Use of Ferrocene as a Primary Standard. This work has shown that ferrocene is easy to purify, is stable and nonhygroscopic in air, reacts stoichiometrically and rapidly with copper(I1) in pure acetonitrile, and has a large potential break at the end point. These factors, in addition to a high equivalent weight, make ferrocene a satisfactory primary standard. Factors to be aware of are the temperature coefficient of expansion of acetonitrile and the volatility of both acetonitrile and ferrocene. None of these is a serious disadvantage at the part per thousand level if appropriate precautions are taken.
ACKNOWLEDGMENT
We thank Robert Long for preliminary work on the purification of ferrocene, Glenn Johanson for the solubility measurements of ferrocene in acetonitrile, and the G. Frederick Smith Chemical Co. for a donation of hydrated copper(I1) perchlorate. RECEIVED for review October 2, 1969. Accepted February 3, 1970. Financial support by the National Research Council of Canada and the University of Alberta is gratefully acknowledged.
Acid-Base Microtitrations Based on Serial Dilution Joseph R. Robinson, Honore Stelmach,’ and Stuart P. EriksenZ School of Pharmacy, University of Wisconsin, Madison, Wis. 53706 An acid-base microtitration procedure, based on a serial dilution technique, is presented together with the necessary mathematical description of the system as well as equations to calculate initial concentrations of the sample solution. The procedure, compared with conventional (buret) acid-base titrimetric techniques, has several advantages, namely, rapidity of operation, small sample size requirements, necessity for only one initial standard solution irrespective of the concentration of unknown acid (or base), and end point accuracy. It is shown that, although small volumes are involved, normal environmental conditions of air velocity, room temperature, and humidity have a negligible effect of the technique because the titration can be performed rapidly. Modifications of the basic proposal can be made to enlarge the scope and potential utility of this titrimetric procedure.
ACID-BASE titrations based on buret addition of titrant are generally time consuming and may require a fairly large sample of acid or base. Belcher ( I ) describes buret titration of microgrRm amounts of acids and bases. In addition, it is sometimes necessary to prepare more than one concentration of standard solution. A microtitration procedure has been developed that overcomes all of the disadvantages described above. The description and application of this procedure, as well as the theory involved, are the objects of this report. The basic approach and necessary equipment for the acidbase microtitration has been adapted from a microdilutor system that has found extensive use for serial dilutions in microbiological assays (2-4). Figure 1 shows the entire microtitration system, which is composed of a transfer loop capable of holding and delivering a precise, constant volume of fluid, a titration plate consisting of a series of pits into which can be placed the same or differing volumes of fluid (this can be an ordinary spot plate), and a microburet that is capable of accurate delivery of small volumes of fluid. 2
Present address, Abbott Laboratories, North Chicago, Ill. Present address, Allergan Pharmaceuticals, Santa Ana, Calif.
(1) R. Belcher, “Submicro Methods of Organic Analysis,” Elsevier, Amsterdam, 1966. (2) W. F. Lewis and E. M. Knights, Jr., Microchem. J., 8, 349 (1964). (3) E. A. Edwards, J . Bacteriol., 87, 1254 (1964). (4) M. J. Rosenbaum, I. A. Phillips, E. J. Sullivan, E. A. Edwards, and L. F. Miller, Proc. SOC.Exp. Bio. Med., 113, 224 (1963).
TITRATION
PLATE
Figure 1. Equipment to carry out acid-base microtitrations by the serial-dilution approach
The titration is carried out by preparing a series of known acid concentrations via serial dilution and titrating an unknown concentration of base against these acid concentrations until an end point is reached. Specifically,a given volume of water plus indicator is placed in the pits using the microburet; known acid is then placed in the first pit with the aid of the transfer loop, and the resulting solution is serially diluted into the remaining pits. This serial dilution is carried out by transferring a given volume from the first pit to the second pit, mixing well, transferring from the second to the third pit and so forth, all of the moves being carried out with the transfer loop. After obtaining a variety of acid concentrations in the pits, a sample solution of base (unknown concentration) is placed on the transfer loop and serially titrated against the acid until an end point is achieved. ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
495
where the degree of dilution is a function of the ratio of transfer loop-to-pit volume, loop volume
=
x
pit volume
=
m
degree of dilution
m+x
= X
and the dilution factor is related to the extent of dilution dilution factor
=
(degree of dilutiony-1
(3)
where n is the pit number involved in the dilution. Equation l can be rearranged to a form more convenient for calculations :
X
As an example of the previous discussion, the concentration of acid in the pits after serial dilution, when the pit volume is 0.075 ml, transfer loop volume is 0.025 ml, and original normality is l.ON, would be pit I A
=
(0’075)(l‘o) (0.075 0.025)l 0.025
+
=
1.875 X lo-* meq./pit
pit 1B
=
(0‘075)(“O) (0.075 0.025)’ 0.025
=
4.688 X
PIT NUMBER Figure 2. Concentration of acid (or base) in each pit after serial dilution EXPERIMENTAL The transfer loops and titration plates were obtained from two commercial sources, Microbiological Associates, Bethesda, Md. and Linbro Chemicals Co., Inc., New Haven, Conn. A 2-ml microburet (Roger Gilman Instruments) was used to fill the pits with the water-indicator solution and for measurement of fluid volumes in dilutions. Water was doubly distilled from acid permanganate in an all-glass distillation assembly. Bases, acids, and indicators were either reagent or analytical grade. Transfer loops were checked for accuracy and precision by weighing the loops when empty and when containing water and were found to consistently contain 0.025 f 0.0001 gram. The volume of solution delivered from the microburet was checked in a similar manner and was found to be reproducible to 0.0001 gram for 0.075 ml (gram). THEORY
For convenience, we will use acid as the titrant and base as the sample throughout this paper, but of course these can be reversed. Calculation of Titrant Concentration in the Pits. Consider placing 75 p1 of water containing 0.004z indicator in pits I A through IG (see Figure l), introducing 25 p1 of a known concentration of acid-e.g., 1 .ON-into pit IA, removing 25 pl of the resulting solution and transferring to pit l B , and continuing the serial dilution until pit IG. The concentration of acid in any pit in column 1 can be calculated by means of Equation 1. meq. of acid per pit
=
(ml in each pit)
original normality
496
0
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
+
meq./pit
The concentration of acid in the various pits after serial dilution is obviously a function of the degree of dilution (Equation 2) which in turn~isrelated to the pit-to-loop volume ratio. Figure 2 demonstrates the various concentrations of acid in the pits, after serial dilution, as the pit-to-loop volume ratio is altered. This plot is a rearranged form of Equation 3: log (dilution factor) = (n - 1) log (degree of dilution) (5) The slope of the line equals the logarithm of the degree of dilution. Note that the lines do not have a common intersection point at the origin and this is because a given volume of solution is removed from each pit after dilution-i.e., we start with 75 p1 of water in each pit, add 25 pl of acid to the first pit, remove 25 pl of the resulting solution and place in the second pit, and so forth. As expected, when the ratio of pit-to-loop volume becomes large, the change in meq. per pit is considerably altered-e.g., when rn = x the concentration changes by a factor of ca. 16 over 5 pits, whereas when m = 5x, the factor is ca. 1300 over the same 5 pits. The ratio of pit-to-loop volume can be altered by changing either the pit or loop volume (at present, the transfer loops are commercially available in 25- and 50-111 size only, but of course other sizes can be constructed). Titration of a Known Concentration of Base. Consider the titration of a 1.ON base using the pits containing the varjous concentrations of acid described above. Twenty-five microliters of 1.ON base contain 2.5 x 10-2 meq., and, thus, when a loopful of base is placed in pit 1A 0.02500 meq. of base 0.01875 meq. of acid in pit 1A 0,00625 meq. of unreacted base remaining a given amount of base is left unreacted and hence the titration must be continued. Removal of 25 p l of solution from pit ZA
removes I/., of the unreacted base remaining and we transfer this to pit I B 0.006250 meq. of unreacted base remaining 0,001560 meq. of unreacted base transferred to pit IB 0,004688 meq. of acid in pit IB ___. over-titration where over-titration occurs. Because over-titration occurred in pit I B we go back to pit 1A for a fresh loopful of unneutralized base, skip pit I B and go to pit IC. 0.001560 meq. of 0,001172 rneq. of 0 000388 meq. of 0.000097 meq. of
unreacted base transferred to pit 1C acid in pit IC unreacted base remaining unreacted base transferred to pit I D
It is apparent that we can continue the process until the dissociation of water prohibits going further (if we assume water to have a pH range of 5-7 and if there is 0.075 ml of water in the pits, the meq. of acid in the pits due to the dissociation of water lies in the range 7.5 X 10-7 to 7.5 X Practical experience shows we can detect 1 X 10-6 meq. of acid using phenolphthalein as the indicator). Calculation of the original concentration of base in the transfer loop is easily accomplished by merely summing the concentrations in the pits used. meq. of base in transfer loop
=
(meq./pit X dilution factor) (6)
I.ON
A
1.875
0.8N
0
(?J 1.500
0.6N
0
0.4N
1.125
1.5 0 0
x
x
10-2
10-3
00 000 0( J O 000 0 2.344
x
x
IO-^
IO-^
5.859
x IO-^
x IO-^
x
1.465
x 1 6 ~ 3.662
x
Id6
x Id6
Using the concentrations in the previous discussion as an example, the loop concentration would be pit pit pit pit
IA IC 1E 1G
= = = =
0.01875 X 0.001172 X 0.0000733 X 0,0000046 X
1= 4 = 16 = 64 =
0.018750meq. 0.004688 meq. 0.001172 meq. 0.000293 meq. 0.024903 meq.
and consequently
As will be seen later, the accuracy of the above results can be improved by having a greater range of acid concentrations available in which to perform the titrations. RESULTS AND DISCUSSION
Establishing an Experimental Procedure. Recall in the previous example that the answer was 0.997N rather than 1.ON. The reason for this difficulty in reaching a precise end point is that too great a change in concentration existed between succeeding pits (a factor of four in the example), so that the leveling effect of water becomes prohibitive before an accurate end point can be reached-i.e., the dilution factor predominates over neutralization. There are at least three ways in which to overcome this problem: 1) use a smaller pit-to-loop volume ratio in all pits so that the degree of dilution is reduced; 2) use a different volume in each co!umn; and, 3) keep a constant pit-to-loop ratio in all pits but use different normalities in each of the columns. Consider the first alternative. The smallest pit-to-loop volume ratio (when m = x ) gives a change in concentration between pits of a factor of two, which is most desirable. However, of more importance in this consideration is that if overtitration is achieved in a given pit we would like to be able to go back to the previous pit, obtain a fresh sample, and con-
Figure 3. Concentration of acid (or base) in the pits for a typical experiment. Pit volume is equal to 0.075 ml and transfer loop volume is 0.025 ml tinue the titration. With equal volumes (pit and loop) this cannot be done because only one pass is possible, and hence we have chosen 75 ~1 as the mort desirable volume because this allows three passes. In addition, with 75 ~1 as the pit volume, the degree of dilution is a factor of four, which, although undesirable, can be circumvented. Suggestion 2 requires different volumes in each of the vertical rows of the titration plate (see Figure 1). This is, of course not a good solution because we are limited to m = x as the smallest dilution, and, as described above, this ratio has a serious drawback. Of some importance to this suggestion is that the mathematical calculations for this approach are considerably more complex. The third alternative is to use different normalities in each horizontal row and maintain a constant pit volume. This gives an acceptable way to achieve accurate end points in the titration. Because we have decided upon the pit-to-loop volume ratio, for the reasons previously discussed, we need now to stipulate the concentrations of acid required. Four initial concentrations of acid (1.0, 0.8, 0.6, and 0.4N) are necessary, and the resulting pit concentration difference between any two pits (horizontal pits) is small enough to effectively titrate an unknown base. The fact that more than one concentration of acid is necessary to achieve precise results is obviously undesirable; however, the 0.8, 0.6, and 0.4N acid can be made directly on the titration plate as will be described in the typical experiment section. It is stressed that the acANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
497
Table I. Microtitration Data for Various Base Concentrationsa Base concn as Base concn as No. of Standard determined by No. of Standard determined by buret titration detns deviation microtitration detns deviation 0.4858 6 0.0010 0.4860 3 0.0015 0.2259 5 0.0008 0.2262 4 0.0009 0.1265 2 0.0025 0.1270 2 0.0010 0.0130 2 0.0004 0.0129 3 0.00001 a Other concentrations of base, in the range 0.01 to l.ON, were titrated using this procedure but were not included in the table since the examples are representative. The concentration range 0.01 to 1.ON does not represent the upper and lower limit to titration using this procedure.
curacy of this procedure is limited only by the concentration difference between pits. Thus, if ten initial concentrations of base were used, a much more accurate end point could be reached. The decision to use only four initial concentrations, as described above, is based primarily on the practical aspects of the time and difficulty of preparing more solutions. A Typical Experiment. A 1.ON HCl solution is accurately prepared, and appropriate dilutions are made to prepare 0.8, 0.6, and 0.4N acid solutions. This can be accomplished directly on the titration plate, using the microburet for fluid transfer, by placing 100 p1 of water into two pits and 150 p1 into a third pit and adding 400 pl, 150 p1, and 100 pl of acid, respectively, into these pits. These stock solutions are then used for serial dilutions into pits containing 75 p1 of water and 0.004 phenolphthalein to generate the concentrations shown in Figure 3. A loopful (25 pl) of 0.127N base (original concentration determined by buret titration) was then introduced into pit I A and over-titration occurred. A fresh sample of base was then introduced into pit 2A with the same result. This process was continued until a pit was reached where no over-titration occurred, which in this case was pit 3B (according to company literature and our own experience, an experienced titrator can manipulate a number of loops at one time so that the number of passes required is minimized). From pit 3B, titration in the vertical direction was begun. (It is most important that titration is initiated a t a pit whose concentration is near the initial unknown concentration; otherwise, the dilution factor predominates in the titration and a n accurate end point will not be reached.) A loopful of unneutralized base from pit 3B was transferred to pit 3C where over-titration occurred. A second loopful from pit 3B was tested in pit 3 0 with the same results. A third loopful from pit 3B was introduced into pit 3E and no over-titration was observed. A loopful of solution from pit 3E was introduced into pit 3F and again no neutralization was observed. A loopful from pit 3F when placed in pit 3G gave overtitration. Thus, the entire titration involved pits 3B, 3E, and 3F, giving a combined meq. of acid required of 0.003165, which is equivalent to 0.1266N as the original sample concentration. The entire titration consumed 0.175 ml of sample and, including the plate preparation, was carried out in less than 5 minutes. (Most of this time was spent filling the pits with solution. Automatic delivery systems, if they are accurate, will considerably reduce the time required.) At this point, if we desire, we can repeat the experiment and try t o improve the end point by using a different pathway--e.g., from pit 3B to pit I E rather than pit 3B to pit 3E. Table I shows the accuracy and precision of this procedure, using the four concentrations of acid described above, as compared to the buret approach of acid-base titration. Effect of External and Internal Variables. Because small volumes are involved in this procedure, variables such as 498
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
temperature, air velocity (evaporation), carbon dioxide absorption, and surface tension could have a significant effect. A systematic study of these factors was not undertaken, but qualitative observations were made. The temperature effect was measured only qualitatively and no attempt was made to thermostat the titration equipment, although this can easily be done by jacketing the titration plate and passing constant temperature water or air through the jacket. Titrations were performed at approximately 20, 25, and 30 "Croom temperature and no differences in end point were noted. Air velocity, and consequently the rate of evaporation, can have a large effect on the results. Performing the titration in a dry box under conditions of varying air velocities indicated that evaporation took place and consequently the end point changed. When the titration was carried out on the bench top in normal and air-conditioned rooms, no effect due to evaporation was noticed. However, if the titration is carried out over prolonged time periods (fifteen minutes or more), the end point will change due to evaporation. Carbon dioxide absorption presented no problems under the conditions of the experiment and no attempt was made to eliminate this species from the titration area. All of the above considerations were discussed with water as the solvent and it should be kept in mind that other solvents could make these factors important-e.g., evaporation of low boiling solvents. In addition to this, surface tension effects of both solvent, and solvent plus solute, can create special problems. The volume of solution delivered by the transfer loop will vary with the surface tension of the solution and, consequently, as the surface tension of the solution changes (due to a different solvent or perhaps addition of a surface active or highly viscous solute) the amount delivered will vary. Of course, the transfer loop can be calibrated with the new solution to overcome this problem. The procedure outlined can be modified in a number of ways to improve the accuracy and to simplify the operation. Jacketing of the titration plate and use of a variety of standard concentrations rather than the four used in this study would be examples, In addition, the detecting device might be thermometric (thermistors in each pit to measure heat of reaction) or potentiometric (electrodes in each pit to measure pH), and, finally, it seems possible to carry out titrations on smaller volumes with the aid of a microscope, although effects such as evaporation and temperature change might be difficult to control. ACKNOWLEDGMENT
The authors are grateful to Vithal K. Pate1 and Lawrence Albrecht for performing many of the titrations.
RECEIVED for review December 10, 1969. Accepted February 11, 1970. This study was financed, in part, by National Institutes of Health, General Research Support 5-Sol-FRO5456.
