orders of magnitude of additional sensitivity should be readily accessible. The response of the flame-ionization detector falls in the range of about 0.1 to 1 square inch/p.p.m. Thus, the flame-ionization response of compounds such as CHF2Cl, CF3ClCF8CF2Cl, CH2=CF2, CHaCHF2, and even some of the dichloro derivatives such as CHFCl2 or C F F C C ~ ~are 10 to 1000 times greater than their electron-capture responses. For other compounds containing two chlorine atoms, and for compounds containing three or more chlorine, bromine, or iodine atoms, the electron-capture response is much greater than the flame-ionization response. If sensitivity is the major consideration, the flame-ionization detector has a place even in the analyses
for many halogenated substances. If specificity is critical, the greater specificity of the electron-capture detector may favor its use even for halogenated substances showing low responses to this detector.
(2) Landowne, R. A., Lipsky, S. R., Zbid., 34, 726 (1962). (3) Lovelock, J. E., G;?gory, N. L., "Gas Chromatography, p. 219, Academic Press, New York, 1962. (4) Warhurst, E., Quart. Revs. (London) 5, 44 (1951).
C. A. CLEMONS A. P. ALTSHULLER
ACKNO W LEDGMENl
We acknowledge the assistance of Andrew E. O'Keeffe, who procured many of the compounds and suggested several worthwhile approaches to the many problems encountered, and of Arthur I. Coleman, who assisted in obtaining the data on relative responses. LITERATURE CITED
(1) Kirkland, J. J., ANAL.CHEM.35, 1295 (1963).
Laboratory of Engineering and Physical Sciences, Division of Air Pollution Robert A. Taft Sanitary Engineering Center, Public Health Service U. S. Department of Health, Education, and Welfare Cincinnati, Ohio 45226 PRESENTED before the Division of Water, Air, and Waste Chemistry, 148th Meeting, American Chemical Society, Chicago, Ill., September 1964. Mention of commercial products does not constitute endorsement of the Public Health Service.
Reaction Rate Measurements with Cation-Sensitive Glass Electrodes A Kinetic Study of Some Tetraphenyl borate Precipitation Reactions SIR: Although cation-sensitive glass electrodes have been used for a variety of chemical measurements (15), they have not yet been employed in rate or kinetic studies. Such electrodes accurately and selectively monitor ion activities in solution, however, and should also be effective in following the appearance or disappearance of appropriate ionic species in the course of chemical reactions. It may be expected that the range of application of glass electrodes to kinetic studies will be limited not only by selectivity and sensitivity considerations but also, in the case of fast reactions, by the finite response times of such electrodes. In this paper, we report on the use of cationsensitive glass electrodes in the study of the kinetics of several precipitation reactions involving univalent cations and tetraphenylborate. The utility of such measurements is extended to fast reactions through the use of a rapidmixing flow technique (1) of a kind similar to that described by Roughton and Chance (17) which employs a pH-type glass electrode. Tetraphenylborate precipitation reactions were chosen for this study because of the great importance of such reactions to chemical analysis (5) and because of the demanding requirements of heterogeneous reaction rate measurements. While crystallization and precipitation reactions have received the attention of many workers (11), precipitation kinetics are by no means as well understood as are homogeneous solution reactions. A variety of techniques (IO), including light scattering, interferometry, potentiometry, conductometry, 136
ANALYTICAL CHEMISTRY
and polarography, have been used to follow precipitation reactions. Tetraphenylborate precipitations of SH4+, K+, Rb+, Cs+, T1+, or Ag+ have not previously been considered from the kinetic viewpoint. EXPERIMENTAL
Apparatus. The experimental arrangement devised to follow fast precipitation reactions is shown in Figure 1 . The mixing chamber consisted of a three-way, T-shaped stopcock (1-mm. diameter bore) and was fed, with the two reactant solutions, from a reservoir under nitrogen pressure and a Radiometer Type ABU l a Auto Burette, respectively. The indicator electrodes were Beckman Model 39047 cation-sensitive glass electrodes and were inserted by ground glass joint into a Beckman Model 46850 microflow assembly which was attached to the outlet of the mixing chamber. h Beckman Research Model pH meter was used to amplify the electrode response, which was displayed as a function of time on a Photovolt hIodel 43 recorder. The slower precipitation reactions were monitored directly in an open vessel, using the glass electrode and saturated calomel reference electrode, after rapid mixing of the two reagent solutions. Reagents. A buffer solution, consisting of 0.1M tris(hydroxymethy1)aminomethane (THAM)-Fisher Primary Standard-and 0.01M acetic acid was prepared by adjusting the p H to 5.1 with G. F. Smith reagent grade HCIOl and was used as the solvent in all experiments. Cesium and rubidium stock solutions were prepared from the chloride salts obtained from Fisher Scientific Company. Thallium(1) solutions were prepared by dissolving T12C03(A. D. Xac-
kay, Inc.) in HC104. Baker reagent grade NH4C1, ,AgiXOs, and KC1 were used for preparing NH4+, Ag+, and K + solutions. Calcium tetraphenylborate was prepared from Fisher Scientific reagent grade NaB(CeH6)4, according to the procedure of Rechnitz, Katz, and Zamochnick (16), and was standardized by potentiometric titration with KC1 and RbCl. rl solution of calcium tetraphenylborate dissolved in the buffer medium served as a source of tetraphenylborate ion in all experiments. Procedure. The precipitation rates of ?JH4+, K+, and Rb+ with tetraphenylborate ion were followed directly with a cation-sensitive glass electrode which had been preconditioned in a buffered l O - 3 X solution of the metal ion to be studied for a t least 24 hours. The reaction vessel initially contained about 20 ml. of a solution of the metal ion (X+)in a THAU buffer (pH = 5.1). The required volume of -0.15 F Ca[B(C&)4]2 was injected into the stirred solution, and the potential of the cation-sensitive glass electrode us. SCE was recorded as a function of time, Millivolt readings were then converted into hI+ concentration values (from a log h l + us. millivolt calibration curve) ; and, with known stoichiometry of reaction between B(C6H5)4- and hI+ @), the B(CsH6)d- concentration corresponding to each M + concentration was calculated. This procedure was repeated for several different initial concentrations of B(C,&)4- and h i + in an attempt t o obtain information leading to the mechanism of the overall reaction
M+
+ B(CdU4-
+
> I B ( C ~ H S4 ) ~
All experiments were carried out a t 24.8' =k 0.3' C. Since Cs+,T1+, and Ag+ react too rapidly with B ( C G H ~ )to ~ -allow meas-
2ri
I
RADIOMETER AUTO BURET
I YP -15 Y
V
I
I
I
I
I
I
I
0
2
4
6
8
10
12
14
I
I
16
18
I(recl EFFLUENT
Figure 1.
Schematic of experimental arrangement
Figure 2. Glass electrode response during precipitation reaction Potential a t to is arbitrary. (a) (Rb+), = [B(CsH&-], = 5 X lO-4M (b) (TI'), = 7.3 X lO-%t, [B(C6HJ4-lo= 6.6 X 10-6M, flow experiment
urement of their rates in the manner described above, it was necessary t o employ a steady-state flow method. This neutralizing a solution of NaOH (colored technique allows rapid mixing of the rewith phenolphthalein) from branch A actants (4 msec. for the system dewith an acid solution from branch B in scribed here) and circumvents any rethe mixing chamber. It was shown that sponse limitations of the electrode and mixing is complete in the first 5% of the recording systems. In each experiment, volume between mixing chamber and A I + solution was allowed to flow from detector. In the system used, the availbranch A (see Figure 1) through the able volume between mixing chamber mixing chamber and detector assembly and indicator electrode totaled 0.325 until a stable potential was recorded. ml. The metal concentration and t The stopcock was then quickly turned were varied by changing the concentraso that both solutions [M+ and tion of the solution in the reservoir B(CeHb)4-] entered the mixing chamber and/or the relative volumes entering the and passed through the detector arm. mixing chamber from each of the The resulting millivolt us. t response was branches. steplike (see Figure 2b), and results from The solubilities of the & I B ( C ~ H salts S)~ dilution of the M + solution (by solution in the THAM buffer solution were estifrom branch B) and a decrease in &I+ mated spectrophotometrically according Concentration due to the formation of to the procedure of Howick and Pflaum XB(C6H5)4precipitate. The contribu(6)* tion to the millivolt decrease (observed RESULTS AND DISCUSSION upon mixing) due to dilution was calcuCrystallization is a two-step process lated by taking into consideration the (4, 7 , 11, 14, 21) which involves nuclearelative volumes of solution entering the mixing chamber from branches d and tion and subsequent crystal growth. B. The amount of solution flowing Nucleation involves formation from from branch B in time t was read from supersaturated solutions of the initial the Auto Burette volume indicator, and fragments which are capable of sponthe amount from branch A was calcutaneous growth into crystals (9). Belated from V A = Titotal- VB, where cause this initial step was not investiV t o t a l refers to the effluent volume colgated in the hIB(CJ35)4 systems, it lected in time t . ?\.I+a t mixing, then, is will receive no further discussion. equal to v A / v t o t a l X M + (reservoir). Various mechanisms of crystal The B (CsHs)c-concentration a t mixing was calculated in a similar manner. The growth have been discussed (2,3,11, 13, dilution-corrected millivolt decrease was 14). Davies and Jones ( 2 ) have conused to calculate the decrease in >I+ due sidered (a) diffusion, (b) reaction conto reaction with B(CeH5)r- in the flow trol (incorporation of ions a t growth tube, and the amount of B ( C ~ H S ) ~ - sites directly from solution), and (c) a consumed in this reaction was calcuprocess occurring a t an adsorbed layer lated from the known stoichiometry. on the crystal surface, as possible The time a t which ;\I+ is measured mechanisms which govern the rate of (time zero is taken a t mixing) was esticrystallization of sparingly soluble salts mated from the flow rate and the volume of the flow system between mixing chamfrom solution. ber and the cation-sensitive glass elecA typical millivolt us. time curve for trode-i.e., ml./(ml./sec.) = t. The the precipitation of NH4+, Rb+, or K+ overall flow rate varied (constant for a by B(CGHS)~-is shown in Figure 2a. given experiment) between 2.8 and 4.3 (At very low initial concentrations an ml./sec. (3.6 to 5.5 m./sec. through the induction period was observed.) mixing chamber), but is rapid enough in Electrode response time studies in this all cases to guarantee turbulent flow (1). laboratory (19) indicate that the reThe efficiency of mixing was tested by
sponse of the glass electrode itself to changes in bulk concentration of M+ is very rapid and, therefore, should not limit the measurement of changes in M + during the precipitation process. The corresponding concentration us. time curves for the precipitation reactions were plotted (via millivolt us. log M + calibration curves), and these data were best described, for equivalent concentrations of M + and B(C,&)a-, by the expression
where dC/dt is the rate of precipitationl Ct is the concentration of M + a t time t , C, is the molar solubility of MB(Cas), (see Table I),k' = k(C, - CJ2/3 where C, is the initial concentration, k is a constant which may be a function of the number of particles ( 7 ) , and (C, - C t ) 2 / 3is proportional to the crystal surface area, which increases during the precipitation reaction ( 7 , f S ) . This rate law is consistent with mechanism c (above) and indicates that the rate determining step in the precipitation of ;MB(CJ35)4compounds is a surface reaction ( 2 , 3 ) . For nonequivalent concentrations of >! and I+ B(C&),-, the crystallization rate obeyed the equation Table I. Molar Solubility of Tetraphenylborate Compounds (24.8' C., THAM buffer solution, each
value average of 4 determinations) hlolar solubility X Ion
104
VOL. 38, NO. 1, JANUARY 1966
137
for the precipitation of R b + [equivalent concentrations of Rb+ and B ( C & ~ S ) ~ ] is shown is Figure 3, and it can be seen that the rate law (Equation 2) is obeyed over a wide range of the reaction course. Similar behavior was observed for the Rb+, NH4+, and K + systems both for equivalent and nonequivalent ionic concentrations of h l + and B(C&)4-. The values of k calculated from the slopes of plots of Equation 4 are listed in Table 11. The fact 0 .2 4 .6 .8 that the slopes calculated for the IO' (C0-C, r~(c,-cJ reaction of a given metal ion with Figure 3. Test of Equation 2 for B(C&J4- show only fair agreement surface-controlled precipitation may be due to differences in the number NH: K' Rb* Cs' Ti' of particles formed in each experiment. (Rb+), = [B(C6H&-]o = 5 X 10-4M Figure 4. Comparison of precipitaThe number of particles and their size tion rates and solubilities during the distribution (4, @-fixed nucleation process-determines the surface area upon which crystallization takes place and, therefore, affects the where k' has the same meaning as in tions are used. Walton and Hlabse precipitation kinetics. It has been Equation 1 and A is the number of (21) attribute the difference in Bas04 suggested (20) that the difficulty in remoles of MB(C,&)4 to be precipitated precipitation rates to differences in producing the number of particles from before equilibrium is reached. A can be polydispersity (affecting the total area experiment to experiment is one reason calculated (2) from the relationship of the precipitate) which result from for differences in kinetic data reported differences in growth rates in localized (M+ - A)[B(C&)h- - A] by various workers. Turnbull (18) has supersaturation areas. The question of K,, (solubility product) (3) shown that the precipitation of BaS04 whether eithzr or both of these pheis much slower if a small volume of Equation 2 is also consistent with nomena are responsible for the variation concentrated reactant is added to a in k values observed in the ; \ I B ( C ~ H L ) ~ mechanism c; a similar expression has solution of precipitating reagent than if been found to hold for the precipitation reaction systems might be settled by a equal volumes of equivalent concentraparticle count and size distribution of AgCl ( 2 ) . A plot of analysis. A procedure which involves seeding with crystals prior to precipitation has been used to control the number of particles and surface area during Table II. Rate Constants for Precipitation of MB(Cf,H& at Various Ratios of precipitation and has led to a le-bb comIonic Concentration plicated analysis of the precipation (24.8' C., pli = 5.1, THAN buffer) kinetics of AgC1 ( 2 ) and magnesium Ion [B(CGHS)~-IO, M M k(?*I-5/3 set.?) oxalate (12). Possibly controlled seeding of the UB(CJ15)4 systems 4 x 10-3 1.3 X lo4 8X K+ 4 x 10-3 0.54 X lo4 4 x 10-3 K+ would lead to more constant values of k. 4 x 10-3 0.45 x 104 4 x 10-3 K+ The values of k for the precipitation 2 x 10-3 0 . 7 x 104 4 x 10-3 K+ of C S B ( C J ~ ~and ) ~ TlR(CJl5)4 were 0.38 x 104 4 x 10-3 4 x 10-3 NH4+ determined from flow experiments be4 x 10-3 0 . 5 x 104 4 x 10-3 NHI + 4 x 10-3 1 . 4 X 10" "; + 8X cause these precipitation reactions were 2 x 10-3 0 . 8 x 104 4 x 10-3 NH4+ too rapid to be followed by the direct 0 . 7 x 105 10-3 10-3 Rb method. Since each flow experiment 5 x 10-4 3 . 0 x 105 5 x 10-4 Rb + 5 x 10-4 3 . 6 x 105 5 x 10-4 gives only one value for hI+ and t , it was Rb + 10-3 2 . 2 x 106 2 x 10-3 Rb not possible to determine the reaction mechanism for these systems. A series of measurements (using several glass electrodes in tandem in a flow system) Table 111. Rate Constants for Precipitation of MB(CsHs)a at Various Ratios of Ionic for a given experiment or a single measConcentration urement of h l + a t t plus a particle count Ion [B(CB&)~-IO, M (?*I+),, kl (iM+)t/(M+)o Ic(M-5/3sec.-l) might afford a better description of these precipitation reactions. It was cs + 1.15 x 10-3 0.964 X 0.53 1 . 9 x 106 0.537 1 . 7 X lo6 0.96 x 10-3 cs + 1.29 x 10-3 assumed that Equation 2 does hold for 0.704 1 . 2 x 106 1.96 x 10-3 cs 1.23 x 10-3 these systems, and the integrated form 1 . 6 X lo6 1.83 x 10-3 0 233 cs 2.77 x 10-3 of this equation was used to calculate k 0.326 1 . 0 x 106 1.84 x 10-3 cs + 2.62 x 10-3 via 0.784 4 . 1 X lo8 6.95 x 10-5 T1+ 3.44 x 10-5
-%++A
+
+
+
+
T1+ T1+
T1+ T1+
T1+
T1+
At3 +
138
4.52 x 9.72 x 5.51 X 6.6 x 5.05 x 6.43 x 8.95 x
10-5 10-5
10-5 10-5 10-5
ANALYTICAL CHEMISTRY
7.55 x 7.0 x 7.43 x 7.32 x 3.71 x 3.67 x 9.7 x
10-5 10-5 10-5 10-5 10-5 10-5 10-6
0.735 0.443 0.708 0.646 0.785 0.67
2.8 X 1.7 X 2.5 x 1.9 x 3.5 x 3.9 x >4.2 X
lo8 lo8 108 108 108 108 lo8
-1- - =1K t At
Ao
(5)
where K = k ( C , - C1)2'3. The values of k for Cs+ and Tlf are listed in Table 111. Preliminary experiments indicate
that k for Ag+ is greater than 4.2 X 108. The variation in k values for a given ion could not be traced to any experimental error, and no trend was observed when initial ionic ratios were varied. Again, these variations may be due to differences in the number of particles involved in each experiment. The rates of the reactions of NH4+, K+, Rb+, Cs+, and T1+ with B(CaHs)4are shown in Figure 4, and a rough correlation between reaction rate and solubility can be seen. It is interesting to note that the experimentally determined reaction rates are in agreement with qualitative observations made during titrations (with cation-sensitive glass indicator electrodes) of these metal ions with B(CaH5)4-. Thus, the time required to attain a constant potential reading after addition of each increment of B(C&)d- is much smaller for Cs+ than, for instance, K f . Cation-sensitive glass electrodes should also be useful in kinetic studies of homogeneous solution reactions. The maximum second-order rate constant (for a reaction which goes essentially to
completion) which can be determined with the flow system described in this study is about 105M-l sec.-l, corresponding to a flow volume of 0.325 ml., 0.1 second from mixing chamber to indicator electrode, an initial reagent concentration of 10-4M, and a potential change of about 18 mv. Faster reactions could be studied if smaller potential changes can be tolerated. LITERATURE CITED
(1) Caldin, E. F., "Fast Reactions in Solution," p. 39, Wiley, New York, 1964. (2) Davies, C. W., Jones, A. L., Trans. Faraday SOC. 51,812 (1955). (3) Doremus, R. H., J . Phys. Chem. 62, 1068 (1958). (4) ~, Fischer. R. B.. Anal. Chim. Acta 22. 501 (1960). (5) Flaschka, H., Barnard, A. J., Jr.,
"Advances in Analytical Chemistry and Instrumentation," C. N. Reilley, ed., Vol. 1, p. 1, Interscience, New York,
1960. (6) Howick, L. C., Pflaum, R. T., Anal. Chim. Acta 19,342 (1958).
(7) Johnson, R. A., O'Rourke, J. D., J. Am. Chem. SOC. 76,2124 (1954). ( 8 ) Klein, D. H., Gordon, L., Talanta 1 , 334 (1958). (9) La Mer, D. H., Ind. Eng. Chem. 44, 1270 (1952).
(10) Lucchesi, P. J., J. Colloid Sci. 11, 113 (1956). (11) Nancollas, G. H., Purdie, N., Quart. Rev. (London) 18, l(1964). (12) Nancollas, G. H., Purdie, N., Trans. Faraday SOC.57,2272 (1961). (13) Nielsen, A. E., J. Colloid Sci. 10, 576 (1955). (14) O'Rourke, J. D., Johnson, R. A., ANAL.CHEM.27,1699 (1955). (15) Rechnitz, G. A., Ibid., 37, 29A (1965). (16) Rechnitz, G. A., Katz, S. A., Zamochnick, S. B., Ibid., 35, 1322 (1963). (17) Roughton, F. J. W., Chance, B;: "Technique of Organic Chemistry, Vol. VIII, Part II,.p. 784, S. L. Fries, E. S. Lewis, A. Weissberger, eds., Interscience, New York, 1963. (18) Turnbull, D., Acta Met. 1,684 (1953). (19) Unpublished results by authors (196.5). (20) Walton, H. G., Hlabse, T., Anal. Chim. Acta 29,249 (1963). (21) Walton, H. G.. Hlabse. T.. Takznta 10, 601 (1963). ' (22) Williams, &I., Ind. Chemist 38, 186 (1962). , \ - - - - I
I
,
'
>
-
J. E. MCCLURE G. A. RECHNITZ
Department of Chemistry University of Pennsylvania Philadelphia, Pa. 19104 WORKsupported by NIH Grant GM10086.
Chemical Analysis of Alkali-Metal Tungstates and Tungsten Bronzes SIR: The method of Raby and Banks (10) for analyzing alkali-metal tungsten bronzes is thorough and excels earlier methods (2, 6-9, 21-15), but is highly sophisticated. The method described in this paper does not require the complicated equipment and procedures used by them to determine the alkali metal-to-tungsten ratio and assumes only that the oxygen-to-tungsten ratio is three to one, and that the residue consists only of the alkali-metal chloride. Spitzin and Kaschtanoff (11, 12) passed gaseous hydrogen chloride over sodium tungstate a t 400' C. and found that tungsten and oxygen were removed quantitatively as W02C12and the residue consisted of sodium chloride. Magndi (6) and Spitzin and Kaschtanoff used gaseous hydrogen chloride to analyze tungsten bronzes but they found it necessary to use oxygen to oxidize the bronze to the tungstate. Spitzin and Kaschtanoff used a two-step procedure, first oxidizing the bronze to the tungstate, then using hydrogen chloride; hlagnkli used a gaseous mixture of hydrogen chloride and oxygen. Magn6li claimed that his method failed to give faithful results for lithium compounds ('7). We attempted to analyze alakli-metal bronzes by using only hydrogen chloride and applying the method to the lithium as well as to the sodium, and potassium bronzes.
ratio of 1:l between two platinum foil electrodes for 6 hours was used to preMaterials. LITHIUM TUNGSTENpare this bronze. The temperature was BRONZE. A lithium tungsten bronze 780' C., the potential difference was 2 was prepared using the method of volts, and the current 0.5 ampere. The Conroy and Sienko ( 2 ) . A melt of resulting well defined cubes of goldenlithium tungstate and tungsten tricolored bronze were treated in the same oxide, present in a 1:1 mole ratio, was manner as was the lithium bronze. electrolyzed a t 780" C. in a porcelain POTASSIUM TUNGSTENBRONZE. A crucible using a platinum foil cathode melt composed of a 1:l mole ratio of and a platinum wire anode. potassium tungstate and tungsten triAfter 1 hour of electrolysis, the elecoxide was electrolyzed between platinum trodes were removed and the molten electrodes a t 780" C. for 1 hour at a material was poured off. The crystals potential difference of 2 volts and a remaining in the crucible and on the current of 2 amperes. The resulting cathode were purified by successive violet needlelike crystals were purified washings with hot water, hot concenin the same manner as was the lithium trated potassium hydroxide, 1: 1 hot bronze. nitric acid, dilute KOH, water, and Apparatus. A regulated flow of hydrofluoric acid. The bronze was then gaseous HC1 was passed through a thoroughly washed with water, heated gas-drying tower containing HzS04 to 400' C., finely ground, and placed in and then into a Vycor combustion a desiccator over magnesium pertube 92 cm. in length and 28 mm. in chlorate. The crystals when purified diameter. A chromel-alumel thermowere a bluish-gray but, when finely couple was affixed to the tube with ground (in an agate mortar), the powder strips of asbestos paper. The combuswas dark blue. tion tube contained the porcelain SODIUMTUNGSTEN BRONZE(RED). sample boat. The furnace was a horizonThe method used was that suggested tal nichrome-wound resistance tube by Gardner and Danielson (4). A mixfurnace 30 cm. in length consisting of ture of sodium tungstate, tungsten two hinged half-cylinders. The upper trioxide, and tungsten in the mole ratio half-cylinder could be raised and of 6.4:4:1 was heated to 1000" C. for 6 temperature was controlled by the use of hours. The resulting red crystals were a Variac. After leaving the combustion purified in the same manner as was the tube, the gas passed through a second lithium bronze. drying tower and out an exhaust tube. SODIUM TUNGSTEN BRONZE (YELLOW), Connections were an appropriate comElectrolysis of a melt of sodium tungbination of rubber tubing, glass tubing, state plus tungsten trioxide in the mole and rubber stoppers. EXPERIMENTAL
VOL. 38, NO. 1, JANUARY 1 9 6 6
139
