Equilibrium and Transport Properties of Concentrated Electrolyte Solutions BY PROF. DR. R. HAASE INSTITUT FUR PHYSIKALISCHE CHEMIE DER TECHNISCHEN HOCHSCHULE AACHEN A historical survey is followed by a discussion of’a number ojproblems associated with concentrated solutions of electrolytes containing two ion constituents: general thermodynamic properties, dissociation equilibria, phase separation, analytical representation of the thermodynamic function5 over the entire range of concentrations, and general relationships in electrical conductivity, diffusion, and sedimentation. A number of relationships valid at all concentrations is formulated, and known relationships pertaining to dilute solutions are derived from these as special cases. The discussion of concentrated solutions is illustrated by numerical examples, most of which are based on recent results. I. Introduction The beginnings of physical chemistry are closely linked with the experimental and theoretical study of the equilibrium and transport properties of electrolyte solutions, a field which also covers investigation of galvanic cells. Consider, for example the contributions made during the second half of the last century by Arrhenius, Gibbs, Helmholtz, Hittorf, Kohlrausch, Nernst, Ostwald, Planck, and van’t Hoff: The properties in question were described in these early investigations on the basis of the theory of ideal dilute solutions. In this simple approximation, the electrolyte solutions are assumed to be so dilute that the interactions between the ions are negligible. Consequently, the only thermodynamic difference between such electrolyte solutions and ideal dilute non-electrolyte solutions is the increase in the number of solute particles as a result of dissociation in the former case. The dissociation equilibrium is described by the classical law of mass action. An effect of the approximation is that the dependence of the equivalent conductivity on the concentration appears to be due only to changes in the degree of dissociation of the electrolyte, whilst the mobilities of the ions are independent of concentration. This statement, together with the classical law of mass action, leads to Ostwald’s dilution law, which was confirmed for dilute aqueous solutions of weak electrolytes, e.g. dilute acetic acid, to within the experimental accuracy possible at that time (Ostwald 1888). The diffusion coefficient of the electrolyte in an ideal dilute solution also can easily be related to the ionic mobilities (Nernst 1888). It soon became clear, however, that even at very high dilutions, solutions of strong electrolytes (e.g. hydrochloric or sulfuric acid or salts in water) exhibit such wide deviations from the laws known at that time that the equations for ideal dilute solutions could no longer be regarded as being applicable. These deviations were even observed for concentrations at which non-electrolyte solutions still show approximately ideal behaviour. Thus these “anomalies of strong electrolytes” are undoubtedly connected with the relatively high concentrations, and consequent interactions, of the ions. Quantitative Angew. Chem. internut. Edit. 1 Vol. 4(1965) 1 No. 6 description of these interactions was soon attempted. It was not until 1923, however, that a useful molecular statistical theory was evolved by Debye and Hiickel. This theory was later extended and re-stated by Onsager (1926- 1927) for application to electrical conductivity. Some consequences of these laws had already been discovered empirically, by Kohlrausch (1869-1880) in the case of conductivity, and by Bjerrum (1916), Bronsted (1922), Lewis (1921-1923), and others in the case of the thermodynamic functions. I t is now known that the equations proposed by Debye, Hiickel, and Onsager are themselves limiting laws: they correspond to the first approximation beyond the laws of ideal dilute solutions. The molecular concepts on which they are based are as follows: The electrolyte solution consists of a system of charged particles embedded in a non-conducting medium with the same density, dielectric constant, and viscosity as the solvent. The ion concentration is so small that elimination of the charges would yield an ideal dilute solution. The ions move in a disordered manner (Brownian movement). When transport processes take place, an ordered motion is superposed on the thermal movement; in particular, during conduction of electricity, cations and anions migrate in opposite directions, giving rise to relaxation and electrophoretic effects, the complete mathematical treatment of which is extremely complicated. The present molecular theories of the equilibrium and transport properties of electrolyte solutions still reduce to the limiting laws of Debye, Hiickel, and Onsager at sufficiently low concentrations. The range of validity has been extended to include higher electrolyte concentrations by taking into account such factors as incomplete dissociation and ion association or solvation. However, general applicability of the equations to electrolyte solutions of any concentration is ruled out right from the start by the fundamental simplification of the theory, according to which ions and aggregates of ions are regarded as discrete entities and the solvent as a structureless continuum. If it is desired to cover the entire range of concentrations from pure solvent to pure liquid electrolyte, as is possible experimentally e.g. with the systems water/acetic 485 acid, water/hydrochloric acid, or water/sulfuric acid, we cannot base our considerations on the theoretical or semi-empirical equations which have been used in the past. Instead, we must build up an entirely new picture in which (at least for the equilibrium properties) the nonelectrolyte and the electrolyte are no longer regarded as the “solvent” and the “solute”, respectively, but as equivalent components. In this new scheme, which is essentially empirical at the moment, and which will be developed below for thermodynamic functions, the DebyeHuckeZ limiting law retains its validity. This law, together with Onsager’s limiting law, is one of the few results of the molecular theory of electrolyte solutions which has been accepted as reliable by all research workers. Our discussion of the equilibrium and transport properties of concentrated electrolyte solutions is confined to solutions of a single electrolyte containing two ion constituents, e.g. CaC12, H2S04, or H3P04, in a n inert solvent, e . g . H2O. For the sake of simplicity we exclude electrolytes with three or more ion constituents (e.g. KHSOd), mixed electrolyte solutions, and fused salts. Moreover, we cannot concern ourselves with details of liquid-vapor and liquid-solid equilibria or osmotic phenomena, since although these are important for experimental detcrrninations of thermodynamic functions, they are not limited to electrolytes. It will also be necessary, in our consideration of transport processes, to omit discussion of viscosity and non-isothermal processes (thermal conduction, thermal diffusion, etc.), as well as of galvanic cells. saturation limit, e.g. H20/NaCI, it represents a hypothetical state ( e . g . “fused sodium chloride a1 25°C and 1 atm”). Nevertheless, the two components are treated in principle as equivalent. It is possible to calculate all equilibrium properties of the electrolyte solution, with the exception of the dissociation constant, provided that we know the chemical potentials p~and p~of the two components or the molar Gibbs free energy, = ( I - x)pl + xp2, of the liquid mixture as a function of T, P, and x. We need not know the absolute values of pl,p2, and G, but simply the differences between these quantities and their values for the pure liquid components. Let polbe the chemical potential of the pure liquid component i at the given values of T and P, and R the gas constant. We then make use of the dimensionless quantities defined by equations (2) and (3), which we consider as functions of T, P, and x. The function is related to the “activity” a1 of component 1 (which we d o not require in this discussion) by the equation $1 = In a ] . Equations (4) and (5) follow from the Gibbs-Duheni eauation. 11. Equilibrium Properties 1. General Consider a binary liquid mixture, in which component 1 is a non-electrolyte (“solvent”), and component 2 an electrolyte containing two ion constituents. At high electrolyte concentrations we therefore have at least four types of particles present : non-electrolyte molecules, undissociated electrolyte molecules, and at least one kind of cation and one kind of anion. We assume for the moment that the liquid is free from electric potential or concentration gradients, erc., since we are at present concerned only with equilibrium properties. As independent variables with which to describe the macroscopic state of the liquid mixture, we choose the absolute temperature T, the pressure P, and a single concentration variable, which we take to be either the stoichiometric mole fraction x of the electrolyte or the molality m (moles electrclyte per kg solvent). The quantities x and m are related as shown in Equation (l), where MI is the kilogram-molecular weight of the non-electrolyte. The other properties of the quantities $1 and $2 or I’, e .g. those relating to the conditions for stability and coexistence, are also similar to those of the chemical potentials p~ and p 2 or the molar free energy -6. Two other quantities are generally used in the literature instead of 41, $2, and these are the osmotic coefficient ‘p of thesolvent and the conventional activity ccefficient y of the electrolyte, which are considered as functions of T, P, and m. r: Let vL and v _ respectively be the number of cations and anions which result from complete dissociation of one 1; molecule of electrolyte (e .g. H2S04: v+ = 2, vH3P04: \I+ = 3, \I_ =- I). Moreover, let p.2”be a standard value of the chemical potential of the electrolyte, depending, like pol and ~ 0 2 only , on T and P. : The functions ‘p and y can then be defined as follows. v.ln ( v + - m y ) E o2+ C2 (7) with v The pure solvent is described according to Eq. (1) by x = 0 or m = 0, and the pure liquid electrolyte by x = 1 or m + co. The pure liquid electrolyte corresponds to a real state only in systems such as H;?O/HCIor H2O/H;?S04; for systems with a 486 v, + v-; v: = V;+-J~- (8) and Angew. Chem. internal. Edit. / Vol. 4 (1965) / No. 6 In the case of electrolytes such as HC1 or NaZS04, which give only two types of ions on dissociation, irrespective of the concentration, it is possible to use the degree of dissociation cc of the electrolyte and the mean ionic activity coefficient y + [on the molality (m) scale] in accordance with Equation (10). The quantity which can be measured directly is y, not y + . y="'y+. (10) Whereas q, C 2 ,a n d u. a r e dimensionless,y a n d y * a s defined in equations (7) a n d (10) have t h e s a m e dimensions a s l / m and M I , namely kg/mola. In this connection, we use t h e following abbreviations : rnt E I mole/kg; yt E Mi = In t h e above equation, yu is t h e activity coefficient of t h e undissociated electrolyte a n d K, t h e dissociation constant of the electrolyte (both quantities o n t h e m scale). Krn is dimensionless and depends only o n T a n d P. For our example (13), we have: v -= 3 ; v f = 4113.However, the dissociation equilibria discussed below are of the simplest type (1 5). HN03 Here v 2; v f = %= HF+NO3. 1 , so that Equation (14) reduces to Since 1 kg/rnole. An ideal dilute electrolyte solution is characterized by the conditiony& = yt. Furthermore, if theelectrolyte in such a solution is completely dissociated, then cp = 1 ; a= l;y* - y - - y t . Using Equations (l), (4),(6), and (7), and integrating betweenm=O(cp= I ; y - y t ) a n d m = m(cp = y ; y = = y ) a t constant temperature and pressure, we obtain Equations (1 I ) and (12), which are important for the evaluation of experimental data. rn it follows from Equation (16) [2,3] that Using Equation ( 1 S), therefore, we can find the dissociation constant K,, at given pressure for any temperature, provided that y(m) and a(m) are known. The standard values of the affinity AQ, the heat of dissociation h:p, and the entropy of dissociation s4p (on the m scale) can be obtained from K, by means of Equations(19), (20), and (21). A 0 = R T In K m rn ( (12) hp,,= RT2( b InbTKm )p= --R b In K, b(l/T) P If both components a r e volatile, t h e quantities $1 a n d $2 can b e found f r o m t h e partial vapor pressures, a n d these a r e used together with Equations (6) a n d (12) t o find t h e functions q and y. If only the solvent is volatile, then vapor pressure measurements (generally by t h e indirect isopiestic method) lead t o $1, a n d hence t o 'p a n d y, b u t not t o $ 2 . If only the electrolyte is volatile, t h e n only $2 can b e obtained from t h e vapor pressure. O n e can also find q, a n d hence $1 a n d y. from freezing point determinations. E.m.f. measurements lead t o t h e quantity y, from which 'p can b e determined by Equation (1 I), a n d hence + I by Equation (6). T h e constant Cp for volatile electrolytes can b e obtained from y a n d +z with the aid of Equation (7). 2. Dissociation Equilibria A dissolved electrolyte such as HC1 or Na2SO4 yields only two types of ions, irrespective of the concentration, e.g. Na2S04 ;-f 2 N a + + S0,2-. (13) Electrolytes such as H2SO4 or H3P04, on the other hand, dissociate in two or three stages. We shall disregard these more complicated cases in the present discussion. A single-step dissociation of the type (13) can be described by the general equilibrium condition (14) [l]. [ I ] R . Haase, Z. physik. Chern. N.F. 39, 360 (1963). Angew. C h e m . internat. Edit. / (15) Vol. 4 (1965) / No. 6 (19) (20) We also have T ( '2 ( )p = (22) Whereas some method can always be found for the measurement of the activity coefficient y, the experimental determination of the degree of dissociation a presents a problem. The usual methods, particularly for strong electrolytes, depend on assurnpions, e.g. that of a certain concentration dependence of the electrical conductivity. It was a great advance, therefore, when several authors, and Redlich in particular, pointed out the possibility of determining the concentrations of ions by the relatively direct spectroscopic methods. Thus values of the function a(m), obtained from Ranian [3] and nuclear resonance spectra [4],are now available for aqueous nitric and perchloric acids at several temperatures. We base our calculations on the results reported by Hood and Reilly [4], since these appear to be the most precise so Far. We have determined the activity coefficients from partial vapor pressure and isopiestic measurements, for the [ 2 ] R . Haase, K . - H . Diicker, and H. A . Kippers, Ber. Bunsenges. physik. Chern., in press. [3] 0. Redlich and J. Bigeleisen, J. Arner. chern. SOC.65, 1883 (1943); 0. Redlich, E. K . Holt, and J . Bigeleisen, J. Amer. chern. SOC.66, 13 (1944); 0. Redlich, Chem. Reviews 39, 333 (1946); Mh. Chem. 86, 329 (1955). 141 G. C. Hood, 0. Redlich, and C. A. Reilly, J. chern. Physics 22, 2067 (1954); G. C. Hood and C. A . Reilly, ibid. 32, 127 (1960). 487 systems H20/HN03 and H20iHC104, as far as possible in the concentration and temperature range for which the degrees of dissociation are known. These activity coefficients were used to calculate K,, A e,hFp, and sp : [2] with the aid of equations (18) to (21) at atmospheric pressure. The results are listed in Table 1. HNO3 and HClO4 are strong acids of comparable strengths. The quantity hp: and hence also [by Eq. (22)] s : ~ , is found to be practically constant over the temperature range studied. Table I . Dissociation constant K, and standard values of the affinity A@, heat of dissociation hFp, and entropy of dissociation spp, for aqueous nitric and perchloric acids 121. A9 Temp. i “Cl [kcal/moIe] S [kcal/molel HNOj HNO, __ 10 25 40 50 75 33.5 41.1 34.5 29.3 20.3 14.5 - 2.08 - 2.09 -’2.10 !- 2.10 -1.99 -1.99 - I .99 -3.51 r 1.94 -3.51 - 1.85 -3.51 g [cal.deg-I mole-’] -4.81 1 HC104 0.36 0.36 0.36 -4.8 I -4.81 We then used the values of a(m), y(m), and K, for both acids, together with Equations (10)and (16), to determine the mean ionic activity coefficient yi (m) and the activity coefficient y,(m) of the undissociated acid [2]. By way of example, Fig. 1 shows the three functions y(m), y* (m), and y,(m) for aqueous perchloric acid at 25 “C. 9- J i 8- f 76 I -~ Y”j i t / 3. Phase Separation In a two-component liquid mixture, phase separation results in two coexistent binary liquid mixtures with different compositions in equilibrium with each other. This phenomenon is relatively rare in electrolyte solutions, and is usually not mentioned even in modern monographs on electrolytes. As early as 1888, Bakhuis Roozeboom [6] observed phase separation at high acid concentrations in the systems H20/HCl and HZO/HBr. The former system has been quantitatively investigated [7] over the entire miscibility gap, together with the solid-liquid equilibria which occur at low temperatures. We have verified these early results with the aid of vapor pressure measurements [ 5 ] , supplemented them by quantitative investigations on the H20/HBr system, and showed that phase separation also occurs in the system H20/HT. All three of these systems exhibit miscibility gaps without accessible critical temperatures for phase separation. Thus the upper limit of the range in which the two liquids coexist is formed by the critical point for evaporation (which almost coincides with the critical point of the pure hydrogen halide), and the lower limit is fixed by equilibrium with a solid hydrate. All the phase separation curves are extremely unsymmetrical, one phase always containing almost preu acid. The miscibility gaps found for the three systems are given in Table 2. The results relate to the pressures at which the three phases coexist (i.e. the vapor pressure over the two liquid phases), but the values at atmospheric pressure should be practically the same. We can therefore construct two isobaric phase separation diagrams from the data given in Table 2 (x” and x”’ as functions of T at constant P). Table 2. Phase separation in aqueous hydrogen halides. Stoichionietric mole fractions x” and x”‘ of the acid in the water-rich and acid-rich phases respectively. as functions of temperature. X”’ System f r o m [71 HzOjHCI ? I0 15 20 25 30 35 HzOiHBr Fig. 1. The system HzO/HCI04 a t 25 “C: Logarithms of the conventional activity coefficient y. the mean ionic activity coefficienr y+, and the activity coefficient yu of the undissociated electrolyte, vs. the square root of the molality m, according lo [21. (yi I kgjrnole, m t E 1 molejkg). = 15 20 25 30 35 HZOIHI 0.485 0.480 0.475 0.470 0.465 0.460 0.455 0.478 0.473 0.468 0.464 0.459 0.454 0.450 0.423 0.418 0.41 1 0.403 0.400 0.346 I from I51 0.9990 0 9985 0.9982 0.9980 0.9977 0.9975 0.9972 0.999 0.999 0.998 0.996 0.994 0.995 Remarkably high values ar e found for yu in concentrated acids, in contrast t o the values of ab o u t 1 kg/mole found for dilute acids. For example, 16 molal aqueous perchloric acid a t 25°C has yu = 5 x 105 kg/mole. On th e other hand, the highest conventional activity coefficient previously known, i. e . that of 35 molal hydrobromic acid at 25”C, is y = 4800 kg/mole, obtained from vapor pressure measurements IS]. Th e occurrence of a miscibility gap in an y binary system can be seen from t h e form of t h e function r ( x ) for given values of T an d P. If the entire curve of r ( x ) is convex towards the x-axis, miscibility is complete. If phase separation occurs, the curve contains two points of inflection and a bend which allows the construction of a double tangent (cf:Fig. 4 below). Th e range o f concentrations over which is concave towards the x-axis corresponds t o labile (absolutely unstable) states. 151 R . Haase, H . Naas, and H. Thumm, Z . physik. Chem. N.F. 37, 210 (1963). [7] F. F. Rupert, J. Amer. chem. SOC.3 / , 851 (1909). 488 r [61 H . W . Bakhuis Rooreboom, Z . physik. Chem. 2, 449 (1888). Angew. Chem. intermit. Edit. Vol. 4 (1965) / No. 6 T h e limits of stability a r e given by t h e points of inflection. T h e region between the points of inflection a n d t h e points of contact of t h e double tangent correspond t o metastable states. All other concentrations correspond to stable onephase systems. T h e points of contact o f t h e double tangent show t h e compositions (x" a n d x"' in Table 2) of t h e tw o coexistent liquid phases. If these points o f contact a r e found from t h e r - x curves for various temperatures a t a given pressure a n d transferred to a T-x diagram, t h e isobaric phase separation diagram results. We shall give some examples of thz shapes of I'-x curves which have been obtained from experimental results for aqueous electrolyte solutions at 25 OC a n d 1 atm. electrolytes in t h e last stage of dissociation ( e . g . CaC12: = -2). Consequently Bo z- = 2; z- = - I ; H2S04: z.+ = I ; z_ is always known a t t h e outset. If component 1 is water, then at 25 "C and 1 atm: M 1 = 15.016 x 10-3 kgimole; a = 1.176 kgl/z/molel/z (27) Equation (27), together with Equations (25) and (26), gives for aqueous electrolyte solutions at 25 "C and 1 atrn the Equations (28) and (29). Numerical values of C and Bo are given in Table 3. C = Cz-v.lnv+ + v.ln (18.016.10-3) (28) 4. Analytical Representation of the Equilibrium Properties To obtain an analytical representation of the equilibrium properties of an electrolyte solution at any concentration, it is best to start with the function (T, P, x). All other thermodynamic quantities can then be obtained by differentiation. r We express function in the form of Equation (23) [I, 81, which is valid for solutions of an electrolyte with two ion constituents over the entire range of concentrations fromx=Otox=l. In equation (23), C, Bo, B I , B2, . . . are dimensionless parameters depending only on T and P and related by Equation (24). The terms in Equation (23) which contain Bl, B2, . . . etc. are empirical terms corresponding to a continuation of the expansion of (x) in fractional powers of x. If the electrolyte is not volatile, there are n independent parameters (B1, B2, . . . BJ, and the quantity C is determined from Eq. (24). For volatile electrolytes ( e . g . HCI, HBr, HI, HNO3), C can be determined from vapor pressure data, so that Equation (24) gives a relationship between B1, B2, . . . B,. We then have (n-1) indepecdent parameters. If v = 1, Bo -- 0, B2 = 0, B4 . = 0, . . . etc., Equation (23) reduces to the ordinary power series for binary solutions of non-electrolytes. r Using Equations (l), (9,(6), and (7), it i s possible to derive expressions for $1, $2, y, and y from Equation (23) [1,8]. We shall confine ourselves here to giving the equation (30) for the activity coefficient y,which is derived from ( I ) , (3,(7), (23), and (25). v.ln I 2 1 2 1 B1- 5 B z + 3 B 3 + 7 B 4 + 4 B g + ...= V - l i C f 2 3 = Cr -v.ln v - + v - I n MM I? (25) The fourth term of Equation (23), which contains Bo, corresponds to the Debye-Huckel limiting law. Thus Bo is related to the Debye-Huckel coefficient a by In this equation, z+ a n d z_ a r e the electrochemical valences of the cations a n d the anions respectively, formed from the [8] R . Huase, H . Naos, and K . - H . Ducker, Z. physik. Chem. N.F. 39, 383 (1963). A n g e w . Chem. internat. Edit. Vol. 4 (1965) 1 No. 6 = + v.ln ( I - X ) - B ~ . X ~ I ~( ~ , - v + 1j.x Bo (24) Differentiation of (23) with respect to T or P gives the corresponding expressions for the dependence of the entropy of mixing and heat of mixing, or of the volume effects, on concentration. The first three terms on the right-hand side of Equation (23) correspond to the equations for ideal solutions of fully dissociated electrolytes. The constant C appearing in the third term is given by the general expression (25), where Cz has the same meaning as in Equations (7) and (9). For volatile electrolytes, Cz can be derived directly from theexperimental results (cf. Section 11, I), so that we can immediately find C. C :'- y7 + (Bs -: B3) ex3 - B4.x7/2 - 3 9 5 . ~ 4 . .. , (30) As can be seen from Equation (30), which does not involve C, the slope of the curve of 1 n(y/yt) against xliZat x 0 is -Bo/v. This corresponds to the Debye-Huckel limiting law. Table 3 shows the values of the adjustable parameters B I , Bz, . . . etc. for aqueous solutions of 17 electrolytes at 25 "C and 1 atm, as obtained by us [2,8] from experimental data. These are practically the only electrolyte solutions for which reliable data covering a wide range of concentrations exist. The constants v , C, and Bo are also included in Table 3. The C values for the hydrogen halides and nitric acid were determined from experimental values of C2, using Equation (28), that for perchloric acid (in brackets) was subsequently determined from Bo, B1, B2, etc., with the aid of Equation (24). I t can be seen that three, four, or five independent parameters are required. Measurements extending to pure liquid electrolyte (x= 1) are possible in only a few cases ( e . g . sulfuric acid). The continuation of the investigations up to x - 1 usually is prevented by fundamental or practical difficulties, e.g. a miscibility gap in the case of the hydrogen halides, a 489 Table 3. Values of the constants in Equations (23) and (30). for concentrated aqueous electrolyte solutions at 25 “C and I atm [2,8] Electrolyte I I BO C I BI I B2 ~ 10.33 16.17 13.99 4.15 (128.3) 17.53 17.53 17.53 17.53 17.53 91.08 17.53 17.53 17.53 17.53 91.08 17.53 17.53 17.53 17.53 91.08 91.08 191.5 206.8 238.6 151.8 161.7 476.9 117.8 163.8 142.2 134.7 1473 149.0 189.2 108.5 96.91 721.6 1469 - 9238 - 1044 - 1335 487.3 449.4 798.2 236.9 - 738.6 - 316.9 - 957.5 -13020 - 345.2 - 1115 - 563.3 - 761.2 - 2121 -12640 - I B3 I B4 __ 2908 3515 4712 768.5 719.7 490.4 250.4 2406 380.2 4483 63 720 484.1 4 449 1662 3 I71 2165 60 500 1Efx __ - 3898 - 4786 - 6784 417.5 1765 2156 3 325 - 3660 2170 - 10320 -14430 8 996 I2090 - 8906 - 2505 - 6439 6 842 I502 5063 -- I 3 630 I 1480 With the constants listed in Table 3, a miscibility gap for the hydrogen halides and complete miscibility for the other systems can be predicted. In the example of Fig. 3 (perchloric acid), the course of the curve is characteristic of complete miscibility. Fig. 4, on the other hand, shows a typical example (hydrochloric acid) of the r - x curve in a system which exhibits phase separation. The r--Y, saturation limit in the case of bases and salts, or decomposition of the electrolyte in the cases of nitric and perchloric acids. Fig. 2 shows a plot of In(y/yf) as a function of m’iz for hydrochloric acid. The calculated values agree closely with the experimental results. The measurements on which the experimental curve of Fig. 2 is based [ 5 ] extend as fat. as the miscibility limit (cf. Table 2). u 0 02 & 17iJj - 06 x”O4 2 08x”’lO -x Fig.4. The systemHlO/HCI at 2 5 T : 1‘ (x) as a function of the stoichiometric mole fraction x of the electrolyte. according to [XI, calculated by Equation (23) using the constants in Table 3 (x”. x”‘: values of x for the two coexistent liquid phases). compositions of the two coexisting liquid phases (x” = 0.35 and x”’ = 0.84) as obtained from the points of contact of the double tangent are reasonably close to the values obtained by direct measurement (Table 2: x” = 0.46 and x”’ = 0.998). Similar results were found for hydrobromic and hydriodic acids f81. 111. Electrical Conductivity 1. General 0 rn I I I 2 i, 6 fi- Fig. 2. The system HzO/HCI at 25 ‘C: Logarithm of the conventional activity coefficient y vs. the square root of the molality m according to [XI. Experimental: ( 0 0 0 ) ; calculated from Equations ( I ) and (30), using 1 kg/mole, the constants in Equation (27) and Table 3: (- -). ( y t mt I mole/kg). = In an electrolyte solution which is situated in an external electric field, bdt which is otherwise homogeneous, i. e. exhibits no gradients other than the potential gradient, conduction of electricity occurs, associated with migration of the ions. If we discregard extremely high field strengths, Ohm’s law expressed in the form (31) applies to each volume element. - + - + 1=x - + = -x grad (3 I ) + In Equation (31), the vectors 1 and ale the electric current density and field strength, respectively, ‘p is the electric potential, and K is the specific conductivity. -EOOL [.KLZiZ 02 I I , I 04 06 08 10 r- Fig. 3. The system H20/HC104 at 25 “C: I? (x) as a function of the stoichiometric mole fraction x of the electrolyte, as calculated by Equation (23) using the constants in Table 3. 490 The result of the mutual opposition of the electrostatic force on the ions and the resistance of the medium (resistance due to friction and electrostatic interaction whith other ions) is that, after a brief acceleration, an ion moves at a constant average velocity with respect to the solvent. If the magnitude of this velocity of migration is divided by the magnitude of the electric field, we obtain a positive quantity u,, the mobility of ions of type i. Within the range of validity of Ohm’s law, u, is indeAngew. Chem. infernat. Edit. Val. 4 (1965) No. 6 pendent of the field strength, but is a function of the intensive variables of the system (temperature. pressure, concentration). It is convenient to replace u i by the ionic conductivity Ai of the ions of type i, as defined in Equation (32); F is the Faraday constant. hi (32) F.uj E It can be shown [9] that, provided that Ohm's law is valid, the relationship (33) must always be satisfied. In this equation, /zd is the magnitude of the electrochemical valence and ci the molarity of ions of type i. The summation must be carried out over all types of ions present. (33) When more t h a n t w o types of ions a r e present, the discussion of equation (33) becomes complicated. I n t h e next section, therefore, we shall confine ourselves to solutions of electrolytes containing t w o types of ions (e.g. HCI or NazS04). We shall also assume, for the s a k e of simplicity, that t h e solvent ( e . g . H z 0 ) does not f o r m ions. After t h e discussion of transport numbers, we shall also examine whethe; t h e ionic mobilities a n d conductivities c a n be derived from experimcntal d a t a in this case. 2. Equivalent Conductivities We shall now deal with electrolyte solutions containing two types of ions, using either the molarity c or the equivalent concentration c* of the electrolyte as the macroscopic concentration variable. We then have [cf. Equation ( I )] : C= pim ;c*= I t M2.m 2, v c = z v-c law of independent migration of ions, first formulated by Kohlrausch in 1893 and repeatedly verified since that time, uo (or A;) is characteristic of ions of the type i in a given solvent at a given temperature and pressure, independent of the oppositely charged ion. Thus i\o is a sum of contributions due to the individual ions. For very dilute solutions of weak e!ectrolytes, we can put hi- hp in Equation (38). We then obtain from (38) and (39) that Ai-40 = a. This relationship leads to Ostwald's dilution law when it is combined with the classical law of mass action for dissociation equilibria of type (15 ) , i. e. with Equations (10) and (16) and y* yu = yt. For very dilute solutions of strong electrolytes, on the other hand, a = 1, and A;, A_,and h contain terms proportional to c'" which can be calculated from the valences of the ions and properties of the solvent, using Onsager's limiting law. An extension of the theoretical treatment of electrical conduction in dilute solutions of strong electrolytes beyond the square root law has recently been developed by Onsuger and FUOJS [lo], again on the basis of the relaxation and the electrophoretic effects. Concentrated electrolyte solutions show a complicated dependence of a, A,, A_,and11 on concentration which is at present not amenable to theoretical treatment. We have determinedA over a wide range of concentrations for the systems H20/HN03 and H20/HC104, for which a-values are available from spectroscopic data [I 11. (34) In this equation p is the density of the solution a n d MZ is t h e formula weight of t h e slectrolyte. We also have c, = v. .LY.c; c.. (35) = V-'OI'C which, together with Equation (34), gives z+ c + = 2- 'C- = E.C* (36) Equation (37) defines the equivalent conductivity A 3. E xjc' (37) which can be measured. This relationship, together with Equations (33) and (36),leads to afundamental equation -1= FxY..(u+T U-) = %.(A- -+ A_) (38) for the electrical conductivity in electrolyte solutions containing two types of ions. For infinite dilution, Equation (38) becomes in which the superscript signifies the limiting value of the quantity in question when c + 0. According to the [9] R . Haase: Thermodynamik der irreversiblen Prozesse. Steinkopff, Darmstadt 1963, p. 281 ff. Angew. Cltem. internat. Edit. Vol. 4(1965) No. 6 vcict Fig. 5. T h e system H 2 0 / H N 0 3at 2 5 ' C : Degree of dissociation n of t h e electrolyte as a function of t h e s q u a r e root of t h e niolarity c according to 141. ( c t 1 mole/i). Fig. 5 shows the degree of dissociation a of the electrolyte, Fig. 6 the measured values of together with the values of (A+ i- h-) calculated with Equation (38), as functions of cIlzfor aqueous nitric acid (at 25 "C and 1 atm). Aqueous perchloric acid presents a similar picture [I 11. The effect of incomplete dissociation at high concentrations can be clearly recognized. n, In order to obtain an analytical representation for the entire concentration range from x = 0 to x = 1 (for which experimental values are available for aqueous nitric acid [ 101 R . M . Fuoss and F. Accascina: Electrolytic Conductance. Interscience, New York-London 1959. [ I l l R . Haase, P.-F. Sauernmnn, and K . - H . Ducker, Z. physik. Chem. N.F. 4 3 , 218 (1964). 49 1 400 h respectively: N a occurs in the species N a ’ a n d Na2S04, a u d sulfate occurs as SO:- a n d Na2S04. If dissociation of an electrolyte is incomplete, it IS necessary to take into account transport of the undissociated electrolyte moIecuIes, relative to the solvent, in the electric field. This relative migration of the undissociated electrolyte may be either direct (association of tbe neutral electrolyte molecules with ions) or indirect (solvation of ions and consequent movement of the solvent reIative to the electrolyte molecules). Corresponding to the mobility ui and the ionic conductance hi, therefore, we also introduce the mobility u, of the undissociated electrolyte and the quantity h, = F.u,. I 0 -_ m?7& . 1 2 1 - 3 9.= u, u ++ u _ - I-a 01 .- - uu - - u+ + u _ 1 l a - (A+ i -.Au) (40) A,+A- I/ c / c i Fig. 6 . The system H*O/HNO, at 25 “ C : Equivalent conductivity A and sum (i.+ i h . ) of the ionic conductances, according to [ I l l (units ohm-1 cmz eq. 1 ; c t I inole/l). and sdfuric acid 1111, it would be necessary to find empirical expressions for A(x) or h-(x) and A-(x) which would reduce, at high dilution, to the equations of Onsager and Fuoas [lo] (cf. the method used in the case of equilibrium properties, Section 11.4). No attempt has so far been made in this direction, partly owing to the complicated form of the Onsager-Fuoss equations, and partly because of the difficulties encountered in the experimental determination of the fundamental quantities h- and 1,- in concentrated solutions (cf. Section 111.4). The general expressions (40) and (41) can be derived for the dimensionless quantities 8, and 9-[13]. The upper (lower) sign applies when the undissociated electrolyte molecules migrate in the same direction as the cations (anions). It can be seen that, when dissociation is complete (a = I ) or if transport of the undissociated electrolyte is negligible (u, = 0; A, = 0), 8, and 3- reduce to the Hittorf transport numbers t, and t- = (1 -t+) of the cations and the anion:, respectively. At infinite dilution (c + 0; 01. + l), we have 3. Transport Numbers Contrary to widely held beliefs, neither the Hittorf transport number nor the true transport number of an ion can be measured at all electrolyte concentrations [9]. The quantity measured is the transport number of an ion constituent. which corresponds to the Hittorf transport number only at sufficiently high dilutions [9]. This fact can be demonstrated for each of the methods used for the determinatim of transport numbers, i. e. Hittorf’s method [12], the moving boundary method [13], and e. m.f. measurements in concentration cells [9,12] and in gravity or centrifugal cells [9]. For the sake of simplicity, let us again consider solutions of a single electrolyte containing two types of ions. The transport numbers of the cation and anion constituents respectively are 9,and 3- = (1 -8,). 8, and 3- are equal to the number of equivalents of the cation and anion constituents, respectively, passing through a reference plane which is stationary with respect to the solvent, during the passage of 1 faraday of electricity through the solution. The term “ion constituent” refers to the parts (atoms or radicals) of the electrolyte molecule which can form ions, irrespective of the extent to which these components are actually present as ions. in which$: and to are the limiting values of the transport numbers at infinite dilution. We have determined transport numbers for concentrated aqueous solutions of HNO3, HC104, and AgN03 at 25 “C,using the moving boundary method [14]. Fig. 7 1 078 b; 076 074 0 72 0701 0 ’ ’ ’ 1 ’ 2 ’ ’ \ 3 c cict T h u s in a n a q u e o u s solution of sodi um sulfate, t h e a t o m N a an d t h e radical SO4 a r e t he cation a n d anion constituents Fig. 7. The system HxO/HNO3 at 25 ‘ C : Consrituent transport number 8, of the cation IK c’I2, according to [ I I]. ( c t I molell). [I21 M . Spiro, J . chem. Educat. 33, 464 (1956); Trans. Fardday SOC. 55, 1207 (1959); A . Weissberger: Physical Methods of Organic Chemistry, Part I V . Interscience, New York 1960, p. 3049. [I31 R . Haase, 2. physik. Chem. N.F. 39, 27 (1963). [I41 R. Haase, G . Lehnerr, and H.-J. Jansen, Z . physik. Chem. N.F. 42, 32 (1964). 49 2 = Angew. Chcni. intermit. Edit. 1 Vol. 4 ( 1 9 6 5 ) 1 N c . 6 shows the curve of a+ against c1I2for aqueous nitric acid. A significant feature is the maximum, which is also found with aqueous perchloric acid. ing feature is the strong dependence of AT and 1,; (for H+) on concentration, compared with that of A_*and : A (NO5 and C10,). This feature is related to the proton jump mechanism of the migration of H+ ions, which becomes increasingly noticeable with increasing dilution. 4. Ionic Conductivities We have seen that, in solutions of a single electrolyte containing two ionic species, it is possible to measure the following quantities: the equivalent conductivity A, the stoichiometric transport numbers and in some cases the degree of dissociation u.Experimental data can also be used to find the limiting values A0 and to. 310 a,, f 200 A It is therefore possible to determine the limiting values A: and!A of the ionic conductivities, usingEquation(44), which is derived from Equations (39), (42), and (43). Aq == tt; ..lo; = . .4o 100 (44) These quantities, which were mentioned earlier, are tabulated in modern monographs and reference books for many ions at various temperatures. I 0 3 VCICt The equations A: 2 1 :$4:7q = 8+-;\; At = 8 :IZ (45) can be used for all concentrations with the experimental values of 9, and11 or of 9+,A, and a. From (38), (40), (41), (45), and (46), we find [I 11: Fig. 8. T h e HzO/HNO, system a t 25 “ C : T h e quantities i : ,.;.7 i.’. and ‘7. as f u n c t i o n s of t h e s q u a r e r o o t of t h e molarity c [molelll, a c c o r d i n s t o [ I I ] (units o h m - ’ cmz eq-1; c t T- 1 mole/l). Sufficient data for the determination of :A over a wide range of concentrations are available for only a few other electrolyte systems ( e . g . aqueous hydrochloric acid [I I], silver nitrate [14,15], and silver perchlorate [15]). IV. Diffusion from which we obtain the identities: A’ f A‘ = A: + A‘ = (51) A,.3- A_. (52) In accordance with Equation (51), AT and : A may be referred to as the equivalent conductivities of the cation and anion constituents of the electrolyte respectively. According to Equations (49) and (50), A; and A‘ may be identified with the ionic conductivities A,. and A- only if dissociation is complete (oc = I), or if the migration of undissociated electrolyte in the electric field is negligible (A, 0). Consequently, at high concentrations A, and A_ cannot be separately determined. Provided that experimental data for a are available, however, it is possible to find the sum (A+ + A-), using Equation (38) or (52) (cf. Fig. 6). Fig. 8 shows values of AT, A;, AT, and A- for aqueous nitric acid at 25 OC, over a wide range of concentrations. These values were determined from the data of Figs. 5, 6, and 7, using Equations (45) and (46). A similar picture is found with aqueous perchloric acid [l I]. A strikAngew. Chem. intermit. Edit. / Val. 4(1965) No. 6 Diffusion is the transport of matter in a mixture, caused by concentration gradients. Let us again consider a solution of a single electrolyte containing two ion constituents. As a result of the conditions of electroneutrality and local dissociation equilibrium (which normally are satisfied by every volume element, even in a medium in which transport processes are taking place), all electrolyte particle types move at the same average velocity. Apart from the (average) velocity of the solvent molecules (vector ), therefore, there is only one other independent velocity, i. e. the common (average) velocity + v2 of the ions and undissociated electrolyte molecules ( ~ . gthe . species H+,HSO,, SO2,, and H2S04 in aqueous sulfuric acid). We also have mly one independent concentration variable, for which (as in the case of electrical conductivity) we shall choose for the moment the molarit4 c of the electrolyte. < The transport of matter is characterized by a vector ) or c( ). The latter quantity is the diffusion current density of the electrolyte in the “solventfixed” frame of reference, (“Hittorf‘s reference system”) (G >; < + and is denoted by 1Jz. Thus -f 1Jz + + c.(vz-v,). (53) [IS] A. N . Campbell and K. P . Singh, Canad. J . Chem. 37, 1959 (1959). 493 < I n this reference system, the velocity of the solvent is taken as the reference velocity. There are also other reference systems, such as that in which the reference veloc+ ity is the mean volume velocity w (Fick’s reference system). The corresponding vector for the diffusion current density is Hittorf’s system is related to Fick’s system by equation (55) [9], where is the molar volume of the mixture, Vl and V2 are the partial molar volJmes of the solvent and the electrolyte respectively, and x is the stoichioinetric mole fraction of the electrolyte. v T h e above discussion is true not only for diffusion but also for other transport processes which occur in t h e absence of a n electric current, e.g. sedimentation (cf. Section V) a n d thermal diffusion. F o r t h e present, however, we shall confine our discussion to pure diffusion, i.r. we shall ignore external force fields, a s well a s pressure a n d temperature gradients. In Section V we shall consider pressure gradients in addition t o concentration gradients. For pure diffusion in a solution of an electrolyte containing two ion constituents, each volume element obeys Fick’s law in the form in which D is the diffusion coefficient. Equation (56) is analogous to Ohm’s law (31), and is always valid unless the concentration gradients are extremely high. As the electric conductivity x in Equation (31), so the diffusion coefficient D in Equation (56) is a measarable positive quantity (in stable mixtures not at their critical points), which depends on the intensive (local) variables of state (temperature, pressure, concentration). It is often desirable to convert from Fick’s reference system to Hittorf’s system, and from the rnolarity c to the molality m. From Equation (34), it is possible to derive grad c = C.(I-C.V2) -. grad m m (57) In the above equations, a1 1, a22, and a12 are phenomenological coefficients related to the ionic conductivities A, and A- by Equations (62) arid (63). A. + ,J2 = - D .c. grad m rn z .all t z:a12 (62) For very dilute, but not necessarily ideal dilute solutions (in the thermodynamic sense), the kinetic theory shows [18] that it is possible to disregard the electrophoretic effect, and use the approximation: .= A: ; A- = At (64) From Equation (64), together with (59)-(63), we obtain Equation (65) [18,19], (58) We shall now restrict the discussion to completely dissociated electrolytes containing two ionic species. Thus we exclude compounds such as H2S04 or H3P04, and set tc = 1. The solution then contains only three types of particles: non-electrolyte molecules, cations, and anions. The condition tc = 1 stipulates dilute solutions of strong electrolytes. Application of the thermodynamics of irreversible processes to such systems leads to the general equation (59) for the diffusion coefficient D [9,16,17]. [I61 R . Haase, Trans. Faraday SOC.49, 724 (1953), footnote on p. 728. [17] R . Haase: Thermodynamlk der Mischphasen. Springer, Berlin-Gottingen-Heidelberg 1956, p. 579. 494 VL’C As previously mentioned, in diffusion the ions move at the same average speed and i n the same direction, namely opposite to the direction of the chemical potential gradient. Consequently, in contrast to the conduction of electricity, only the electrophoretic effect is active, the relaxation effect being absent. The coefficients a1 1, a22, and a12 in (61) must therefore lead to elimination of the relaxation effect which is still accounted for in Equations (62) and (63). Thus if we have a kinetic molecular theory of electrolytic conduction with explicit exrressions for h, and A_,the condition of non-occurrence of the relaxation effect in Equation (61), together with Equations (62) and (63), provide the three equations required for the calculation of all, a22, and a12 from molecularphysical data. Consequently, any kinetic treatment of electrical conduction in dilute solutions of strong electrolytes, combined with Equation (59), leads to an explicit expression for D. Onsager and Fuuss [18] first reported such an expression. At higher concentrations, the molecular-kinetic theory of diffusion, like that of electrical conduction, meets with difficulties which cannot at present be overcome. a J 2= 0; h, Combination of Equations (55), (56), and (57) gives Equation (58), which is Fick’s law expressed in Hittorf’s system. F2 = which relates the diffusion coefficient in very dilute solutions of strong electrolytes to the limiting values : A and :1 of the ionic conductances and to thermodynamic properties of the electrolyte solution. At infinite dilution (m -+ 0), combination of (66) with (65) gives the limiting law (67): [18] L. Onsager and R . M . Fuoss, J. physic. Chem. 36, 2689 (1932). [I91 G . S. Hartley, Philos. Mag. J. Sci. Z2, 473 (1931). Angew. Chern. internat. Edit. 1 V d . 4 (1965) 1 No. 6 After sufficient time, the opposing effects of sedimentation (“seraration”) and diffusion (“mixing”) lead to the + establishment of a steady state characterized by 1 J l = 0, which under the conditions assumed (uniform temperature) corresponds to an equilibrium state. According to classical thermodynamics [9], this sedimentation equilibrium is described by proposed by Noyes in 1908. For 1 : I electrolytes (z+ = -z- = 1) Equation (67) reduces to given by N e m s f in 1888. --> V. Sedimentation On the other hand, by applying the condition to Equation (73), we obtain Sedimentation is the transport of matter in a mixture caused by gravitational or centrifugal fields. If we confine the discussion to solutions of a single electrolyte containing two ion constituents, then the general considerations regarding concentration variables, velocities, and diffusion current densities as discussed in Section IV are still valid. Consider first an electrolyte solution subject to no fields other than the external force field (gravitational or centrifugal acceleration and no gradients other than the pressure gradient (grad P). We may assume local mechanical equilibrium, so that if p is the density of the solution, then z), S. M1.m.T=D. VI m 1J2 . gra d m ~ 0 (75) The equilibium conditions (74) and (75) immediately lead to D .mz -(>yz/>-m)~.p __ M I . s c.V1.(Mz-Vzp) (76) Equations (l), (2), (7), and (9) give the following relationships: M I . m2 - c =m.(I + MI.m).V (77) 4 p .g = grad P Moreover, if we disregard extremely high force fields, each volume element satisfies the equation vz-w and from these, together with Equation (76), we obtain + + + = s-g or, combining this with Equations (54) and (69): ---f = c.s.g = c s. F .grad P, (71) or with Equations (l), (34), and (55): Equations (71) and (72) correspond respectively to (56) and (58). The measureable quantity s is the sedimentation coefficient. It may be either positive or negative, and (like the diffusion coefficient D) depends on the intensive variables of the volume element. Sedimentation in a mixture initially uniform in concentration gives rise to a concentration gradient, which in turn leads to diffusion. In general, therefore, we must consider the simultaneous occurrence of a pressure gradient and a concentration gradient, and hence a superposition of the two transport processes (diffusion and sedimentation). Experience has shown that this superposition is linear. Starting with Equations (58) and (72), we can therefore write (73) Equation (73) describes the simultaneous occurrence of diffusion and sedimentation in the solvent-fixed reference system. Angew. Chem. internor. Edit. / Vol. 4(1965) 1 No. 6 Equation (79) is valid at all concentrations, and relates the transport coefficients D and s. The quantities on the right-hand side can be found from equilibrium data alone, i.e. from experimental values of p(m) and yfm). Equivalent expressions were derived earlier by various methods [9,20]. Our derivation [21] has the advantage of generality and simlicity. The above form of Equation (79) is particularly suitable for electrolyte solutions. For other purposes, however, particularly for high molecular weight non-eletrolytes, other forms of this relationship, which can also be derived from Equation (76), are more suitable [9,20]. Creeth [22] has recently confirmed experimentally a n equation corresponding to (79) (but using the “c” scale and not involving and V,) for aqueous solutions of T12S0.4 at 25°C at electrolyte concentrations of 8 to 50 g/l. The functions V,(m) and p(m) were determined by density measurements, y(m) by e. m.f. measurements, v [20] For a review containing historical data, see R. Haase in J. W . Williams: Ultracentrifugal Analysis in Theory and Experiment. Academic Press, New York-London 1963, p. 13. [21] R. Haase,Z.physik. Chem.N.F.25,26(1960); R. Haaseand H. Schonert, 2. Elektrochem., Ber. Bunsenges. physik. Chem. 64, 1155 (1960). [22] J . M . Creeth, J. physic. Chem. 66, 1228 (1962); J. M. Creeth and B. E. Peter, J . physic. Chem. 64, 1502 (1960). 495 D(m) from diffusion experiments, and s(m) from experiments with the ultracentrifuge. The order of magnitude of the diffusion coefficient D is 10-5 cmZ/sec in this system, and that of s is 10-13 sec. In the limit m i 0, we find from Equations (81) and (79), together with Equations (66), (SO), and (83): Equation (65) applies to very dilute solutions of strong electrolytes containing two ionic species. In this case we can also apply the approximations v! Thus from Equations (65) and (79) we obtain in which M; is the equivalent weight of tk.e electrolyte, defined by Since the molecular theory of sedimentation is fundamentally simpler than that of diffusion, Equation (79) is useful in calculating D from s. On the other hand, D is the more easily measured quantity, so that (79) will also be used for the reverse calculation. and in which we have made use of (60) and V? = M z . V2 I n Equations (84) and (85), is the limiting value of the partial specific volume of the electrolyte at infinite dilution, and pol is the density of the pure solvent. The limiting law (85) is known as Svedberg’s equation (Svedberg 1925), particularly under the condition -I == I , (nonelectrolyte solutions). This relationship can be used to determine the quantity M ~ / vEquation . (85) can also be derived from Equations (67) and (84) using (60) and (82). (83) (v2 is the partial specific volume of the electrolyte). Received: October 21st, 1964 [A 427/224 tE] German version: Angew. Cheni. 77, 517 (1965) Translated b y Express Translation Service, London Chemistry and Stereochemistry of Fluorophosphoranes [*] BY DR. R. SCHMUTZLER UNIVERSITY CHEMICAL LABORATORY, CAMBRIDGE, ENGLAND [ * *] Fluorophosphoranes are a recently discovered new type of phosphorus compound derived ,from phosphorus pentafluoride by substitution of fluorine atoms with various groups. Synthesis, chemistry, and stereochemistry of this class of compounds containing phosphorus in the comparatively rare coordination number 5 will be discussed. A. Introduction Until recently, relatively few examples of pentacoordination were known; s x n e halides of group V elements were recognized as typical representatives of pentacoordinated species. For phosphorus in particular, pentacoordinated halides with trigonal-bipyramidal configuration (in the gas phase) have long been known, r.g. PBrs, PCls (covalent form), PFs, and the covalent forms of the halofluorides PX,F,-, (X = C1, Br; n = 2,3,4). The chemistry of P(V)-halofluorides, which are distinguished in several instances by the interconversion of covalent and ionic forms, has recently been reviewed [I -31. [ * ] Presented in part as lectures a? Newark, Delaware (U.S.A.) (Feb. 23rd, 1963); Argonne, Illinois (U.S.A.) (Sept. 4th, 1963); Birmingham (England) (Dec. I3th, 1963); Cambridge (England) (Feb. I Ith, 1964); Saarbrucken (Germany) (Feb. 18th, 1964); Glasgow (Scotland) (April 28th, 1964); Heidelberg (Germany) (May 22nd, 1964); Wien (Austria) (Sept. 9th, 1964). [**I Present address: E. I. duPont de Nemours and Co., Inc.: Experimental Station, Wilmington, Delaware, U.S.A. [ I ] D.S . Puyne, Quart. Rev. I S , 173 (1961). [2] R. R. Holmes, J. chem. Educ. 40, 125 (1963). [3] L. Kolditz, Z . Chem. 2, 291 (1963). 496 In the present article, a review is presented on-chemical and stereochemical aspects of a further class of phosphorus-halogen compounds containing pentacoordinate phosphorus. The compounds of this type are derived from phosphorus pentafluoride by substitution of fluorine atoms with various groups. The following types of these “fluorophosphoranes” will be considered : I . Fluorophosphoranes containing hydrocarbon groups as substituents, RnPF5-, (n -- 1,2,3). 2. Aryltrifluorophosphorus hydrides, ArPF3H. Compounds of this type are not true fluorophosphoranes within the scope of this article. Because of the stereochemical relationship to other fluorophosp horanes, however, aryltrifluorophosphorus hydrides will also be considered here. 3. Arylchlorotrifluorophosphoranes, ArPF3CI. 4. Alkyl(ary1)-dialkylaminotrifluorophosphoranes, R(Ar)PF3NR’2. 5. Dialkylaminofluorophosphoranes, (R2N),PF5-, (n = l,2). 6. Perhaloalkyldihalodifluorophosphoranes, RH,,PF2X2 (Hal =: F,CI; X := CI, Br). Angew. Chem. internnt. Edit. Vol. 4 (1965) / Nu. 6

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