465
V O L U M E 2 6 , NO. 3, M A R C H 1 9 5 4 curves prepared, using these solutions, a t slit openings of 0.15 and 0.25 mm., respectively. The very small change in slope indicates that straight-line interpolation between standards differing by 10 p.p.m. of lithium which bracket the unknown could be used for the final calculation without introducing any appreciable error in the determination. The maximum error encountered would be about +0.02y0 lithium oxide. For spodumene concentrates (6y0lithium oside), the error would be about 0.3y0,, which is within theprecisionof the method. BURXYIYG PROCEDURE
h burning procedure was devised to eliminate the necessity of continually reproducing a standard curve, the necessity of correcting for blanks or flame background, and errors caused by unexpected changes in meter response during sample aspiration. -4 series of solutions of unknowns and the standards necessary for bracketing are burned in consecutive order. The emission readings recorded a t 671 mp constitute the first set (Table V). For the second set the solutions are again burned in the same order. This process is repeated until adjacent sets check within about 0.4%. In this instance, the average of the emission values for the third and fourth sets is used for the final calculation. This technique assures that all samples are burned under identical conditions. The calculation of percentage lithium oxide is performed by straight line interpolation between the standards that bracket the unknown. PRECISION AND ACCUR4CY
B Foote Mineral Co. standard spodumene sample having a value of 5.69y0 lithium oxide (established by repcntrtl gravimetric
analyses)y a s analyzed 10 times in replicate by the flame photometer method described yielding 5.694 f 0.042% lithium oxide. The precision of the method is *o.i49;b; the accuracy is of the same order of magnitude. ACKNOU LEDG\IE\T
The authors wish to acknoi\leclge the able assistance of L. D. Zwone in obtaining many of the t ~ \ p c ~imrntxl i data. LITER .tTL'RE CITED
Barnes, R. B., Berry, J. IT., and Hill, W. B., Eng. Mining J . , 149, No. 9, 92 (1948). Barnes, R. B., Richardson, David, Berry, J. W., and Hood, R. L., IND.ESG.CHEM.,-4w.4~.ED.,17, 605 (1945). Berry, J. W., Chappel, D. G., and Barnes, R. B., Ibid., 18, 10 (1946). Rroderick. E. J.. and Zack. P. G.. ANAL.CHEM..23. 1455 (19513. Diamond, J. J., and Bean, L., Sm. SOC.Testing Materials, Preprint 128 (1951). FQX,C . L., ANAL.CHEY.,23, 137 (1951). C;illiland, J. L., Am. SOC.Testzng Materials, Preprint 129 (1951). W c h , F. A., Am. Chenr. J . , 9, 33 (1887). Ilosher, R. E. Bird, E. J., and Boyle, -4. J., A N ~ LCHEM., . 22, 715 (1950). Myers, A. T., Dyal, H. S., and Barlnnd, J. W., Soil Sci. SOC. Anaer., Proc., 12, 27 (1947). Smith, J, L., Am. J . Sci., (2) 50, 269 (1871). Standford, G., and English, L., Argon J., 41, 446 (1949). Strange, E. E., ASAL. CHEM.,25, 650 (1953). West, P. W., Folse, P., and hlontgomery, Dean, Ibid., 22, 667 (1950). Wilberg, E., Z. anal. Cheni., 131, 405 (1950). RECEIVED for review .4upmt 28, 1953
Acrepted December 18, 1'253,
Effects of Anions on Calcium Flame Emission in Flame Photometry GRAEME L. BAKER and LEON H . JOHNSON Department o f Chemistry Research, Montana State Collage, Bozeman, M o n t .
This investigation was prompted by variations in calcium flame intensity as measured by the flame photometer. Perchlorate, phosphate, sulfate, and dichromate ions have been examined for the influence that they exert on the calcium flame. The results obtained indicate that pyro- ions of phosphorus or sulfur may be responsible for the flame anomalies resulting from calcium solutions containing phosphate or sulfate ions. Perchlorate ions intensify the flame emission from calcium chloride solutions, whereas mixtures containing sulfate or phosphate ions in addition to the perchlorate ions may show lower values than those containing sulfate or phosphate alone. These effects must be considered in the use of the flame photometer for calcium analyses. Methods of obviating the difficulties which accompany these effects are outlined.
V
ARIOUS ions, both cations and anions, will affect the inten-
sity of the characteristic calcium flame emission. The quantitative appects of cationic influence have been investigated by many workers, but consideration of the effect of anions (1-3, 5-8) has been limited. Some quantitative data for phosphate ( 3 , 5, 6 ) and sulfate effects (1,d, 6) have been presented, but the data provided by these have been insufficient to the fundamental study of anionic action. This paper presents an accumulation of data illustrative of the calcium flame variation to be found upon the addition of increments of the following acids: hydrochloric, acetic,
boric, nitric, phosphoric, arsenic, sulfuric, chromic, periodic, or perchloric. EXPERIMENTAL
A Beckman DU spectrophotometer equipped with Model 9200 flame photometry attachment and using acetylene as a source of fuel was used for the cursory examinations of most of the anions considered, but was supplemented with a photomultiplier attachment before completion of the work. This change did not invalidate any of the preliminary work and all strictly comparative data were taken with the photomultiplier attached. All readings were made with standard calcium chloride solutions containing increments of the various acids. iicids were selected as a means of introducing the appropriate anions only after the hydrogen ion influence had been shown t o be negligible. The hydrogen ion effect was established as insignificant on the evidence that hydrochloric acid had no significant effect when added to a calcium acetate solution; acetic acid produced no significant variation when added to a solution of calcium chloride, nor did increments of hydrochloric acid introduce significant deviations in the calcium flame intensities resulting from calcium chloride solutions. It was felt that if the hydrogen ion did exert any appreciable influence upon the calcium flame intensity, one of these systems should yield results showing the effect. Since no significant variations were to be noted in the calcium flame emissions from any of these systems, it seemed reasonable to assume that any variations that might be produced by added acids could be attributed solely to the added anion and not to the influence of hydrogen ion.
ANALYTICAL CHEMISTRY
466
The wave-length setting for all readings was 584 ms. This wave length was an arbitrary choice based on the detection limits of the Beckman instrument as established by Beckman Instruments, Inc. The slit width was 0.4 mm. for readings with the standard instrument and 0.02 mm. with the photomultiplier attachment. The instrument settings were arbitrarily adjusted to give a transmittancy reading of 80.0 for a standard 0.001M solution of calcium chloride. This 0.001X standard calcium chloride solution was constantly referred to, and when necessary, minor adjustments of the sensitivity control were made to restandardize the instrument a t the established reading. “Per cent transmittancy” is used throughout this paper as a convenient scale for recording the relative intensities of calcium flame emissions. The standard calcium chloride was prepared by dissolving calcite in hydrochloric acid, evaporating to dryness, and diluting with distilled water to produce 0.OlM calcium chloride. This in turn was used to prepare the individual standards by adding 10 ml. of the standard calcium chloride and the desired increments of acids, to produce solutions 0.001.V with respect to calcium chloride and having varying acid concentrations.
I
,001
MOLAR
I ,002 ,003 ,004 C O N C E N T R A T I O N P H O S P H O R I C ACID
Figure 2. Effect of Varying Phosphoric Acid and Calcium Chloride Concentrations on Intensity of Calcium Flame Emission
DISCUSSION
The influence to be noted from individual acids is indicated by Figure 1, which represents the cursory examinatiorl of the various acidic effects. On the basis of this examination, sulfuric, phosphoric, and perchloric acids were chosen for further study.
I9 0
r
0
CH,COOH H.0 0, HCI HNOl
0
4 0 .-
A X
n
L
,001 M C o C I t + I n c l e t n e n l s H,SO+ .001 M CoCI, + Increments H, PO, ,001 M C aClr ,001 M H,SO,+ Increment8 H, PO, . 0 0 1 M C a C I % .0007M n,Po,+ Incremenls H,S
+ +
HlO, H,As 0 ,
I
H,SO*
,001
MOLAR
Figure 3.
401-
I .GO1 MOLAR
,002
,003
.o 01
C O N C E N T R A T I O N OF ACID
Figure 1. Effect of Various Acid Concentrations on Intensity of Calcium Flame Emission
Figure 2 shows the results obtained when the indicated increments of phosphoric acid are added to solutions of different calcium concentrations. The atomic ratio of phosphorus to calcium a t the inflection point appears to be 1 to 1 in every case and the addition of phosphoric acid beyond this ratio has no additional depressant action. Similar curves for sulfuric acid additions indicate that the limiting atomic ratio for this system is 1 calcium to 2 sulfur. Figure 3 is illustrative of the data obtained when both sulfuric acid and phosphoric acid are present in 0.001ilf calcium chloride solutions. The results indicate that any influence upon the calcium flame will result first from the competitive nature of the respective anions for the calcium ion, and secondly on the individual effect produced by the anions upon the intensity of the calcium flame. Thus, the curves resulting from solutions containing both acids will vary between the limits imposed by the acids acting individually.
,002
1
. 0 03
1 ,004
CONCENTRATION OF ACID
Effect of Sulfuric-Phosphoric Acid Mixture on htensity of Calcium Flame Emission
The evidence depicted in Figure 4 appears anomalous in the light of the preceding statements. It was expected that a solution containing both perchloric acid and sulfuric acid in conjunction with calcium chloride should give results of an intermediate nature, dependent on the competitive characteristics of anions for the calcium cation and the subsequent action of the compounds formed. The competitive nature undoubtedly encompasses both relative concentration of anions and solubilities of the compounds formed with calcium. With this in mind it was expected that data obtained by varying the sulfuric acid concentration in solutions containing 0.002M perchloric acid and 0.001M calcium chloride would produce an intermediate curve which would drop rather rapidly to the singular sulfuric acid curve and then follow the curve virtually as if no perchloric acid were present. The results indicate that this particular mixture is a decidedly different type of system from any thus far encountered. As indicated by Figure 5 the phosphoric acid-calcium chlorideperchloric acid system provides results analogous to the sulfuric acid-calcium chloride-perchloric acid values (though not as pronounced). The minimum values are identical to values from the individual acids but the perchloric acid apparently produces this minimum value a t lower concentrations of sulfuric and phosphoric acid. This necessitates a revisal of the concept that the depressant action of sulfuric and phosphoric acids is due
467
V O L U M E 26, NO. 3, M A R C H 1 9 5 4 to the sulfate and phosphate ions, respectively. The action initiates that the depressant effect is the result of fewer calcium ions being in an activated state through the formation of some stable intermediate and that a maximum concentration of this intermediate is brought about a t a lower sulfate or phosphate ion concentration through the action of perchloric acid. The pyro compounds of sulfur and phosphorus are possible configurations for the intermediate postulated. These anions n-ould be in keeping with high temperature reactions and will fit the observed mole ratios of calcium to anion that exist a t the inflection points-that is, the atomic ratio of 1 calcium to 2 sulfur as exhibited by calcium pyrosulfate (CaSkh) is in keeping with the I to 2 ratio indicated by the inflection point of the sulfuric acid curve. I n the same manner calcium pyrophosphate (Ca2Pz07)will fit the 1 to 1 ratios shovm a t the inflection points on the phosphoric acid curves. The possibility that the pyrosulfate ion could in some way be involved led to the use of chromic acid because of the similarity in anions. The dichromate ion (Crz07--) would be analogous to the pyrosulfate ion ( S 2 0 1 - - ) mentioned but would exist entirely
in the indicated form in the solutions used. This led to the prediction that if chromic acid were used in lieu of sulfuric acid with a calcium chloride-perchloric acid solution, a depressant effect would be noted down to a minimum value which would be reached a t a 1 to 2 calcium-chromium ratio. Furthermore, this curve should follow in the intermediate fashion to be expected on the basis of perchloric and dichromate ion competition for the available calcium and should not exhibit the anomaly in evidence with the calcium chloride-perchloric acid-sulfuric acid system. The experimental data did verify this prediction as indicated by Figure 6. 100
K I-
"t
50
I
0
,001 M CoCI,
0
,001 M CaCI, ,001M C a C l a
A
I ,001
MOLAR
0 [I
B
.WI M CoCI, t Increments Of HCO, ,001M CoCI. lncremenk of H,SO, .001M CoCI, + ,002 M HCIOS+ Increments
,002
,003
M O L A R CONCENTRATION
of
H,SO+
OF
,004
ACID
Figure 4. Effect of Sulfuric-Perchloric Acid Mixture on Intensity of Calcium Flame Emission
I
I
z a
K
I-
o ,001 M CaCI,
a
,001 M t a c t ; A ,001 M CaCI,
,001
MOLAR
+
! 3002
CrO,
I
,003 CONCENTRATION O F ACID
,004
+
,001
rr
+
Increments H C l O + Increments C r 0, 0 0 2 M "210, Increments
Figure 6. Effect of Perchloric-Chromic Acid Mixture on Intensity of Calcium Flame Emission
40
IUU
+ +
+ +
+
Increments of HC104 Incrementa of H,PO+
,002 M HClO,
+
This explanation of the action is highly problematical and other oxidizing agents (nitric acid and hydrogen peroxide) were tried in an effort to produce an effect similar to that shown by perchloric acid. Nitric acid and hydrogen peroxide failed to show any similar action and the results neither add nor detract from the suggested possibilities. The perchloric acid may be releasing energy within the flame, either directly or indirectly, in such a manner that pyro-ion formation is facilitated. The solutions containing perchloric acid, as outlined previously, give luminosity values which result in curves, portions of which fall below the curves obtained from like systems which contain no perchloric acid. This increased depressive action might then be explained on the basis that increased pyro-ion concentrations are afforded through the action of perchloric acid on the anions available a t the concentrations indicated by these portions of the curves. There is no direct evidence for the existence of pyro intermediates of the type mentioned. The evidence does indicate that neither the sulfate nor phosphate ions are directly responsible for the lowered calcium flame intensities observed in their presence. The effect of dichromate ion on the flame does suggest the possibility of pyrosulfate and pyrophosphate ions acting as intermediates. Other anions are being investigated in an effort to establish whether or not such a situation does exist. ANALYTICAL SIGNIFICANCE
lncnmcns H,PP
.002 ,003 C O N C E N T R A T I O N O F ACID
,004
Figure 5 . Effect of Phosphoric-Perchloric Acid Mixture on Calcium Intensity of Calcium Flame Emission
The work done shows that the anions existent in a test solution being used for calcium flame photometry must be considered. Two possibilities for analytical control seem feasible a t this time, on the basis of the anions checked. If the anion concentration is to be determined along with the calcium concentration, a series of curves obtained by running the calcium a t different anion levels can be used. This method, which offersthe maximum res-
ANALYTICAL CHEMISTRY
468
‘1
I
2
M O L A R CONCENTRATION nonr .00018
n,
hand so that the acid concentrations can be adjusted within predetermined limits, establishing the flat portion of the predominant acid curve.
PO.
SUBKMARY
I 00025 MOLAR
I
,0005
.OW75
,000
CONCENTRATION C O c I z
Figure 7. Effect of Varying Phosphoric Acid Concentration on Intensity of Calcium Flame Emission At varying calcium chloride concentrations
olution possible, is illustrated by the series of curves in Figure 7 , which were obtained by running calcium curves a t various phosphoric acid levels. A second and simpler procedure would be to add an excess of the predominant anion present which exhibits a depressant action. h sample containing calcium in conjunction with sulfate, phosphate, perchlorate, and chloride ions can he cited as an example. I n this particular example the sulfate and phosphate ions present v-ill promote diminished flame intensities. If in this particular system sulfate is the predominant of the two, additional sulfuric acid could be added to such an extent that the presence of phosphate, perchlorate, and chloride ions become insignificant as seen in Figures 3 and 4. Dippel, Rricker, and Furman (4) have demonstrated that the calcium flame intensity will increase markedly with higher relative concentrations of phosphoric acid. It is necessary, therefow, that some ickn of the relative anion concentrations be a t
Perchloric acid will act on solutions of calcium chloride to increase the calcium flame intensity as measured in flame photometry. The results observed when various combinations of sulfate, phosphate, dichromate, and perchlorate ions are added to standard calcium chloride solutions has led to the conclusion that sulfate and phosphate ions are not directly responsible for the depressant effects noted with calcium solutions containing the respective acids. Pyrosulfate and pyrophosphate ions have been suggested as the intermediate ions to which the decrease in calcium flame intensity might be attributed. ACKNOWLEDGRlENT
The authors wish to express their appreciation for the valuable advice and assistance offered by Berenice W. DeHaas, Rose L. Baker, Elmer E. Frahm, Ray Woodriff, and Janice Birrer. LITERATURE CITED
Berry, J. W., Chappell, D. G., and Barnes, R . B., ISD. Esc. CHEM.,ANAL.ED.,18, 19 (1946). Brown, J. G., et al., Proc. Am. SOC.Hort. Sci., 52, 1 (1948). Cooky. AI. L., Cereal Chem., 30, 39 (1953). Dippel, W.A , Bricker, C. E., and rurman, N. H.. private communication.
Fieldes, l l . , et al., Soil Sci., 72,219 (1951). Lehman. H., and Pralow, W., Tonind. Ztg. u. Keram. Rundschau., 76, 33 (1952). Snyder, J. Q., Proc. Oklahoma Acad. Sci., 31, 134 (1950). West, P. W., Folse, P., and Nontgomery, D., 4 x . 4 ~ CHEM.. . 22, 667 (1950). RECEIVLD for reliew Juiy 14, 1953. Accepted Soveniber 27, 1953. Contribution from Montana State College, Agricultuial Experiment Station, Project No. LIS 825. Paper No. 308, journal series.
Minimum Error Titrations of Mixtures of Two Weak Acids ALVIN FRISQUE’
and
VlLLlERS W. MELOCHE
University o f Wisconsin, Madison, W i s .
The titration of a mixture of two weak acids, in general, is said to be “feasible” only when distinct breaks in a titration curve are observed for each acid. By enlploying the pK’s in the calculations, however, binary acid niixtures which give titration curves with a single sharp inflection point can often still be analyzed with good accuracy. The optimum pH at which the concentration-dependent variable (volume) should be nieasured has been defined as a function of the pK’s of the two acids in a mixture of this type. This reading, used iii conjunction with the volume required for the total titration, enables one to calculate the amount of each acid present with a minimum error.
T
HE titration of a mixture of weak acids or a mixture of a weak and a strong acid has been described by Dole ( 3 ) and others. I n the cases where the pK’s for the weak acids are sufficiently different, one observes a break in the pH titration curve for each wid and the equivalence point for each acid can be locnted. EIoTever. when the pK’s for the acids lie too close to1 Present address, Standard Oil Research Laboratories (Indiana), Whiting, I d .
gether, the p H titration curve exhibits only one break and thi6 is equivalent to the total of the acids titrated. Some authors have used the differential plot to improve the accuracy obtained in the titration of mixed acids. This method too is only applicable to cases in which the pK’s are sufficiently different to provide a break in the titration curve for each acid in the mixture. Even in the cases where the pK’s lie so close together that a characteristic break is not obtained in the titration curve for each acid in the mixture, it is possible to calculatc the proportionate amounts of the acids in a mixture from data in a titration curve. A mathematical treatment of this type of a problem has been described by Buerbach and Smolczyk ( 1 ) . iilthough these authors state that the error would be great near the beginning and the end of the titration, they failed to calculate the point of minimum error for such a titration. Furthermore, the final equations seem t o be unnecessarily complicated for practical use. The purpose of the present paper is to illustrate a mathematical development for location of a pH value which represents a point of minimum error to be employed in calrulating the concentrations of two weak monobasic acids in a mixture, the pK’s of these acid8 being so d o s e together that only one break is observed in the pH titration curve. Under the conditions descrihed, it is not necessary to employ a complete pH curve but onsLy to determine
