mental results. Unfortunately, there is little information about the kinetics of such a reaction. Neither a pair of complexing agents nor one precipitant is superior throughout the rare earth series. One or more selective processes are operating. Somehow one rare earth cation is preferentially released in solution while the other tends to remain complexed. How this selectivity is achieved has not been deduced. A determined attempt was made to develop an equation that would predict lambda values for the system under study. Such an equation would provide a theoretical basis for understanding the separations achieved as well as having practical utility. Using solubility product (6) and formation constant expressions (9, I O ) , a set of equations was developed. Despite the awkward form of the final equations, the calculation of approximate lambda values was made with a computer. The (9) E. V. Kleber, "Rare Earth Research Developments," Uni-
versity of California, Conference Center, Lake Arrowhead, Calif., October 1960, p. 1. (10) S. Chaberek and A. E. Martell, "Sequestering Agents," Wiley, New York, 1959, p. 505.
details of the derivation and the Fortran program will be furnished upon request. Limited success was realized in making computer calculations. The chief correlation is in systems using the chelating agent DTPA. The order of magnitude of the calculated values is fairly good and the trends are obvious (Table VIII). With other chelate systems the calculations were of questionable value. Even though a wide variety of concentrations of all forms of both rare earths could satisfy a given lambda, the computer calculation came close to predicting the actual concentrations (Table IX). ACKNOWLEDGMENT
The authors thank Orville Goering and D. W. Kraushaar for their assistance with the Fortran programming and calculations. RECEIVEDfor review January 6, 1967. Accepted September 29, 1967. Supported by the U. S. Army Research OfficeDurham through grant number DA-ARO(D)-31-124-G517. Symposium on Analytical Chemistry, St, Louis Society of Analysts, March 1965, St. Louis, Mo.
Viscosity of Liquid Water from 25" to 150" C Measurements in Pressurized Glass Capillary Viscometer Alexander Korosi and Bela M. Fabuss Monsanto Research Corp., Boston, Laboratory, Ecerett, Mass.
An apparatus containing a pressurized glass capillary viscometer has been developed for application in the measurement of the viscosity of liquids over, or near, their atmospheric boiling point. The assembly is pressurized with hydrogen and the diffusion of hydrogen through a palladium-silver membrane is used to lift the test liquid into the efflux bulb of the viscometer. The apparatus provided relative measurement, with an estimated precision of &0.2%, on liquid water in the temperature range 7 5 O to 150' C. I t can be used wherever the presence of hydrogen is compatible with the test liquid. Measured water viscosities, over the range 25" to 150" C, were correlated. The correlation represented the data with an average deviation of &0.17% and a maximum deviation of 0.49%. Recommended values for water viscosities are given. A detailed description of the apparatus, the experimental method, and results of measurements on liquid water are reported.
KNOWLEDGE OF THE VISCOSITIES of sea water brines is important in the development and operation of desalination processes. To obtain systematic information on the electrolyte solutions involved a new apparatus was developed that allows viscosity measurements on these and on other liquids under hydrogen pressure at temperatures up to 150O C . The apparatus was first used to determine the viscosity of water in the 75-150" C temperature range. The experimental results were evaluated and compared with literature information. T t h this new set of measurements, the uncertainty among -the generally used reference data was reduced, and we feel strongly that the precision of water vis-
02149
cosity data, especially in the 75" to 150" C temperature range, has improved. Numerous high temperature viscosity measurement methods, devoted mainly to establishing the pressure dependence of viscosity, are reported in the literature (1-8). With few exceptions, these measurements were of limited precision and required elaborate equipment. However, a simple and accurate method was reported by Hardy and Cottington (9) for measuring the viscosity of water and deuterium oxide up to 125" C. They used a pressurized glass capillary viscometer and found that pressurization to 35 psig, to prevent boiling, had no effect on the efflux time measured. Their results were confirmed by Heiks et af. ( I O ) , who used a falling body viscometer equipped with a radioactive plummet. (1) E. Kuss, Z. Angew. Phys., Bd. IV., 203 (1955); Ibid.,Bd. VII, p. 372. (2) N. H. Spear and L. P. Herrington, ANAL.CHEM.,23, 148 (1951). (3) F. Glaser and F. Beghardt, Chem.-lng-Tech.,31,743 (1959). (4) P. E. Parisot and E. F. Johnson, J. Chem. Eng. Data, 6, 263 (1961). (5) B. E. Eakin and R. T. Ellington, Trans. Am. Inst. Mining Met. Perrol. Engrs., 216, 85 (1959). (6) F. Walter and W. Weber, Angew. Chemie ( E ) , Bd. 19, 123 (1947). (7) W. Weber, Rheol. Acta, 2,131 (1962). (8) W. Weber, 2.Angew. Phys., Bd. XV, 342 (1963). (9) R. C. Hardy and R. L. Cottington, J . Res. Natl. Bur. Std., 42, RP1994 (1949). (10) J. R. Heiks, M. K. Barnett, et al., J . Phys. Chem., 58, 488 (1954). VOL 40, NO. 1, JANUARY 1968
0
157
-0
Figure 1. Assembled viscometer apparatus Figure 2. Schematic diagram of high temperature viscometer ap p aratus
APPARATUS Preliminary Testing. To elaborate Hardy and Cottington's findings on the pressurized viscometer, we built a prototype apparatus. This viscometer had the following essential features. The two arms of the glass viscometer were interconnected, with a valve between them, providing means for their eventual separation. The liquid filled instrument was pressurized with hydrogen and efflux times were measured under varying pressures. The return of liquid from the lower reservoir back to the efflux bulb was achieved by reducing the pressure in the efflux side of the instrument by diffusing hydrogen through a palladium-silver membrane, while keeping the separating valve closed. The liquid could not have
Table I. Typical Dimensions of the Cannon Master Viscometers Open Pressurized instrument instrument * Charge volume, V, cc 6.64 6.26 Efflux volume, V, cc 3.08 3.02 Total volume, cc n.d. 39.4 Mean head, h, cm 48.3 35.6 Capillary radius, r, cm 0.0165 0.012 Caoillarv 45.6 3 ~.~ 3.6 . . workine- leneth. -~~,/.,cm Lower reservoir radius, R, cm 1.5 1.5 Receiving side tube, i.d., cm 0.3 0.5 Instrument constant, C, cs/second X IO-' 11.8290 2.9823 Kinetic energy factor, E, cs second' 32 97 ~~~
158
ANALYTICAL CHEMISTRY
been raised in the viscometer by simple pressure release from the efflux side because of evaporation losses. Additional pressure increments on the receiving side would have led to the ultimate bursting of the instrument. Two sets of Cannon master viscometers were used to study the effect of pressure on the efflux time measured. Typical dimensions of the open and pressurized instruments are listed in Table I. The open instruments filled with water were used to measure viscosities at atmospheric pressure. The pressurized instruments were attached to the viscometer assembly, pressurized with hydrogen from 0 to 200 psig, and used for the same measurements. All measurements and calibrations were based on the viscosity value of 1.002 cp at 20" C, as the accepted primary standard (11) for water. Table I1 shows the experimental results of the measurements on water at 40", 60",and 15" C. Each viscosity measurement shown represents the average of six duplicate readings made in six different glass viscometers. The table also gives the standard deviation of a single determination for each set of data. A statistical t-test on the data sets at 0 and 100 psig and at 0 and 200 psig pressures, respectively, showed no significant difference between these data at a 95% confidence level. The results of the preliminary testing clearly indicated that the measured efflux times (viscosities) remained virtually (11) J. F. Swindells, J. R. Cce,and T. B. Godfrey, J . Res. Nut/. Bur. Std., 48,RP2279 (1952).
Table 11. Kinematic Viscosity of Water in Centistokes Measured at Atmospheric and at Elevated Pressures Open instrument Pressurized instrument Literature __ Temperature, O C 40" 6oo 40 O 75O 40" 60O 75 Pressure, psig Atmospheric 0.6517 0.4744 0.6582 ... 0. 6578a 0.4748 0.3889 0 . 6582b 0.4746 0.3886 100 ... ... 0.6578 0.3883 200 ... 0,6576 0.3882 Std dev. f0.0002 *d.'&l f0.0003 *0.0002 a Ref. 12. * Ref. 13.
unaffected by the pressure, up to 200 psig, and that the rate of hydrogen diffusion, even at 40" C, was adequate to raise the liquid in approximately 2 minutes in the closed pressurized viscometer. Following these tests the final version of the apparatus was built. Detailed Description of the Apparatus. Figure 1 shows the assembled apparatus with two separate glass viscometers. Figure 2 gives the details of the high temperature viscometer. (For simplicity only one half of the symmetrical arrangement is shown.) A specially built liquid-filled Cannon master glass capillary viscometer ( A ) (the pressurized instrument of Table I), with 470-mm overall length is secured into a metal support frame ( B ) by means of two screw clamps (C). The 0.375-inch 0.d. receiving, and the 0.25-inch capillary side glass tube endings of the viscometers are connected to a manifold and valve system with glass-to-metal O-ring fittings (D). The capillary side of the viscometer joins the housing of a palladium-silver coil membrane ( E ) ; then the line continues through a normally open air pressure-operated bellows valve (F). The loop between the two arms of the glass viscometer is closed through the T-fitting (G). The upper run of this T-fitting leads to a normally closed, air pressureoperated inlet valve ( H ) . Terminals of the lines are located on the panel ( I ) . The palladium-silver membrane housed in the coil holder ( E ) is a 1-foot long, 0.0625- by 0.003-inch wall, thickness tube, with one end closed. It is wound into a 1.5-inch high, 1-inch diameter coil. The open end is connected to the vacuum line through the terminal on panel ( I ) . Directly under the coil holder ( E ) , the line is branched out to receive a miniature strain gauge transducer housed in a liquid-proof adaptor ( K ) . With the help of the transducer and auxiliary equipment the internal pressure in the viscometer can be continuously monitored and recorded. All connecting tubing, fittings, valves, and parts in direct contact with the inner space of the viscometer are made of stainless steel. The entire assembly, supported by the frame (B), is submerged in an oil-filled thermostat bath where vertical alignment is made with the help of the adjusting screws ( J ) . The apparatus is completely surrounded with a transparent safety hood. The activation of valves, pressurization of the viscometers, and hydrogen diffusion are all controlled from a panel outside of the safety hood. The thermostat bath is a jacketed 10-gal glass tank, filled with polyphenyl ether (Monsanto OS- 124), and equipped with stirrer and electrical immersion heaters. The temperature is measured with calibrated mercury-in-glass thermometers (0.01 " C graduated) and maintained within i0.003" C precision, by means of a thermistor-based solid-state temperature controller. (12) P. M. Kampmeyer,J . Appl. Phys., 23,99 (1952). (13) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth, London, 1959, p. 457.
Procedure. Two Cannon master viscometers are inverted and filled at room temperature by immersing the efflux tube into the test liquid and applying moderate suction on the receiving side. When the liquid reaches the filling mark the suction is discontinued and the viscometer is returned to its upright position. The charged viscometers are attached to the assembly, and the unit is lowered into the thermostat bath. Respective hose connections are then made at the top panel terminals and the unit is aligned. In the next step, the viscometers are pressurized with hydrogen, by opening the air pressure-operated valve ( H ) , while leaving valve F open. Valve H is then closed and the bath with its contents is brought to test temperature. The test liquid is raised into the efflux bulb. This operation is achieved by closing the air pressure-operated valve F , thus separating the arms of the viscometer and allowing the hydrogen to diffuse through the palladium-silver coil from the capillary side of the viscometer. To increase the rate of diffusion, the pressure inside the diffusion coil is reduced by applying vacuum. As the hydrogen diffusion proceeds, the liquid gradually rises into the efflux bulb. Upon filling this bulb, the hydrogen diffusion is stopped by closing the vacuum line. The equilibrium through the membrane is attained shortly. The pressure in the two arms is then equalized by opening valve F, a pressure measurement is taken with the transducer, and the efflux time is measured. After the measurements at the lowest temperature of the series are completed, the temperature is raised to the next level and the efflux time is measured again by the repetition of the procedure described. VISCOSITY OF LIQUID WATER
Method. Water viscosities were measured in the opentype Cannon master viscometers a t atmospheric pressure between 25" and 60" C as described under preliminary testing. The pressurized apparatus was used for the measurements over 75" C, up t o 150' C. Double distilled Cos-free water was used throughout these tests. For calculation of viscosities from the measured efflux time, Equation 1, derived from the Poiseuille equation, was used in the form
where v
=
9
=
d C M
= =
I
E
= = =
kinematic viscosity, cs dynamic viscosity, cp density of liquid, gram/cc viscometer constant, cs/second combined factor for driving head corrections efflux time, seconds kinetic energy factor, cs. seconds2 VOL. 40, NO. 1, JANUARY 1968
159
Table III. Summary of Water Viscosity Correctionsa
3 d
Type of correction Temperature, XT Surface tension, X, Air column, X ,
Combined correction factor M M M M Kinetic energy correction Efflux time (approximate), seconds
=
Y
= CMt
- Et'
M = 1
+XT+
X,+
X.
Total test pressure, psig
40
60
50 100 150 200
-0.oooO7 0.00012 -0.00033 -0.00060 -0.00087 -0.00114
-0.00023 0.00025 -0.oOo40 -0.00065 -0.00091 -0.00116
50 100 150 200
0.9997 0.9994 0.9992 0.9989
0.9996 0.9994 0.9991 0.9989
0.9994 0.9991 0.9989 0.9986
0.9990 0.9988 0.9985 0.9983
0.9986 0.9984 0.9982 0.9980
0.9980 0.9978 0.9976 0.9973
0:9972 0.9970 0.9968
0:9966 0.9964 0.9962
0:9962 0.9960 0.9958
2200
1600
1300
1000
900
800
750
700
700
0
0
0
o.Ooo1
0,0001
0.0002
0.0002
0.0002
0.0002
Test temperature, T, " C 75 100 110 125 -0,00040 -0.00070 -0.O0090 -0.00120 0.00027 0.00053 0.00061 0.00072 -0.00050 -0.00084 -0.00106 -0.00153 -0.00074 -0.00107 -0.00129 -0.00175 -0.00099 -0.00131 -0.00152 -0.00197 -0.00124 -0.00154 -0.00175 -0.00220
135 145 150 -0.00140 -0,00160 -0.00170 0.00082 0.00089 0.00094 -0:&217 -0:&270 -0.'&301 -0.00239 -0.00292 -0.00323 -0.00261 -0.00313 -0.00344
Corrections are related to the high temperature viscometer assembly described, with Cannon master viscometers in the right column of Table I.
The value of the instrument constant, C, was determined by calibration with water. The kinetic energy factor E was calculated as recommended by Cannon and Manning (14) :
T = measurement temperature, "C T, = calibration temperature, "C Air column correction:
X4 = 0.001179 - 1.00118d4 di
where V = efflux volume, cc I = length of working capillary, cm r = radius of the capillary, cm
where d, and dl are the densities of the air (gas) and liquid, respectively, at the measurement conditions. Surface tension correction :
The combined correction factor, M , as suggested by Hardy (15) can be expressed as:
M
=
1
+ XT + X4 + Ky
(3)
The individual corrections encompassed in Equation 3 are listed below. Correction for the temperature of the run:
where
* V
= charge volume, cc
R
=
h CY
= mean head of liquid, cm = cubical thermal expansion coefficient of the
fl
= cubical thermal expansion coefficient of glass,
e
= linear thermal expansion coefficient
radius of the lower reservoir, cm liquid, "C-l
"C-1
"c-'
of glass,
(14) M.R.Cannon, R. E. Manning, and J. D. Dell, ANAL.CHEM., 32,355 (1960). (15) R. C. Hardy, Natl. Bur. Std. Monograph 55 (Dec. 26,1962). 160
a
ANALYTICAL CHEMISTRY
(5)
x, = 0.1235 -h0.8346a 2
(6) (7)
where 2 = surface tension of the liquid, dynes/cm g = acceleration due to gravity, cm/second2 In calculating the air column correction for the open instruments, densities of moist air with dew points 5" C below the test temperature were used, because the exact degree of saturation was not known. For the pressurized instruments the partial pressures of hydrogen, air, and water vapor were calculated at each test temperature, and gas densities related to the respective partial pressures were used. Numerical values of the corrections applied at various temperature and pressure levels are listed in Table 111. The measured and corrected water viscosities are reported in the first column of Table IV. The standard deviation of a single measurement over 75 O C at the 95 confidence level was calculated to be +0.19 Correlation of Results. To facilitate the interpolation of the measured data, the correlation given in "Report to the
z.
z
Comparison of Experimental and Correlated Water Viscosity Data in CP (i =z 1.0020) o
Table IV.
z
Temp, “C 20 25 40 60 75 100 110 125 135 145 150 a
Exptl 1.0020 0.8903 0.6527 0.4665 0.3784 0.2820 0.2548 0.2219 0.2040 0.1884 0.1815
(12)
(9) 1.0020 0.89550 0.6531 0.4665 0.37880 0.2822 0.2549 0.2220
1.0020 0.8904 0.6527 0,4669 0.3792 0.2840
(13) 1.0020 0.8903 0.6531 0,4666 0.3788 0.2829
(17) 1.0018 0.8904 0.6510 0.4630 0.3740 0.2790 0.2520 0.2200 0.2030 0.1880 0.1810
(19)
(18)
1.0020 0.8890 0.6493 0.4668 0.3781 0.28% 0.254 0.2210 0.2020 0.189~ 0.183
Interpolated between closest available data by formula log 7
1.002 0.899 0.653 0.466 0.381~ 0.282
(21)
1.002 0.883
0.654 0.467 0.375~ 0.282 0.2811
=
B + T+C
I
I
(0) (+O. 26)
(t-0.49) (+0.24) (-0.08) (-0.18) (-0.16) (- 0.09) (0)
(+O. 16) (f0.22) (*O. 17)
The constants of Equation 8 were calculated by the method of least squares. Higher weight was assigned to the reference value of 1.0020 cp at 20’ C. The numerical values of the constants compared with those calculated by Kestin and Whitelaw (17) are presented in Table V. It must be mentioned that Kestin and Whitelaw used this correlation over the 0’ to 300’ C temperature range, even though only five experimental data points were available over 100’ C. The authors recommended a tolerance of +2.5 %. The measured and correlated water viscosities along with the generally used reference data from the literature are listed in Table IV for comparison. The data were reduced
Constants of Equation 8 Present correlation - 1.64779 262.37 - 133.98
A B C
Kestin & Whitelaw (17) - 1.6173 247.8 -140.0
O t
I
20
40
0
60 80 Temperature,’C
(1)
A(9)
(4)
D(7)
our data
(See Table
I
I
120
140
.(lo)
+ (6)
x (5) 0
100
(8)
A (2) 0 (3) (3
Y
Figure 3. Deviation of experimental viscosity data from calculated data by Equation 8 (16) Report of the U. S. Commission on the Properties of Steam to the 2nd Formal Meeting of the International Coordinating Committee, Munich, Germany, 1962. (17) J. Kestin and J. H. Whitelaw, Trans. Am. SOC.Mech. Ennrs., . 88,82 (1966). (18) International Critical Tables, Vol. V, McGraw-Hill, 1929, p. 10. (19) Landolt-Bornstein, “Zahlenwerte and Functionen,” 6th ed., Vol. IV, Part 1, Springer-Verlag, Berlin, 1955, p. 613. (20) J. R. Moszynski, J. Heat Transfer, 83, 111 (1961). (21) A. Jaumotte, Reo. Unicerselle Mines, 7,213 (1951). (22) E. C. Bingham, Bull. Bur. Std., 14,59 (1918). (23) J. F. Swindells, unpublished measurement, quoted in J . Res. Natl. Bur. Std., 48, 1 (1952). ’
Calcd 1.0020 0.8926 0.6559 0.4676 0.3781 0.2815 0.2544 0.2217 0.2040 0.1887 0.1819
A 3. BIT.
Table V.
I
(23)
1.0020 0,8903 0.6526 0.4666
0.1848
where Tis given in OK.
-0.6
(22)
1.0020 0.8910 0.6535 0.4712 0.3781
0,2266
U. S. Commission on the Properties of Steam” (16, 17) was used : log7 = A
(20)
Dev between calcd and exptl data
Table VI.
Recommended Water Viscosities, in Centipoises, for the Temperature Range of 20-150’ C OC
CP 1.0020a 0. 8903b 0. 6527b 0. 4665b 0.4045 0. 3784b 0.3546 0.3143 0.2820b 0.2548 0.2317 0.2219b 0.2125 0.2040b 0.1961 0. 1884b 0. 1815b
20 25 40 60
70 15 80
90 100
110 120 125 130 135 140 145 150 Reference value: 1.0020 cp at 20’ C. Experimental values.
VOL 40, NO. 1, JANUARY 1968
161
to 1.002 cp, common basis at 20" C. The last column of the table gives the per cent deviation (in parentheses) between our measured and calculated data. The correlation represents the data with an average deviation of *0,17%, and with a maximum deviation of 0.49% at 40" C. It is interesting to note that Kampmeyer (12) also found the largest deviation from a similar correlation at approximately the same temperature. The fit was very satisfactory at higher temperatures where the literature data are most controversial. The excellent agreement of our data, up to 125" C, with the measurements of Hardy at the National Bureau of Standards is encouraging. The new correlation represents all tabulated reference data with an average deviation of k 0.0018 cp. Figure 3 shows a deviation plot of the data given in Table IV from the correlation. The correlation represented by the zero line is centered between the experimental data, while the correlation given by Kestin and Whitelaw, which is represented by the dotted line, remains consistently on the low side. Finally, Table VI lists the recommended water viscosity
values over the entire temperature range. Whenever experimental values were available, those were entered in the table, In reviewing the paper, R. E. Manning recommended the use of the following equation for interpolation: ?p40 log =
A(t
- 20)
+ B(t - 20)2
9 C+t where A = 1.37023, B = 0.000836, C = 109, t
=
"C.
This correlation represents the experimental data within f 0.05% average deviation. ACKNOWLEDGMENT
The authors thank A. S. Borsanyi for his help in the development of the apparatus. Viscosity measurements were made by T. R. Middleton.
RECEIVED for review June 8, 1967. Accepted September 18, 1967. Work sponsored by the Office of Saline Water, U. S. Department of Interior.
Study of Cerium(1V)-Thallium(1) Reaction and Analysis of Thallium(1) Mixtures by Kinetic Differences George H. Schenk and William E. Bazzelle Department of Chemistry, W a y n e State University, Detroit, Mich. 48202
The uncatalyzed cerium(lV)-thallium(1) reaction in 0.125M sulfuric acid exhibits an extremely slow but measurable rate in the dark, while in room light, the rate of disappearance of cerium(lV) increases, presumably because of thallium(1)-catalyzed photoreduction. Catalysis by manganese(ll1) was so effective that photometric titration of thallium(1) with cerium (IV) titrant was possible. Two types of thallium(1)metal ion mixtures can be analyzed on the basis of kinetic differences alone. In the first type, metal ions such as iron(l1) react rapidly with the cerium(lV) titrant in the absence of catalyst before thallium(1) reacts significantly. Then the catalyst is added and the thallium(1) i s titrated with cerium(1V). In the second type of mixture, the catalyst is added at the start, and thallium(1) reacts rapidly with the cerium(lV) titrant before the other metal ions or reducing agents react significantly. The reducing agents studied were mercu ry( I), a rsen ic( I I I), and ch romi um( I II). Theoretical calculations indicate the reactions of these substances with cerium(lV) should be negligible, but weakcatalysis by manganese(ll1) apparently causes significant reaction above equivalent concentrations.
THAT OXIDATION-REDUCTION reactions involving the exchange of unequal numbers of electrons (and little structural change) tend to be slow has often been postulated (1, 2 ) . A survey of this type of reaction involving cerium(1V) in sulfuric acid (Table I) provides a useful test of this postulate. There is a fairly large spread in the magnitude of the rate constants, but only the cerium(1V)-uranium(1V) reaction appears to be rapid at high (0.1M) concentrations. For analytical (1) P. A. Shaffer, J . Am. Chem. SOC.,55, 2169 (1933) and J. Phys. Chem., 40, 1021 (1936). (2) J. Halpern, Can. J . Chem., 37, 148 (1959).
162
ANALYTICAL CHEMISTRY
purposes, all of the reactions in Table I are run at high temperatures, with catalysts, or in hydrochloric acid solvent. None of the reactions are as rapid as the cerium(1V)-iron(I1) reaction which has a rate constant of about 10GM-'set-1 in 0.5M sulfuric acid (3). An even slower reaction than those listed in Table I is the cerium(1V)-thallium(1) reaction. It has a complex rate law in 6.18M nitric acid ( 4 ) with rate constants of k l = 0.055 hr-1 and kz = 1.221V-~ hr-I at 54" C. No one has studied the uncatalyzed reaction in sulfuric acid although Shaffer (1) reported qualitatively that no reaction is observed. Photoreduction of cerium(1V) in sulfuric acid is slow compared to other acids, but Sworski ( 5 ) reported that thallium(1) enhances the rate of photoreduction. Because other potential interferences, such as those in Table I, react slowly with cerium(1V) in sulfuric acid, it is of interest to study the uncatalyzed reaction and to investigate catalysts for the purpose of determining thallium(1) by titration with cerium(1V) in sulfuric acid. Historically, of course, thallium(1) has been determined with numerous oxidizing agents. Koreman (6) has summarized the gravimetric and titrimetric methods (7-10) which do not involve cerium(1V).
(3) G . Dulz and N. Sutin, Inorg. Chem., 2,917 (1963). (4) M. K. Dorfman and J. W. Gryder, Ibid.,1,799 (1962). (5) T. J. Sworski, J. Am. Chem. SOC.,79,3655 (1957). (6) I. M. Koreman, "Analytical Chemistry of Thallium," Daniel Davey and Co., Inc., New York, 1960, pp. 76-84. (7) A. J. Berry, Analyst, 51, 137 (1926). (8) G. S. Deshmukh, Anal. Chim. Acta, 12, 319 (1955). (9) E. Rother and G . Jander, Z . Aneu. Chem., 43,930 (1930). (10) C. D. Fresno and J. Valdes, Z . Anorg. Allgen. Chem., 183, 258 (1929).
