Sq ua re Wave Titri met ry H. A.
LAITINEN and LARRY C. HALL’
Noyes Chemica! laboratory, University o f Illinois, Urbana, 111.
Square wave titrimetry has been applied to redox, precipitation, and complex formation reactions. Iodinearsenite, ferrous-cerium(IV), and ferrocyanide-cerium(lV) reactions gave successful titrations. Equimolar mixtures of iodide, bromide, and chloride were titrated with silver nitrate to yield three successive end points. Cyanide can be titrated to silver(!) cyanide complex in the presence of ammonia.
T
wo
METHODS of electrometric end point detection are fundamentally based upon the measurement of the slope of the current-voltage curve in the zero current region. The first method, introduced by Willard and Fenwick (47) and modified and extended by several recent workers (2, 7 , 15-15, 40) involves potentiometry a t constant current. The other method, commonly called the “dead stop” titration after Foulk and Bawden (11), involves the measurement of current passing between two indicator electrodes a t a small constant applied potential and dates back t o Salomon (42). I t has been thoroughly studied by several investigators (5, 5, 18, 25, 5.9, 44) and the principle explained in terms of polarization and depolarization. Kolthoff (26) and Duyckaerts (8) have recently given excellent comparisons between various closely related techniques. The object of the present investigation was to study the alternating current analogs of the two direct current methods, by applying to a pair of microelectrodes a square wave signal of constant current or voltage amplitude and measuring the voltage or current output during the course of a titration. Franck (1.9) recently described “POlarization titrations” which involved the application of a sinusoidal voltage of low frequency through a large resistance to a pair of microelectrodes in solution. The alternating voltage between one of the microelectrodes and a third electrode was measured as a function of the volume of reagent zdded. I n this method. a limitation is the relatively large charging current due t o the double layer capacity associated with 1 Present address, Department of Chemistry, Vanderbilt University, Nashville, Tenn.
1390
ANALYTICAL CHEMISTRY
the electrodes even in the absence of electrode reactions. In the present method, a square wave alternating signal is used. By proper adjustment of the experimental variables in such a way that the charging current occurs as a pulse at the beginning of each half cycle, and that the meter does not respond t o the charging pulse, s n improvement over the sine wave method should result in principle. Square wave applied signals generated by means of motor-driven commutator switches (20, 82) or electronic circuits (1, 10) have been used in polarographs but apparently not in titrimetry. THEORETICAL
The two square wave methods (constant potential and constant current) applied to a pair of identical electrodes both yield a measure of the slope of the current-voltage curve in the zero current region, and in fact are recipro-
.-0 n
a1
cally related, provided that three conditions are fulfilled. These are as follows: The amplitude of the applied signal should be small enough so that the current-voltage curve may be regarded as linear in the zero current region. The charging pulse should be of very short duration compared with the alternating current cycle. A steady state should be reached in a small fraction of the alternating current cycle.
Charging Pulse. For a supporting electrolyte involving no electrode reactions, the duration of the charging pulse can be estimated from the RC constant, taken as the product of the solution resistance and double layer capacity. Taking 100 ohms as the cell resistance, 0.1 square cm. as the area of each electrode, and 100 pf. per square cm. of geometric area as the double layer capacity, the RC value
-
1500-
-
-0
W
LL
0 1200Ld
3 1 Q
’ W
Lc
5
w K
-
900-
600-
3 00-
R E L A T I V E CONCN. OF O X I D A N T Figure 1. Theoretical responses for reversible case of oxidant and reductant in solution
See Equation 1
is 5 X second. This corresponds to charging the double layer to 99% of its final charge in 10% of each half cycle of a 20-C.P.S.square wave signal. Clearly, the cell resistance must be minimized, and a relatively low square wave frequency must be used, The simplest method of applying a constant current square wave-i.e., applying a signal of high voltage through a high resistance-is thus a t once eliminated from practical consideration. For this reason, only the constant voltage method was applied in the present investigation. An applied signal of 20 to 50 mv., while compromising with the linearity of the current-voltage curve, was used to permit the use of simple measuring equipment. The presence of a reversible potentialdetermining system in appreciable concentrations causes the appearance of a relatively large effective capacitance [pseudocapacity (17) 1, which causes the charging pulse to be slow, particularly a t regions far removed from the end point of a titration curve. By using an oscilloscope as a detector, the charging pulse can be ignored unless it persists to the end of the square wave cycle. If the charging pulse can be
kept sharp (of the order of 1% of each half cycle), an alternating current voltmeter does not respond to the charging pulse. Attainment of Steady State. Owing to the cyclic character of the applied square wave voltage, reproducible values of current can be achieved even if steady state conditions are not reached during each half cycle. However, the current-time relationship is not mathematically simple ($3, 4 4 . If steady state conditions are rapidly reached, simple direct current theory can be applied to calculate the change of slope of the current-voltage curve in the zero current region during the course of the titration. At first thought it would seem necessary to have extremely rapid mass transfer processes (convection control) to reach a steady state in a time interval of the order of a millisecond. This is indeed true for the limiting current region where the mass transfer rate is the current controlling process (21, 29). However, a t small applied voltages, the current is controlled by the electron transfer rate even for a relatively rapid reversible process a t low concentrations
of reactants. Consequently, the stirring rate has practically no effect on the rate a t attainment of the steady state. Theoretical Response. For a reversible process the exchange current density a t equilibrium is large compared with the limiting cathodic and anodic current densities, and the slope of the current-voltage curve in the zero current region can be written
(6,8, 41) nFKt
[Ox][Redl
where [Ox]and [Red] are the concentrations of oxidant and reductant and K t is the transport process constant, or the proportionality constant between limiting current and concentration. For a diffusion controlled process, K c depends on the diffusion coefficients of oxidant and reductant (here assumed to be equal) (35). For convective control, K t depends on the convection coefficient (61, 29), For a totally irreversible process, the analogous expression can be readily derived by differentiating the currentvoltage relationship (6, 8, 9, 16, 46) to yield
n 2 F 2 A K h[Ox]1--or [Redla (2) RT
where A is the area (square cm.), K i is the heterogeneous rate constant (cm. sec.-1) a t the formal potential, where [Ox] = [Red], and a! is the transfer coefficient for the cathodic reaction. For a process in which the current is controlled partly by the rate of electron transfer and partly by mass transfer, the electron transfer rate may be written in terms of the surface concentrations of oxidant and reductant, which are determined by the mass transfer coefficient. The resulting equation is (8)
[Ox1 [Redl [Ox] Kt[Ox]l-. [Red].
+
+ [Redl
(3)
Depending upon the magnitudes of
K h and K t , various shapes of response
POTENTIAL IN
mv.
FROM E e q
Figure 2. Effect of stirring on rate of electrode process with Kh = cm. sec.-l
A . No stirring B. i 1 = 20 ma. per square cm. C. i l = 4 ma. per square cm. D. i l = 2 ma. per square cm. [Ox] = 10-7 mole mL-7; [Red] = 10-4 mole m1,-1; temp. = 25' C.; na = 1.0
curves can be calculated (19) for the various regions of titration curves. Only one example, for the reversible case, will be given here (Figure 1). calculated from Equation 1 and its reciprocal. The constant potential method gives (Ai/AE){-o, while the constant current method gives (AE/A.i)i-o. As pointed out above, the latter quantity cannot readily be observed experimentally, but it can be calculated from reciprocals of the values from the constant potential method. The reciprocal method gives a response analogous to a potentioVOL. 2 9 , NO. 10, OCTOBER 1957
1391
metric end point, whereas the direct method is more nearly analogous to an amperometric end point. If the reagent is electrochemically irreversible, the response beyond the end point will remain constant a t the levels PI or Pz in Figure 1. Curves similar to Figure 1 have been reported for amperometry a t constant potential, using the directi current method (8, 24, 25, 40, &, 48). The effect of stirring is shown by the theoretical curves in Figure 2, considering the combined effects of mass transfer and electron transfer rate (M),and cm. set.-'. Various taking Kh = values of K t , corresponding to different rates of stirring, give corresponding limiting current density values. It should be noted that for small values of the applied potential, the current is insensitive to stirring. EXPERIMENTAL
Apparatus. B Heathkit Model SQ1 square ware generator was provided with an attenuator which could be turned off t o provide unmodified square wave signals (up to 55 volts), or adjusted to give small signals (down t o 1 mv.). For preliminary work, the output was calibrated by means of a DuMont 304 H. oscilloscope. For routine work, square wave voltages were read on a Heathkit Model AV-2 alternating current voltmeter calibrated against a Tektronix Type 531 oscilloscope. Provision was made to measure the voltage drop across a standard decade resistor (iR1in the text) as a measure of the current, and the voltage across the terminals of the cell. Most of the measurements were made with a constant applied voltage, thus determining ( A ~ / A E ) ~ -A, few measurements were made at constant current, using a large resistor in series with the cell and a large voltage from the signal generator. Current-voltage curves were recorded on a Leeds & Northrup Electrochemograph with a polarization rate of 3.3 mv. per second, or a Sargent Model XXI Polarograph with a polarization rate of 2.5 mv. per second. The electrolysis cell was a 300-ml. lipless beaker. Two platinum microelectrodes, one of which could be rotated, mere mounted in a No. 13 rubber stopper. The stopper was drilled to provide for a gas inlet tube, a buret tip, a salt bridge for a saturated calomel reference electrode, and an auxiliary stirrer. The stirrer had four glass blades, each approximately 1 cm. long and 0.8 cm. wide, with provision for rotation a t 1200 r.p.m. =t 10%. The platinum electrodes were constructed of No. 26 platinum wire, 5 mm. long, sealed into soft glass tubing and carefully annealed a t the wire-glass interface to prevent large and erratic residual currents (90). The tips of the wires were fused to produce a smooth, rounded end (49). The projected area of each electrode was estimated to be 0.067 square cm. Silver electrodes were prepared by
1392
ANALYTICAL CHEMISTRY
sealing KO. 26 gage silver wire into soft glass so that 1 cm. of the wire was exposed to the solution. The resistance across a pair of silver electrodes in a typical titration solution was 55 ohms. A gas train was provided so that nitrogen could be passed through an iodine solution and then over the solution in the cell to avoid loss of iodine by volatilization during stirring. Solutions. All solutions mere prepared from reagent grade chemicals and deionized water that had been boiled to ensure the absence of ammonia, carbon dioxide, and chlorine. Stock iodine solutions were standardized weekly against arsenite. Dilute iodine solutions were prepared for individual experiments by adding stock triiodide t o a solution which contained 2.5 grams of potassium iodide and 1.0 gram of sodium bicarbonate in a final volume of 150 ml. As dilute iodine solutions cannot be made accurately by dilution of a stock solution (4, 28),the final solutions were standardized amperometrically, using a rotating platinum electrode a t a potential of 0.0 volt (us. S.C.E.) as an indicator electrode. Before each titration the indicator electrode was polarized cathodically in 0.1M perchloric acid (see below). Ferrous ammonium sulfate was checked against cerium(1V) sulfate
and dichromate; ferrocyanide was standardized daily with cerium(1V) sulfate. Chloride, bromine, and iodide solutions were standardized against silver nitrate prepared determinately, using dichlorofluorescein, eosin, and Volhard procedures, respectively. Cyanide was standardized with silver nitrate using the Liebig-DenigBs method. PRELIMINARY OBSERVATIONS
Preliminary studies were carried out with the iodine-iodide system, which behaves reversibly (28, 29) a t a platinum surface. The behavior of 10+M iodine in 0.1M potassium iodide buffered with sodium bicarbonate differed markedly depending on the pretreatment of the electrodes. In Figure 3 the results of several electrode treatments are shown. Anodization and cathodization were accomplished by connecting the microelectrode and a larger platinum electrode across the terminals of a 3-volt direct current source. Upon cathodization in 0.1M perchloric acid, the behavior became more nearly reversible. In all subsequent experiments with iodine the cathodization treatment was used. The sensitivities of the platinum
12.0-
I
9.0In
a
I
-
i
6
x
1
0
5 6.0-
-z I-
z W
-
K
c
3 U 3.0-
POTENTIAL VS S . C E.
Figure 3. solution
Effect of electrode treatment for
lou5M iodine
A . Cathodized in 0.lM HClOl B. Soaked in 10% NaCN for 2 hours C. Anodized in O.IM HC104 D. Residual current Rotating platinum electrode used at 1000 r.p.m.; curves recorded automatically with polarization rate of 3.3 mv. per second
A
'"4 ,
I
I
C
1.
Table
Platinum Electrode Sensitivities
(lo-4M iodine in 150 ml. of O.1M potassium iodide and sodium bicarbonate. Currents read at 0.0 volt us. S.C.E.) Sensitivit , Pa.7 Equiv. per Liter Electrode@ Stirring x 103 RPE 1000 r.p.m. 50 RPE 600 r.p.m. plus aux. stirrer a t 1200 r.p.m. 1086 SPE Aux. stirrer a t 1200 r.p.m. 52 a RPE = rotating platinum electrode, SPE = stationary platinum electrode. b Convection control was obtained ( 2 1 , 99).
Table II.
Mmoles of I2
2.92 X
1.954 X 1.704 X
lo-'
electrodes with various combinations of stirring are shown in Table I. By varying the experimental conditions (applied e.m.f., current measuring resistor R,, frequency, stirring rate), a number of conclusions were reached which will be briefly mentioned here; the details are given elsewhere (19). For small applied signals, the same response was obtained with moderate stirring (magnetic stirrer) as with violent stirring, using both the rotating electrode and the auxiliary stirrer. Departure from square wave character increased with increasing R1, the applied e.m.f., or the frequency. When R1 was 100 ohms, the applied e.m.f. was 20 mv., and the frequency was 20 c.P.s., the charging pulse was a sharp peak a t the beginning of each half cycle. As R1 was increased to 500 or 1000
D
Figure 5. Effect of iodine concentration
f = 20 c.P.s.; R1 = 1000 ohms; EapPl,= 30 mv., c,onstant; solution volrime, 150 ml. A , B. Eappl, and iR1 when IP = 3.86 X loF2 yes. ( , D. and iR1 when IZ = 1.93 X lo-' meq.
ohms, or the applied e.m.f. was increased to 50 mv., or the frequency was increased beyond 20 c.P.s., the trace lost more and more of its square wave character.
Square Wave Titration at Constant Potential of Iodine with Arsenite (R1 = 1000 ohms, EBpp~. = 30 mv., andf = 20 c.p.e.)
Approx. Molarity of I2 2 x 10-4
Normality of As( 111)
1.02 x 10-2
1.3 x 10-4
4.98 X
1.1 x 10-6
5.00
a
20 mv. signal used; not constant.
c
R,
x 10-4
Square Wave End Point (MI.) 5.75, 5.75,, 5.85, 5.80, 5.75a 5.80, 5.75, 5.75, 5.75 5.80, 5.75, 5.75, 5.75b 7.79, 7.80, 7.80, 7. 85c 6.80, 6.80, 6.85, 6.80
AmperoStd. Dev. metric End from Mean Point (MI.) (Ml.) 5.75 0.04
Dev. of
h 6 a n from
Amp. End Point (%) +0.52
5.75
0.025
+ O . 17
5.75
0.025
1-0.17
7.85
0.037
-0.38
6.82
0.025
0.00
* Oscilloscope used to detect end point. =
500 ohms.
VOL. 29, NO. 10, OCTOBER 1957
1393
Table 111.
Square Wave Titration of Iodine with Arsenic(ll1) at Constant Current (f = 20 C.P.S.)
Approx. Mmoles Molarity of I2 of I2 1.932 X 10-8 1 . 3 X 10-4
of As( 111) 4.98 X 10-3
1.58 x lo-*
5 00
1 . 1 x 10-6
Normality
x
lo-'
A practical demonstration of the effect of frequency is shown in Figure 4. The applied e.m.f. across the cell was kept constant a t 20 mv.; the potential drop across R1 (500 ohms) was measured with the alternating current voltmeter, using iodine-iodide (a reversible system) and arsenate-arsenite (an irreversible system). As the frequency is increased, the charging pulse occupies a greater fraction of the square wave cycle, and the meter responds increasingly to the charging pulse, until a t frequencies beyond 1000 C.P.S. both systems are giving practically a pure charging response. At low frequencies the meter does not respond t o a rapid charging pulse, so that the response current is due to the electrode reactions, and a large difference exists between the two systems. Another effect is that the iR drop within the solution includes that due to charging current, so that the actual difference of potential corrected for internal iR drop is decreasing as the frequency is increased. The internal cell resistance was of the order of 150 ohms in the experiments cited. Another practical consideration is that, even with relatively large values of R1, the applied e.m.f. approaches a square wave character and the current approaches a steady state rapidly when the iodine concentration becomes very low, as in the vicinity of the end point. This behavior is illustrated in Figure 5.
Experimental Conditions R1 2. Eout (ohms) (pa.) 1.2 volts 1 meg. 1.0 100 mv.
300 kilo
Ampero- Std. Dev. of metric Dev. Mean from End from Amp. End Point Mean Point (M1.) (MI.) (7%) 7.76 0.016 -0.26
Square WaveEnd Point (Ml.) 7 . 7 5 , 7.72, 7.73, 7.76 6.35, 6 33, 6.30, 6.30, 6.30
0.4
6.32
0.023
-0.16
31
26t\
A \
22
I-
-30 Z W
a: U
U -202
0 m I .
L
-10 ij
I
I
I
l
I.o
I
2.0
I
l
,
1
1
3.0 4.0 VOLUME OF A s (Ill)
!
1
5.0 6.0 ADDED I N M L
70
Figure 6.
Comparison of square wave and amperometric titrations of 2 X 10-4M iodine with arsenic(ll1)
A . Square wave a t constant applied potential B. Amperometric
e4
I
I
I
I
I
I
1
I
I
I
ANALYTICAL APPLICATIONS
Titration of Iodine. Table I1 gives the results of a series of square wave titrations a t constant applied potential for various initial iodine concentrations. I n Figure 6 a typical square wave titration curve is compared with a n amperometric curve. Solutions more dilute than 10+M were not tried because the amperometric method failed a t these concentrations. A lower pH (5 to 6) than was used for Table I1 probably would extend the range to 1OU6M. The magnitude of the change in current around the region of the end point was greater for the square wave method than for the amperometric method. It is estimated that the square wave technique should be 10 times more sensitive 1394
ANALYTICAL CHEMISTRY
I Figure 7. method
I
1.0
I
4.0 5.0 6.0 VOLUME OF AS (Ill) ADDED IN ML.
2.0
3.0
Titration of 1.3
I
7.o
, 80
X lO-'M iodine with arsenic(ll1) by constant current
Amperometric end point, 7.76 ml.
A . 6.70 ml. (11.0 pa.) B. 7.50 ml. 2.6 pa.) C. 7.76 ml. il.0 pa.)
Table IV.
Titrations of Dilute Iron(ll) Solutions at Constant Current and Constant Potential
(10 nil. of 0.1OOO.V ferrous ammonium sulfate or 10 ml. of 0.0507N ferrocyanide with 0.1000N potassium dichromate and 0.0857N cerium(IV) sulfate; final volume was 150 ml. whlch was 0.2N in chloride and sulfuric acid)
Solution Ferrous ammonium sulfate
Titrant Dichromate
Method Const. i5
Ce( IV) sulfate Ferrocyanide 5
*
Rs E,
Ce( IV) sulfate
Theoretical Std. Dev. End Point from Mean (MI.) (iczl.) 10.00 0.037
Dev. of Mean
(%I
Const. Eb
Square Wave 9.97, 9.90, 10.00, 9.97, 9.95 9.95, 9.97, 9.97,
10.00
0.021
+o. 1
Const. i Const. E Const. i Const. E
10.00 11.70, 11.72, 11.70
11.67
0.012
11.63, 11.65, 11.67 5.90, 5.95, 5.95 5.95, 5.92, 6.00
11.67 5.92 5.92
0.016
$0.34 -0.43
0.029 0.058
-0.4
+ O . 17 +1.18
= 1 megohm, Eout= 2.4 volts,f = 20 c.p.5. = 1000 ohm, EapPl.= 30 mv., f = 20 c.p.s.
to dilute solutions than the amperometric method. Table I11 gives the results of titrations of two dilute iodine solutions using
the constant current method. The choice of current was critical (Figure 7). When the current was too large, as in curves A and B, the end point came
Figure 8. Current-voltage polarization curves in O.2M potassium chloride and 0.2N sulfuric acid
A . 5 X 10-aNcerium(1V) sulfate B. 5 X 10-aN cerium(1V) and cerium(II1) sulfate C. 5 x 10-SN cerium(II1) sulfate D. 5 X 10+N ferricyanide, cerium(IV), cerium(II1) E. 5 x 10-aN ferricyanide and 8 ferrocyanide with electrode anodized in
0.1M perchloric acid F. Same as E but with cathodic Dolarization as pretreatment G . 5 X 10-8N ferrocyanide All curves recorded on Sargent XXI polarograph; rotating platinum electrode driven a t 1000 r.p.m.
early. The fact that a very small current must be passed for low concentrations places a serious limitation on the constant current method because the change in applied e.m.f. becomes small. Titration of Ferrocyanide. Figure 8 shows a series of polarization curves which were obtained with a rotating platinum electrode for various concentrations of ferro- and ferricyanide and cerium(II1)-cerium(1V) in a supporting electrolyte of 0.2N potassium chloride and sulfuric acid. None of the curves are reversible in the polarographic sense (SI), although in concentrated chloride, the iron(II1)-iron(I1) couple is nearly so (35, 39). However, the slopes of the curves do change at the null potential. All of the curves except E were o b tained after the platinum microelectrode had been cathodically polarized in 0.1M perchloric acid. A pretreatment of anodic polarization (curve E ) made the ferri-ferrocyanide couple more irreversible, which is not what Laitinen and Kolthoff (35) found in a potassium chloride medium. Table I V gives the results of titrations carried out at constant potential and constant current for dilute solutions of iron(I1) present as ferrous ammonium sulfate or ferrocyanide. Figure 9 shows some titration curves for the reaction between ferrous ammonium sulfate and cerium(1V) sulfate. Curves A and B, which represent the constant current and applied voltage methods, respectively, compare favorably with the theoretical curves given in Figure 1. Curve C is a graph of the reciprocal values of B. The advantage of this procedure is that one obtains a measure of the constant current method when the square wave is not being distorted by a large value of the electrode eapacity and external resistance. Curve D was obtained when the electrodes were anodically pretreated and its poor response is borne out by curve E VOL. 2 9 , NO. 10, OCTOBER 1957
1395
of Figure 8. None of the titrations showed reversible behavior beyond the end point. Titration of Chloride, Bromide, Iodide, and Cyanide. Recently, Masten and Stone (36) titrated chloride, bromide, and iodide alone and as mixtures with the dead stop method, in which they applied a voltage of 10 mv. t o two silver electrodes. For the titration of a mixture of chloride, bromide, and iodide they obtained three peakshaped curves in succession when current was plotted vs. milliliters of silver nitrate added. The authors suggested that there m s enough silver halide adsorbed on the cathode so that it was reduced to silver, while a t the anode silver was oxidized to silver(1). They concluded that the current was limited by the adsorption of silver halide up to the midpoint of the titration and that the halide ion limited the current during the remainder of the titration. Earlier, Bradbury (3) had suggested that chloride might be titrated with silver nitrate using silver-silver chloride electrodes. He postulated that the theoretical treatment of the dead stop method for this system would be identical to that of the ferrous-ferric and cerous-ceric systems if the following reactions proceeded reversibly: Ag -+ A g + e- (anode) AgCl eAg C1- (cathode)
+
+
-f
>
IS
a
f i a
4
W
n lo
z 4
-
tx
._
2
0
4 6 VOLUME OF Ce
8
10
(H) ADDED
12
IN ML.
Figure 9. Titration of 10 ml. of 0.1000N ferrous ammonium sulfate with 0.0857N cerium(lV) sulfate A . Constant current method: R2 = 1 megohm, Eout =
2.4 volts, f = 20 c.p.5. B . Constant potential method: RI = 1000ohms, EaPpi. = 30 mv.,f = 20 c.p.5. C. Reciprocal of B D. Same as B except electrodes anodically pretreated
+
Titration of Chloride, Bromide, Iodide, and Cyanide with 0.1 OOON Silver Nitrate at Constant Applied Potential varied from (Halide and cyanide concentrations approlrimat,ely 6.7 X IO-SM except where noted. R1 varied from 100 to 500 ohms; EaPpi. 20 to 35 mv.: f = 20 c.D.s.) - . Theoretical Av. Dev. Titration Square Wave End Points End Points Std. Dev. from Mean, No. Solution Composition Species Titrated (M1.1 (MI.) (Ml.) % 0.038 -0.10 10.00 10.04, 10.01, 9.97, 9.96 0.013 -0.20 10.00 9.95, 9.97, 9.97, 9.98 0.014 0.0 10.57 10.55. 10.58. 10.57. 10.58 (0.036) +1.2 10.00 io. i5, -10.io (0.00) 0.0 20.00 20.00, 20.00 +4.0 . . . 10.40 BrC1-, Br-, no KNOJ + O . 15 20.03 c1+0.70 ( 0 :Oi4) 10.06, 10.08 BrC1-, Br-, A~(NOI)P +0.10 (0.014) 20.03, 20.01 c1+1.0 0.025 10.00 10.12. 10.10. 10.07 BrC1-, Br-, KNO,, +o. 12 0,012 20.00 20.03; 20.03; 20.01 c1A(NOs)a -0.09 0.013 10.57 10.55, 10.56, 10.57, IC1-, Br-, I-, KNOI 10.56, 10.58 + O . 24 0.044 20.57 20.63, 20.58, 20.57, Br20.67, 20.25 +o. 10 0.027 30.57 30.63, 30.60, 30.58, c130.56, 30.57 +0.5 (0.014) 1.00 1.006, 1.004 9 c1... 1.00 1.00, 1.00 c110 1.00 1.oo c111 Table V.
I
CN- a8 complex
12
CN- as ppt. 0
e
CN 13 CN-, 0.1M NHa Al(NO& was 0.002M. C1- wm 5 X lO-'M; 0.1M Ag+ and a 1.0-ml. buret were used. Gelatin was 0.1%.
1396
ANALYTICAL CHEMISTRY
"
9.875, 9.875, 9.86, 9.86 19.70, 19.73, 19.70, 19.75 9.92, 9.90, 9 . 9 3
+0.71
9.86
0.009
19.72
0.025
0.0
0.015
-0.17
9.93
Laitinen, Jennings, and Parks (34)reported that poor end points were obtained in the amperometric titration of chloride unless gelatin was added to prevent reduction of silver chloride. Kolthoff and Stock (33) found that silver bromide and silver iodide films were formed on platinum microelectrodes during an amperometric titration and that these films were reducible. The above facts are correlated by Nightingale (37), who reported a series of polarization curves t,hat were obtained with a rotating silver electrode in a system of silver ions, bromide ions, and
suspended, solid silver bromide. The curves showed that silver bromide was as reversibly reduced a t a silver electrode as silver ion. Furthermore, the slopes a t the null potential changed with bromide ion concentration. If the same type of polarization curves exist for the iodide and chloride systems, as it is reasonable to suppose, then the response curves of Masten and Stone (and Figure 10) can be explained. The square wave method involving a constant applied potential to two silver electrodes was used to determine chloride, bromide, iodide, and cyanide.
I-
I
U
1
,
41)
,
,
,
,
,
IO
,
,
,
~
20 VOLUME
OF A g N O 3
,
,
~
30
I N ML.
Figure 10. Titration of equimolar concentrations of chlorine, bromine, and iodine with silver nitrate
See titration 8, Table V; A represents general behavior with only one halide present
Table V gives the results of t,he titrations performed and Figures 10 and 11 show typical titration curves. A time of 2 minutes was allowed for reaching equilibrium after each addition of silver nitrabe. When chloride, bromide, or iodide n-as alone (runs 1, 2, and 3) and a t a concentration greater than 10-3M, the square wave method gave results which were the same as can be obtained with the dead stop or amperometric methods. However, the square wave method yielded better results when mixtures were determined (runs 4, 6, 7 , 8) and at, low concentrat,ions of chloride (runs 9, 10. 11). The effect of mixed crystal formation between silver chloride and silver bromide was briefly studied. The theoretical error for mixed c,rystal formation is 4.8% (27’) when the precipitate which is formed is homogeneous-i. e., in a colloidal state. A heterogeneous precipitat>e-i. e., a flocculated precipitateshows a theoretical error of 1.1%. I n titration 5 conditions were such that a homogeneous precipate formed. There n-as a 4% relative error in the bromide end point which agrees with the theoretical value. Titrations 6 and 7 were run t o test the effect of a multivalent cation on the coagulation. The results were generally the same whether aluminum nitrate was present or a larger concentration of potassium nitrate as might be expected from the rule of Schulze-Hardy. Gelatin an3 acetone showed a marked improvement on the dilute chloride titrations (rune 9, 10, 11). Still, the end points were not very pronounced. A titration of 5 x 10-5M chloride was unsuccessful. ACKNOWLEDGMENT
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I
The authors are indebted to the Sational Science Foundation (Grant NSF-G750) for partial support of this work. LITERATURE CITED
(1) Barker, C. G., Jenkins, L. I., Analyst
77, 685 (1952). (2) Bertin, C., Anal. Chim. Acta 5 , l(1951). (3) Bradbury; J. H., Trans. F a r a d a ~ Soc. 49, 304 (1953); 50, 959 (1954). (4) Bradbury, J. H., Hambly, A . N., Australian J . Sci. Resear6.h A5, 541 (1952). (5) Delahay, P., Anal. Chim. Acta 4, 635 (1950). (6) Delahay, P., “New Instrumental
Methods in Electrochemistry,” Chap. 10, Interscience, New York, 1 R54
Duyikaerts, G., Anal. Chim. Acta 8 , 5 7 (1953).
Duyrkaerts, G., Ind. chim. belge 18, 795 (1953).
Figure 1 1.
Titration of cyanide with silver nitrate
See titrations 12 and 13, Table V ; -4 represents behavior in 0.lM ammonia
Eyring, H., Marker, L., Kwoh, T. C., J . Phys. & Colloid Chem. 53, 1453 (1949).
Ferrett, D. J., Milner, G. W. C., d n a l g s t 80, 132 (1955).
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(11) Foulk, C. W., Bawden, A. T., J . Am. Chem. SOC. 48, 2045 (1926). (12) Franck, U. F., 2. Elektrochem. 58, 348 (1954). (13) Gauguin, R., Anal. Chim. Acta 5,200 (1951). (14) Gauguin, R., Bertin, C., BadosLambling, J., Ibid., 7, 360 (1952). (15) Gauguin, R., Charlot, G., Ibid., 7, 408 (1952). (16) Glasstone, S., Laidler, K. J., Eyrin$: H., “Theory of Rate Processes, McGraw-Hill, New York, 1941. (17) Grahame, D. C., J . Electrochem. SOC. 9 9 , 3 7 0 ~(1952). (18) Gusman, J., Rancano, A., 2. anal. Chem. 103,445 (1935). (19) Hall, L. C., Ph.D. thesis, University of Illinois, 1956. (20) Ishibashi, M., Fujinaga, T., Bull. Chem. SOC. Japan 25, 68, 238 (1952). (21) Jordan, J., ANAL. CHEM.27, 1708 (1955). (22) Kalousek, M., Collection Czechoslov. Chem. Communs. 13, 105 (1948). (23) Kambara, T., Bull. Chem. SOC. Japan 27,523,527,529 (1954). (24) Kies, H. L., Anal. Chim. Acta 6, 190 (1950).
(25) Kies, H. L., Ibid., 10, 161, 575 (1954). (26) Kolthoff, I. M., ANAL. CHEM.26, 1685 (1954). (27) Kolthoff, I. M., Eggertsen, F. T., J . Am. Chem. SOC. 61, 1036 (1939). (28) Kolthoff, I. M., Jordan, J., Ibid., 75, 1571 (1953). (29) Ibid., 76, 3843 (1954). (30) Kolthoff, I. M., Jordan, J., Heyndrickx. A.. ANAL. CHEM. 25. 884 (1953). ‘ (31) Kolthoff. I. M.. Linnane. J. .J.. “Polarography,” 2ndoed.,’ p; 420; Interscience, New York, 1952. (32) Kolthoff, I. M., Pan, Y. D., J . Am. Chem. SOC.61,3402 (1939). (33) . . Kolthoff. L. M.. Stock. J. T.. Analust 80,860 (1955). (34) Laitinen, H. A., Jennings, W. P., \ - - - - I -
\
I
(35) . . (36) (37) (38)
Parks. T. D.. IND.ENG.CHEM.. ANAL:ED. 18,’355,358 (1946). ’ Laitinen. H. A.. Kolthoff. I. M.,. J . Phis. Chem.’45, 1074 (1941). Masten, M. L., Stone, K. G., ANAL. CHEM.26, 1076 (1954). Nightingale, E. R., Ph.D. thesis, University of Minnesota, 1955. Oldham, K. B., J . Am. Chem. SOC. 77,4697 (1955).
(39) Randles, J. E. B., Somerton, K. W., Trans. Faraday SOC. 48, 937 (1952). (40) Reilley, C. N., Cooke, W. D., Furman, N. H., ANAL. CHEM. 23, 1223, 1226 (1951). (41) Riha, J., Collection Czechoslov. Chem. Communs. 16, 479 (1951). (42) Salomon, E., 2. Elektrochem. 4, i l (1897). (43) Shoemaker, K., A N A L . CHEM.27, 553 (1955). (44) Stone, K. G., Scholten, H. G., Ibid., 24, 671 (1952). (45) Tachi, I., others, Bull. Chem. SOC. Japan 28,25,31,37 (1955). (46) Tanaka, N., Tamamuslq R., Proc. 1st Intern. Congr. Polarography, Prague, 1 , 563 (1951). (47) Willard, H. H., Fenwick, F., J . Am. Chem. SOC.44,2516 (1922). (48) Wooster, W. S., Farrington, P. S., Swift, E. H., ANAL. CHEM.21, 1457 (1949).
RECEIVED for review October 20, 1956. Accepted May 25, 1957. Division of Analytical Chemistry, 130th meeting, ACS, Atlantic City, ru’. J., September 1956. Based on the Ph.D. thesis of Larry C. Hall presented at the University of Illinois, June 1956.
Quantitative Radiochemical Methods for Determination of the Sources of Natural Radioactivity JOHN N. ROSHOLT, Jr. U. S. Geological Survey, Denver, Colo.
b Study of the state of equilibrium of any natural radioactive source requires determination of several key nuclides or groups of nuclides to find their contribution to the total amount of radioactivity. Alpha activity measured by scintillation counting is used for determination of protactinium-23 1, thorium-232, thorium-230, and radium226. The chemical procedures for the separations of the specific elements are described, as well as the measurement techniques used to determine the abundances of the individual isotopes. To correct for deviations in the ore standards, an independent means of evaluating the efficiencies of the individual separations and measurements is used. The development of these methods of radiochemical analysis facilitates detailed investigation of the major sources of natural radioactivity.
T
RE radioactivity of rocks and minerals is caused primarily by the presence of uranium-238, uranium-235, thorium-232, and their disintegration products. These radioactive series are shown in Figure 1. If, during the
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500,000 years since the minerals were deposited, no parents or their daughter products were lost and no radioactive elements were added to the mineral, equilibrium in any of the three series is established. If gains or losses occurred, the radioactive isotopes are in a state of disequilibrium, and knowledge of the isotopes not present in equilibrium abundances often provides important clues to the geochemical history of the mineral. The usefulness of a knowledge of the isotopic sources of natural radioactivity and the determination of radon-222, lead-210, and thorium-232 have been discussed (17)- The present study deals with the determination of the long-lived radionuclides and equilibrium-established short-lived daughter products needed in the investigation of radioactive disequilibrium in rocks and minerals. A study of the relationships in Figure 1 shows that the extent of disequilibria can be rigorously defined if the abundances of the following components are known: (1) uranium group, (2) thorium-230, (3) radium-226, (4) radon222 group, ( 5 ) lead-210 group, (6) protactinium-231 group, and (7) thorium-
232 series. Components 1 through 5 define the extent of equilibrium in the uranium-238 series. The equilibrium of the uranium-235 series can be defined by the amounts of uranium and protactinium-231 present. The thorium-232 series, though not involved in the equilibrium, is a major contributor of radioactivity that must be determined. Measurement of these nuclides will show that the isotopes are present in equilibrium concentrations or that disequilibrium has resulted from either recent mineral formation or gains or losses of isotopes since the mineral was formed. Other methods for the determination of some of these isotopes have been published (1, 3, 6, 7, 14, 15). Throughout this paper equivalent units are used. Uranium and thorium contents are given as actual per cent uranium or thorium. All disintegration products in the three decay series are expressed as equivalents to parent nuclides using the unit per cent equivalent, and not as the actual percentage of these daughter products. Per cent equivalent is defined as the per cent amount of primary parent, under the assumption of radioactive equilibrium,
