Photometric Determination of Indicator End Points TAKERU HIGUCHI, CARL REHM, and CHARLES BARNSTEIN Scbool of Pharmacy, University o f Wisconsin, Madison, W i r .
Titrimetric indicator end points can be determined readily by means of plots of the relative concentration of the acidic and basic forms of the indicator in solution against the volume of standard acid or base added or its K the indicator reciprocal. For systems where ~ I >>pK color ratio is preferably plotted directly against the I pK linear volume (Type I). For systems where ~ K S plots are only possible if the plots are made against the reciprocal of the volume (Type 11). Actual data are given to show the extreme precision possible by use of Type I plots. Application of the Type I1 plot to titrations of urea in acetic acid is also demonstrated.
M
UCH of the recent interest in photometric titration has
been focused on systems in which the light-absorbing species was the component being titrated or was present in concentration comparable to it. Among others, Goddu and Hume have shown that this approach often permitted greater discrimination between weak acids or bases being titrated than conventional indicator or potentiometric methods (4, 6). The method, however, is largely restricted to situations where the indicator color (in terms of absorbance) develops linearly with the added standard solution. Two types of a photometric titration plot are presented here, which are directly applicable to interpretation of ordinary indicator titrations both in aqueous and nonaqueous solutions. Because of the sensitivity inherent in these methods, much higher precision and accuracy are possible than by any previously suggested procedure for titrimetric end point determination. These methods, for example, make possible the titration of extremely weak acids and bases ahich produce very gradual color changes. Unambiguous stoichiometric end points can be located, furthermore, by means of linear plots based on data obtained some distance from the theoretical equivalence points.
where
HA and A- = the acid and its conjugate base IH+ = the acid form of the indicator I = the basic form of the indicator The equilibrium constant, K , is then equal to
If the total amount of the acid in the system is equivalent to S nil. of a standard base and if X is the volume of the base added, then
This equation is valid within the accuracy of the mass action law and if the amount of the free base in the system is assumed to be negligible. Because the application of this relationship would normally involve concentrations rather than activities, the value of the constant would be somewhat sensitive to salt and other solute concentrations which would affect the activity coefficients of the chemical species involved. I
THEORY
Where indicators are employed in trace amounts, as in normal visual titrations, the color developed is not linear with respect to the added reagent except near the end point or for the special case where the pK of the titrated substance is identical with that of the indicator. For example, in Figure 1 are shown idealized plots of volume of added base bs. the absorbance of the indicators a t a wave length chosen such that only the basic (or acidic) form absorbs. This is similar in form to the curves of Fortuin, Karsten, and Kies ( 1 ) calculated for ethylene (dinitrilo) tetraacetic acid systems. For the plot the ~ KofI the indicator was taken to be 1 unit greater than that of the acid being titrated and the concentration of the free base was assumed to be negligible through the end point. Goddu and Hume have had some success utilizing similar plots with linear extrapolation near the end point to determine their end points (6). The main objection to this approach is that the line is not straight, especially a t some distance from the end point where interfering effects (hydrolysis and the like) are often less pronounced. This objection can be readily overcome by a different method of plotting. In the titration of a weak acid with a strong base in an aqueous system, for example, the equation is
A-
i 20
I 40
I 60 %
I
I
80
100
I
I
TITRATED
Figure 1. Idealized plots of indicator absorbance during titration of weak acid with strong base where K = 0.1 Plots correspond to systems where acid form or base form of indicator is colored T Y P E 1 PLOT (K < 0.05)
For systems having relatively small K values-Le., of the order of 0.01-Equation 2, by transposing, can be put into a form which is linear with respect t o the added reagent near the end point:
+ I H + e HA + I
13)
1506
1507
V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6 For the case where X is nearly equal t o S, this approximate relat,ionship can be set up:
['?+I
SK __
- 8 - X
+
should, for best results, become less than 1 only after substant,ially all of the necessary base had been added. OR. per
1
IH
I : +
K
1
x =3 s
(4)
IH+ If -is now plotted against X , a straight line results whose I intercept on the X axis is equal to S, the amount of base stoichiometrically required to neutralize the acid. This approach is useIH ful only for systems having small K values, in that ratio I
This is evident in Figure 2 where the idealized plots of
strength. In such cases another modification of Equation 2 can be used. By transposition the following equation is obtained: +
It is apparent that if
IH
[TI IH+
I is plotted +
against
1 x, a straight line
will result which will intersect the latter axis at
1 p the reciprocal
of the stoichiometrically required amount of the standard base. Because this equation is based on firmer ground than Equation 4, it is substantially valid throughout the entire titration range and permits extrapolation from data collected some distance from the stoichiometric end point.
cent neutralization are shown for K = 0.1, 0.01, and 0.001.
EXPERIMENTAL
Equipment. A Cary recording spectrophotometer was used to record absorbances during the titration. A 1-cm. Cary cell was fitted with a rubber plug through which were inserted the tubes from the titration flask and a Transferator. A small hole was drilled through the sample compartment cover t o accommodate the tubes. A Transferator (Gilson Medical Electronics, Madison, Wis.) was used t o transfer the solution back and forth between the titration flask and the sample cell. The contents of the titration flask were stirred by means of a magnetic stirrer. Reagents. Sodium hydroxide solution, approximately lN, carbonate-free. Benzoic acid, primary standard. Bromothymol blue, 0.04% solution in water.
@I
I
I
I % TITRATED
Figure 2.
Idealized plots of I F + us. per cent titrated 1. K = 0.1 2. K = 0.01 3.
K
=
0.001
As shown, the method permits ready location of the stoichiometric end point for the latter two cases. For the iargest K value (0.1) the intersection point is more difficult to establish. If readings are taken over a wider range (Figure 3), the resulting departure from a straight line makes precise determinations rather difficult. Thus, to achieve highest accuracy, it is desirable to select indicators which are a t least 2 or more pK units weaker than the acid under titration. For many systems the ionization ratio,
IH I ' +
can be readily determined to better than 1 part in 100. This would correspond to ultimate accuracy, as far as detection of end points is concerned, of better than 1 part in 100,000 for the case K = 0.001. TYPE I1 PLOT (K > 0.05)
In certain systems it is often impossible to obtain indicators having K values of the order of 0.01 or less, or it may be desired t o use an indicator having a relatively large constant in order to detect and determine an acid in the presence of another of weaker
3 % TITRATED
Figure 3.
IH + Expanded plot of - us. per cent I titrated where K = 0.1 Deviation from linearity shown
Triphenylguanidine, Eastman Kodak, recrystallized from alcohol-water and dried under vacuum. Glacial acetic acid, analytical grade. Perchloric acid solution, approximately 0.2N in glacial acetic acid, prepared according to the method of Fritz ( 2 ) . Quinaldine red saturated solution in glacial acetic acid. Urea, recrystallized from ethyl alcohol-water and dried under vacuum. Procedures. STANDARDIZATION OF SODIUMHYDROXIDE.A weighed amount (about 50 ml.) of an approximately 1N sodium hydroxide solution (specific gravity reviously determined) was added t o an accurately weighed sampre of benzoic acid in a 125-ml.
ANALYTICAL CHEMISTRY
1508 Table I. Standardization of Sodium Hydroxide against Benzoic Acid from Photometric Data of Bromoth>-mol Blue Indicator Sample
Benzoic Acid, Grams
KO.
1 2 3 4 5
6.3471 6,3780 6.3673 6 3604 6.3552
Equivalent Volume of NaOH Solution, M1.
50,420 50.662 50.574 50.526 50.494
Calcd. Normality of NaOH Solution
1 ,03082 1,03089 1.030E 1,03082 1.03083 Av. 1,03086 Std. dev. 4 X 10-6
as in the sample solution was also recorded, this value representing the absorbance of the pure base form of the indicator. Values I of were computed from the absorbances by means of EquaIH tion 6 and plotted against the volume of perchloric acid solution added. The end point was determined from the intercept as shown in Figure 5 . + -
Table 11. Standardization of Perchloric .4cid against Triphenplguanidine from Photometric Data of Quinaldine Red Indicator Aliquot No. (25 MI.).
flask to neutralize approximately 98% of the acid. The excess acid was dissolved by slight warming. An accurate 1 to 10 dilution of the base was prepared with carbon dioxidefree mater and sufficient bromothymol blue indicator solution to give an indicator concentration of 0.008%. Sufficient indicator was also added t o the partially neutralized sample to give the same indicator concentration. The residual benzoic acid was titrated with the diluted sodium hydroxide solution from a 2-ml. microburet. Absorbance readings a t 615 mp were recorded every 0.1 ml. until the absorbance reached a constant maximum value which represented the absorbance of the pure base form of the
IH +
Titrimetric End Point, 311.
Calod. Normality of HClOc Solution
1 2 3
3.4319 3,4323 3,4321
0.24599 0,24596 0.24597 0.245973
4 5 6
3,4772 3,4778 3.4780
0.24592 0.24588 0,24587 Av. 0.245890 Std. dev. 2.6 X 10-
Av. Std. dov. 1.5 X 10-6
0 Aliquots 1 through 3 from solution containing 0.97030 gram of triphenylguanidine/100 ml.; aliquots 4 through 6 from solution containing 0.98288 pram/100 ml.
indicator. Values of __ were computed from the absorbance I readings by means of the equation
where Ab = absorbance of the pure base form of the indicator A = absorbance during the course of the titration
="I
I
DETERMINATIOX OF CRE1. An accurately weighed sample of urea was dissolved in approximately 50 ml. of glacial acetic acid in a 100-ml. volumetric flask and 10 ml. of a 0.01% acetic acid solution of malachite green added. The volume of the ureaindicator solution was adjusted to exactly 100 ml. Accurately measured 20-ml. aliquots were titrated with a standardized perchloric acid solution containing the same concentration of indicator. Absorbances at 622 mp Rere recorded a t the beginning of the titration and every 0.2 ml. during the titration until a minimum absorbance (approximately zero) was obtained.
I
Values of were computed from the measurements by means IH of Equation 6 and plotted against the reciprocal volume of perchloric acid added as shown in Figure 6. The linear plot obtained was extrapolated to the z axis, the value of the intercept corresponding to the reciprocal volume of perchloric acid a t the neutralization end point. The above procedure was followed using Nile Blue A indicator except that absorbances were recorded at 632 mp (Figure 7 ) . + -
POSSIBLE APPLICATIONS
Aqueous Systems. The Type I plots of photometric titration data are capable of yielding extremely good precision. Figure 4 is a typical graph obtained during titration of a sample of benzoic 0
Figure 4. Type I plot for titration of benzoic acid with sodium hydroxide using bromothymol blue indicator
IH The values of thus obtained Tere plotted against the I volume of base added and the end point was determined from the intercept as shown in Figure 4. STANDARDIZATION OF PERCHLORIC ACID. .4n accurately weighed sample of triphenylguanidine was dissolved in approximately 50 ml. of glacial acetic acid in a 100-ml. volumetric flask. An accurately measured volume of perchloric acid solution containing 8 ml. of quinaldine red indicator solution per 100 ml. was added t o neutralize approximately 90% of the base. A41iquotsof 25 ml. of the partially neutralized sample solution were titrated with the perchloric acid-indicator solution. The absorbance a t 533 mp was recorded every 0.01 ml. until a minimum absorbance (approximately zero) was obtained. The absorbance of a solution of the indicator of the same concentration
O
j
+
~
O
4
00
L
330
332
334
336
338
340
342
344
ML OF 0 25 N PERCHLORlC ACID
Figure 5. Type I plot for titration of triphenylguanidine in acetic acid with perchloric acid using quinaldine red indicator
V O L U M E 28, NO. 10, O C T O B E R 1 9 5 6 acid with approximately 1.Oh' sodium hydroxide. For the particular run bromothymol blue was used as the indicator; from the slope the K value was calculated to be 7.5 X I t is apparent that the end point can be readily ascertained to better than 1 part in 50,000. With some care it seems possible to achieve precisions of the order of a few parts per million. The slight deviation from linearity near the end point is probably due to the presence of small residual amounts of carbonic acid picked up by the solutions, although the presence of this impurity does not interfere with the determination of benzoic acid. Titration of weak bases with strong acids can be carried out with
1509 ples of benzoic acid by means of the photonietric method discussed are shown in Table I. The neutralization end points n-ere determined from plots of
IH +
Iagainst
volume of base added
(Type I plot, Figure 4). The data in Table I indicate that the method affords a high degree of precision in locating the neutralization end point. The standard deviation for this series of titrations was found to be approximately 1 part in 25,000.
I
In this case, the ratio of +or its equivalent IH is plotted against milliliteis of acid added. Nonaqueous Systems. Photometric methods probably have their greatest potential value in acid-base titrations carried out in nonaqueous media. Because the end point breaks experienced in many organic solvents are not so great as those found in ti-ater, the ultimate precision is often less than satisfactory. Fritz estimates, for example, that suitable bases may be titrated in glacial acetic acid by the more conventional methods with an acciiracy and precision within 0.2% (2). Weaker bases such as nitroaniline give even less certain results by the usual approaches. 17eryweak bases such as urea cannot be titrated at all by the usual methods (3). Application to these same systems of photometric procedures described here, however, yields satisfactory results.
equal precision.
I 1H'
0050
O.IO0
0.150
0.200
0.250
0.300
0350
l / M L . PERCHLORIC A C I D
Table 111. Determination of Urea from Photometric Data of Malachite Green Indicator by Titration with Perchloric Acid Vrea, Gram/ 100 Ml
4liquot I o (30 1\11 )
Titrimetric End Point, A I 1
~Iillinioles Found
Figure 6. Type I1 plot for titration of urea in acetic acid with perchloric acid using malachite green indicator
Triphenylguanidine in Acetic Acid (Type I Plot). The npplic:ihility of the method to titration of bases in acetic acid is denionstrated by the data in Table 11, ahich show the results of standardization of a perchloric acid solution against triphenylguanidine in glacial acetic acid. Three aliquots from two solutions of weighed samples were titrated with a perchloric acid solution and
I I H + ainst
the neutralization end points determined from plots of _ _ a The estrnsion of these procedures to titrations in acetic acid, for example, has been facilitated by the fact that the effective K values for a large number of indicators and sample types have been recently evaluated for this solvent (7). Although the situkction existing in mcdia of low dielectric constant is basically different from that i n nxter, i n acetic acid the following relationship exists :
K=
( IHA) (SH-Lc) ( IHAc) (SHA)
where IIlAc = the acetate form of the indicator, exhibiting its baFe color IHA = the acid form of the indicator resulting from interaction with HA S = the protophilic base present SHA = the interaction product of a strong acid HALand the base S I t is evident from this that plots of both Types I and I1 n-odd also hold for these systems. RESULTS
The photometric procedures developed were applied to an aqueous and several nonaqueous systems both to verify further the expected relationships and to determine the precision of the method. Benzoic Acid in Water (Type I Plot). The results of standardization of a sodium hydroxide solution against five weighed sam-
the volume of perchloric acid added (Figure 5). Again, the high degree of precision obtainable with the Type I plots is demonstrated. The standard deviation betxeen aliquots of a given snniple is approximately 1 part, in 10,000. The difference in average normality of the perchloric acid solution calculated on the basis of each series of aliquots is approximately four times as great as the standard deviation for each series and can probably be attributed to errors in weighing and diluting thc samples to volume. Urea in Acetic Acid (Type I1 Plot). Urea, an extremely weak base, even in acetic acid, cannot be titrated potentionietrically in this solvent with any degree of accuracy. It has keen found poasiblc, hoivever, to determine the neutralization end point of this compound with precision, using the method discussed. Plots I of + I H against the reciprocal volume of perchloric acid solution added \yere found to be linear (Type I1 plot) for malachite green and for Nile Blue .4indicators, and permitted fairly accurate determination of the neutralization end points by extrapo1at)ion as shown in Figures 6 and 7 . The results of titrations of urea samples using malachite green are shown in Table 111. The standard deviation for this series was found to be approximately 6 parts in 1000. Results of titrations of urea with Nile Blue A as the indicator were somewhat more precise, the standard deviation being about 1 part in 1000. I n the case of malachite green I the region of most sensitive color change (in the range n-hcre __ IH is approximately 1) occurred R-hen the sample wns only approximately 30yc titrated.
+
ANALYTICAL CHEMISTRY
1510
Reasonably good values of indicator interchange constants in acetic acid can be calculated from the slope
G)
and the end
point ( 8 )data. For the malachite green-urea perchlorate system the K value was calculated to be 2.5. The K value for the Nile Blue A-urea perchlorate system was calculated to be 0.47, identical with the value obtained by Higuchi, Feldman, and Rehni (7).
methods, they offer a number of advantages. [Gran ( 6 ) has developed a method by which potentiometric data can be linearly extrapolated to the equivalence point from some distance away.] The greatest advantage is that the location of the end point is practically unambiguous for either known or unknown samples. Because the end point is fixed by the intercept of a straight line, little doubt exists as to its position. With visual or potentiometric methods, the end point cannot always be located so definitely; usually a preliminary run with a known sample is required so that the end point can be fixed more or less empirically. Interference from trace amounts of weaker acids or bases, which can seriously affect these other methods, has little or no effect on the methods described. Although Type I plots probably yield the ultimate in achieving sensitivity of end point determination, they are of limited practical value, because systems amenable to this treatment can usually be analyzed satisfactorily by the more conventional methoda. This is not the case, however, with Type I1 plots. There are a large number of systems which give meaningless results by potentiometric or by visual indicator methods but yield excellent results by the use of these plots. The use of this approach, furthermore, can probably be extcnded to analytical areas such as complexometric titrations with indicators where gradual color changes are often encountered. ACKNOWLEDGMENT
I/ML.
PERCHLORIC ACID
Figure 7. Type I1 plot for titration of urea in acetic acid with perchloric acid using Nile Blue A indicator
DISCUSSION
The examples cited above illustrate the wide applicability of these photometric methods to aqueous and acetic acid systems; undoubtedly the methods can be extended to other nonaqueous systems as well. Because the procedures described are not dependent upon data obtained necessarily near or a t the end point, as is the case with earlier photometric methods based on indicators and essentially all potentiometric and visual indicator
These studies were supported in part by the Research Committee of the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation. LITERATURE CITED
Fortuin, J. 11. H., Karsten, P., Kies, H. L., Anal. Chim. Acta 10,356 (1954). Fritz, J. S., “Acid-Base Titrations in Nonaqueous Solvents,” The G. Frederick Smith Chemical Co., Columbus, Ohio, 1952. Fritz, J. S., .&N.~L. CHEM.22, 1028 (1950). Goddu, R. F., Hume, D. N., Ibid.,26, 1679 (1954). Ibid.,p. 1740. Gran, G., Acta Chem. Scand. 4, 559 (1950). Higuchi, T., Feldman, J. A., Rehm, C. R., ANAL.CHEM 28, 1120 (1956). RECEIVED for review AMMrtrch2 4 1956.
Accepted July 9, 1956.
Coulometric Titrations with Electrolytically Plated Copper JOHN M. DUNHAM and PAUL S. FARRINGTON Department of Chemistry, University o f California, Lor Angeles, Calrf.
A method is described for using metallic copper as a coulometric intermediate for reduction. Excess copper is plated from a cuprous halide solution and the oxidant is added to the cell. After the reaction between the copper and the oxidant is substantially complete, the copper is stripped electrolytically. The iodine or copper(I1) subsequently produced in the solution is detected amperometrically. Titrations of copper(I1) give an accuracy and precision within 0.6q‘ with amounts from 0.16 to 3.2 mg. Modifying the technique of sample addition gives an accuracy within A 0 . 3 q ~ with 0.5 to 0.8 mg. of copper. With samples containing 0.4 to 0.8 mg. of iron(II1) accuracy is within 1%.
P
REVIOUS investigators have generated cuprous ( 8 ) ,
ferrous ( 2 , 9 ) , ferrous ethylenediamine tetraacetate (IS), titanous ( I , 6, 7 , IO), and uranous (14) ions as coulometric intermediates for reduction. Electrolytically generated iodine has been used in the determination of dichromate and ferric iron ( I d ) . I n this procedure, the oxidizing agent liberates iodine from an iodide solution. An aliquot of standard thiosulfate solution is added, and the excess thiosulfate is titrated coulometrically with iodine. The coulometric generation of ferrocyanide ( 5 ) has been used to precipitate zinc and its use as a reductant suggested. Copper metal in contact with a cuprous halide solution is a more powerful reductant than cuprous, ferrous, ferrocyanide, or uranous ions and is as effective as ferrous ethylenediamine tetraacetate or titanous ions. The desirability
