Degree of dissociation

Since electrolytes transport charge in the solid, aqueous or vapor state, it is worthwhile mentioning that the degree of dissociation of a compound added to a solvent can be estimated by the degree of dissociation parameter ai. Electrolytes hereafter are treated as aqueous electrolytes (solutions) unless otherwise stated. In general, if ai 1, the solution is a weak electrolyte and if cxi 1 the solution is a strong electrolyte since the compound being added to a solvent completely dissociates into ionic components, such as cations and anions. 

Consider the following reaction for a salt MxOy dissolved in a solvent 

The standard free energy change for chemical equilibrium and the equilibrium constant are, respectively 

The activity or molar concentration Oj, the degree of dissociation ai, and the total molar activity [Ct are define as follows [3] 

This expression indicates that the degree of dissociation increases with increasing concentration that is, ai t as [Ct] T- Further, iftti 1, a hydroxyl ion activity is related to a hydrogen ion activity through the dis- 

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Therefore, in the cases of both additives, the kinetic law for the catalysis will assume a linear form when the concentration of the added species, or, in the case of sulphuric acid, the nitronium ion generated by its action, is comparable with the concentration of the species already present. This effect was observed to occur when the concentration of additive was about o-2 mol 1, a value in fair agreement with the estimated degree of dissociation of nitric acid ( 2.2.1). 

Hemiketal (Section 17 8) A hemiacetal derived from a ketone Henderson-Hasselbalch equation (Section 19 4) An equa tion that relates degree of dissociation of an acid at a partic ular pH to its... 

The basic thermodynamic data for the design of such reactions can be used to assess the dissociation energies for various degrees of dissociation, and to calculate, approximately, tire relevant equilibrium constants. One important source of dissociation is by heating molecules to elevated temperamres. The data below show the general trend in the thermal dissociation energies of a number of important gaseous molecules. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

In the case of hydrogen, for example, at a teiuperamre of 2500 K, the equilibrium constant for dissociation has the value, calculated from the tlrermo-dynamic relation between the Gibbs energy of formation and the equilibrium constant of 6.356 x 10 " and hence at a total pressure of 10 atmos, the degree of dissociation is 0.126 at 2500 K, which drops to 8.32 x 10 at 2000 K. 

From a chemical point of view, the common amino acids are all weak polyprotic acids. The ionizable groups are not strongly dissociating ones, and the degree of dissociation thus depends on the pH of the medium. All the amino acids contain at least two dissociable hydrogens. 

The ease of dissociation of the X2 molecules follows closely the values of the enthalpy of dissociation since the entropy change for the reaction is almost independent of X. Thus F2 at 1 atm pressure is 1% dissociated into atoms at 765°C but a temperature of 975°C is required to achieve the same degree of dissociation for CI2 thereafter, the required temperature drops to 775°C for Br2 and 575°C for I2 (see also next section for atomic halogens). 

The determination of the degree of dissociation of cotarnine ° and the good agreement with the values derived from measurements of electrical conductivity with those from the spectrophotometric methods is indirect evidence that no significant part of the undissociated cotarnine is in the amino-aldehyde form. In the conductance calculation, the undissociated part was neglected. If this included a significant amount of amino-aldehyde (i.e., a secondary base), there would be a noticeable discrepancy in the degree of dissociation obtained by the two methods. 

Near room temperature there is scarcely any difference between the two. When a deuteron has been removed from a molecule in D20, the electrostatic energy associated with the negative ion will scarcely differ from that associated with the field of a similar ion in H20 from which a proton has been removed. Furthermore, the energy associated with the electric field surrounding a (D30)+ ion in D20 will scarcely differ from that of the field surrounding a (H30)+ ion in 1I20. We must conclude then that the observed differences between the degrees of dissociation of weak acids in D20 and H20 are due entirely to a difference in the quantum-mechanical forces. 

Using (204), let us attempt to predict the degree of dissociation of nitric acid in methanol solution. According to (204) the occupied proton... 

Although benzene-sulfonic acid, CnITsSChH, is a strong acid in aqueous solution, it is not completely dissociated in formic acid solution. In a 0.1-molal solution the degree of dissociation was estimated at 60 per cent.2 This is comparable with the dissociation of HIOs in aqueous solution and is compatible with J = 0.14 electron-volt for the formation of (HCOOH2)+. Using this value the level has been included in Fig. 65. 

It is found that IIC1 is likewise incompletely dissociated in formic acid solution. There do not appear to be any accurate data on the degree of dissociation so we do not know whether it is necessary to place the proton level of HC1 below that of (H30)+ in formic acid solution. 

Where [KF], [KTaF6] and [K2TaF7] are molar concentrations of KF, KTaF6 and K2TaF7 respectively Nt = variable molar fraction of TaF5 = variable degree of dissociation of K2TaF7. 

Using the defined dependence on TaF5 concentration of the degree of dissociation P the molecular composition of the melt was calculated and is presented in Fig. 65. 

For very weak or slightly ionised electrolyes, the expression a2/( 1 — a) V = K reduces to a2 = KV or a = fKV, since a may be neglected in comparison with unity. Hence for any two weak acids or bases at a given dilution V (in L), we have a1 = y/K1 V and a2 = yjK2V, or ol1/ol2 = Jk1/ /K2. Expressed in words, for any two weak or slightly dissociated electrolytes at equal dilutions, the degrees of dissociation are proportional to the square roots of their ionisation constants. Some values for the dissociation constants at 25 °C for weak acids and bases are collected in Appendix 7. 

Example 8. What effect has the addition of 0.1 mol of anhydrous sodium acetate to 1 L of 0.1 M acetic acid upon the degree of dissociation of the acid ... 

As shown above the sulphide ion concentration of a saturated aqueous solution of hydrogen sulphide may be controlled within wide limits by suitably changing the concentration of hydrogen ions—a common ion—of the solution. In a like manner the hydroxide ion concentration of a solution of a weak base, such as aqueous ammonia (Kb = 1.8 x 10-5), may be regulated by the addition of a common ion, e.g. ammonium ions in the form of the completely dissociated ammonium chloride. The magnitude of the effect is best illustrated by means of an example. In a 0.1M ammonia solution, the degree of dissociation is given (Section 2.13) approximately by. 

Equation (3.7) describes the equality of the chemical potentials of the mobile ions on both sides of the gel boundary expressed through the Donnan ratio KD and the ion charges z, Eq. (3.8) concerns the dissociation equilibrium of ionizable (carboxyl) groups of the network a is the degree of dissociation, eg is the concentration of the hydrogen ions in the gel Eq. (3.9) represents the gel electroneutrality condition. 

Fig. 15. Energy of proton dissociation (Ez) from Z times ionized polyelectrolyte molecules as function of the degree of dissociation (a). (A) - PPAL (1), PPAS (2), PPA (3), polyfmethacrylic acid) (4), copolymer of acrylic acid with ethylenesulfonic acid (50 50) in aqueous solutions (5), (B) - PPAL (1), PPAS (2), PPA in the presence of NaCl (3) ( ) INaClj = 0 (X) fNaCll = 0.25 mmol/1 (o) 0.50 mmol/1...

Reactivity ratios for the copolymerization of AN and DM WS in DMSO were found to be rj =0,53 and r2=0,036, and in water r1=0,56 and r2=0,25. The higher reactivity of DM VPS in the copolymerization with AN in aqueous medium, as compared with its reactivity in DMSO, can be explained by a higher degree of dissociation of DMVPS in aqueous medium. This fact also produces a considerable effect on the character of the distribution of monomeric units within the copolymers, which manifests itself in the change of their solubility in water. Copolymers containing 30% of monomeric units AN obtained from a 90 10 mixture of AN and DMVPS in DMSO, irrespective of the level of conversion, are completely soluble in water, whereas copolymers of the same composition, but obtained in aqueous medium with a yield 40%, are insoluble in water. 

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