the case of strong 1 1 electrolytes for weak electrolytes the equilibrium constant for dissociation must be considered. 

If A° can be found and A is known for various stoichiometric concentrations, then values of a can be found at the various concentrations, and from these the equilibrium constant for dissociation into ions for the specihc electrolyte can be found. This provides an alternative route to Ks for acid/base equilibria. 

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 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. 

K is the equilibrium constant at a particular temperature and is usually known as the ionisation constant or dissociation constant. If 1 mole of the electrolyte is dissolved in Vlitres of solution (V = l/c, where c is the concentration in moles per litre), and if a is the degree of ionisation at equilibrium, then the amount of un-ionised electrolyte will be (1 — a) moles, and the amount of each of the ions will be a moles. The concentration of un-ionised acetic acid will therefore be (1 — a)/ V, and the concentration of each of the ions cl/V. Substituting in the equilibrium equation, we obtain the expression ... 

Solid Bi2S3 does not appear in the expression for K,p, because it is a pure solid and its activity is 1 (Section 9.2). A solubility product is used in the same way as any other equilibrium constant. However, because ion-ion interactions in even dilute electrolyte solutions can complicate its interpretation, a solubility product is generally meaningful only for sparingly soluble salts. Another complication that arises when dealing with nearly insoluble compounds is that dissociation of the ions is rarely complete, and a saturated solution of Pbl2, for instance, contains substantial... 

The excess electrolyte is often termed the indifferent electrolyte. From the practical point of view, solutions containing an indifferent electrolyte are very often used in miscellaneous investigations. For example, when determining equilibrium constants (e.g. apparent dissociation constants, Eq. 1.1.26) it is necessary only to indicate the indifferent electrolyte and its concentration, as they do not change when the concentrations of the reactants are changed. Moreover, the indifferent electrolyte is important in the study of diffusion transport (Section 2.5), for elimination of liquid... 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

Optical and nuclear magnetic resonance methods apphcable to moderately strong electrolytes have been made increasingly precise (14). By these methods, it has proved feasible to determine concentrations of the undissociated species and hence of the dissociation constants. Thus, for HNO3 in aqueous solution (14) at 25°C, K is 24. However, in dehning this equilibrium constant, we have changed the standard state for aqueous nitric acid, and the activity of the undissociated species is given by the equation... 

Barnett and co-workers recently reported that it might be possible to utilize hydrocarbons directly in SOFC with Ni-based anodes. " ° First, with methane. they observed that there is a narrow temperature window, between 550 and 650 °C. in which carbon is not as stable. The equilibrium constant for methane dissociation to carbon and Hz is strongly shifted to methane below 650 °C. and the equilibrium constant for the Boudouard reaction, the disproportionation of CO to carbon and COz, is shifted to CO above 550 °C. Therefore, in this temperature range, they reported that it is possible to operate the cell in a stable manner. (However, a subsequent report by this group showed that there is no stable operating window for ethane due to the fact that carbon formation from ethane is shifted to lower temperatures. ) In more recent work, this group has suggested that, even when carbon does form on Ni-based anodes, it may be possible to remove this carbon as fast as it forms if the flux from the electrolyte is sufficient to remove carbon faster than it is formed.Observations by Weber et al. have confirmed the possibility of stable operation in methane. Similarly, Kendall et al. showed that dilution of methane with COz caused a shift in the reaction mechanism that allowed for more stable operation. 

Ion pairing is due to electrostatic forces between ions of opposite charges in a medium of moderate to low relative permittivities. It should be distinguished from complex formation between metal cations and anionic ligands, in which coordinative bonds (donation of an electron pair) takes place. One distingnishing feature is that, contrary to complex formation, the association is nondirectional in space. The association of a cation and an anion to form an ion pair can, however, be represented as an equilibrium reaction by analogy to complex formation with an equilibrium constant A)ass [3,5]. If a is the fraction of the electrolyte that is dissociating into ions and therefore (1 - a) is the fraction that is associated, then... 

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. 

From Eqn. (14) it follows that with an exothermic reaction - and this is the case for most reactions in reactive absorption processes - decreases with increasing temperature. The electrolyte solution chemistry involves a variety of chemical reactions in the liquid phase, for example, complete dissociation of strong electrolytes, partial dissociation of weak electrolytes, reactions among ionic species, and complex ion formation. These reactions occur very rapidly, and hence, chemical equilibrium conditions are often assumed. Therefore, for electrolyte systems, chemical equilibrium calculations are of special importance. Concentration or activity-based reaction equilibrium constants as functions of temperature can be found in the literature [50]. 

The equilibrium constant of dissolution of an electrolyte (describing the equilibrium between excess solid phase and solvated ions) is often called a solubility product, denoted Ksol or Ks (or KSoi or K as appropriate). In a similar way the equilibrium constant for an acid dissociation is often written Ka, for base hydrolysis Kb, and for water dissociation Kw. 

The equilibrium constant given by Eq. (9) using a values obtained from Eq. (8) differs from K, the true equilibrium constant in terms of activities, owing to the omission of activity coefficients (y ) from the numerator of Eq. (9) and the approximations inherent in Eq. (8). At the very low ionic concentrations encountered in the dissociation of a weak electrolyte, a simple extrapolation procedure can be developed to obtain from the values of Since y is an excellent approximation, it follows that... 

Weak acids are weak electrolytes and do not dissociate completely. An equilibrium exists between the reactants and the products, and the equilibrium constant must be taken into account to solve for the pH value. When a weak acid (HA) is dissolved in water, the conjugate base (A ) and conjugate acid (H+) are... 

In a medium of reasonably high dielectric constant, the ion pair undergoes electrolytic dissociation into the free ions A and B ". This process (step II) may be characterized by the equilibrium constant K gp which may be termed ion pair separation constant ... 

In a medium of high dielectric constant, such as in water, the concentration of associated ions is negligibly small form sep cannot be measured separately and this is the reason why in water and in other solvents of high dielectric constant only the overall (classic) equilibrium constant K is meaningful. On the other hand, in solvents of low dielectric constant (e.g., tributylphosphate), there will be practically no electrolytic dissociation, so that the ionized substrate will be present nearly exclusively as associated ions. Consequently, the ionization process is best characterized by rorm-... 

Firstly, ion exchange resins when hydrated generally dissociate to yield equivalent amounts of oppositely charged ions. Secondly, as with conventional aqueous acid or alkali solutions, resins in their acid or base forms may be neutralized to give the appropriate salt form. Finally, the degree of dissociation can be expressed in the form of an apparent equilibrium constant (or pK value) which defines the electrolyte strength of the exchanger and is usually derived from a theoretical treatment of pH titration curves. ... 

Compounds of this type may be classified as strong electrolytes, which dissociate almost completely into ions in solution, or as weak electrolytes, which only dissociate to a small extent in solution. Since strong electrolytes are almost completely dissociated in solution, measurement of the equilibrium constant for their dissociation is very difficult. For weak electrolytes, however, the dissociation can be expressed by the law of mass action in terms of the equilibrium constant. 

Curve C is a plot of K (XIO ), the concentration quotient for the equilibrium involving the dissociation of acetic acid, as a function of electrolyte concentration. Here again, the ordinate function approaches a limiting value A, which is the thermodynamic acid dissociation constant for acetic acid. 

TPVT titrations of cis-[Co(en)2(H2O)2] and [Co(tren)(H20)2] gave similar results . The equilibrium constant of (12) was approximately 1 in these three ions, so that in dilute solutions (< 10" M) the tetrapositive, binuclear ions will be almost completely dissociated into dipositive hydroxoaqua ions. The last conclusion was confirmed by Feltham-Onsager plots of the equivalent conductance (at 0°C) versus the square-root of the concentration of four salts [Co(NH3)4(H20)(OH)](N03)2 Cr(NH3)4(H2O)(OH)]-(NO,), [Co(NH3)4(H2O)(OH)]Br2 = and [Cr(H2O)d(NO3)3 -F NaOH . The conductivity data were for solutions of concentrations between 10 and 10" M. At these concentrations the Feltham-Onsager plots are linear. All four plots had the typical slope of 1 2 electrolytes which was less than half of the slope of 1 4 electrolytes. 

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