Automatic Thermometric Titrations HARRY W. LINDE, L. B. ROGERS, AND DAVID N. HUJIE Department of Chemistry and Laboratory f o r Nuclear Science and Engineering, Mussachusetts Institute of Technology, Cambridge, Mass. With a relatively simple apparatus consisting of a thermistor, recording potentiometer, and constant-flow buret, a wide variety of titrations may be carried out automatically with ease, speed, and accuracy, Good results have been obtained with strong acid-strong base reactions; the titrations of acetic, boric, and phosphoric acids (the latter gives three clearly defined breaks); the determination of weak bases, such as ammonia, and heterocyclic amines; and precipitation and ion-combination reactions such as those of chloride with silver or mercuric ions. The method has been applied with success to systems containing emulsions, thick slurries, and organic solvents, and has been shown to be applicable over a wide range of concentrations.
T
HERMOLIETRIC titrations \yere performed as early as 1921 by Dutoit and Grobet (Q, showed that curves obtained by plotting temperature rise Of titrant exhibited changes in slope in the vicinity of the equivalence point. They and subsequent investigators ( 2 , S , 5 , 6, 9-11,15-15,18,20) have found the method applicable to acid-base, complex-formation, precipitation, and redox reactions. Most of the results were not of sufficiently high accuracy for analytical purposes but MaYr and Fisch (9) showed that, with refinement, the method was capable of a fair degree of precision. Although the thermometric titration method appears to be widely applicable, the tediousness of making the many careful measurements necessary for a curve n ith the conventional Beckmann thermometer-Dewar flask apparatus has discouraged potential users. I t occurred to the authors that the use of a thermistor and a recording potentiometer for measurement of temperature together a i t h continuous addition of titrant from a constant flow buret would make rapid, automatic, thermometric titration entirely feasible. Thermistors entirely sealed in glass and well suited to measurement of temperature changes in solutions have been described by several authors ( 1 , 4,1 2 ) and are commercially available (Graybar Electric Co., 420 Lexington Ave., New York, N. Y.) a t surprisingly moderate cost. These have excellent sensitivity (-0.04 ohm per ohm per O C.) and, because of their lorn heat capacities, show a rapid response. The apparatus described below was constructed from readily available components.
'.
ure 2, operates on the principle that the flow through a capillary is a function of the pressure or head on that capillary for any given solution and temperature. The large head and the RiIariotte bottle assured a constancy of flow. The temperature of the titrant flowing through the buret was held to within =k0.08' C. by means of a thermostated water jacket. This buret, although perfectly satisfactory as to constancy of flow (Table I ) was far from convenient in many respects, particularly when it was necessary to change titrants. The authors suggest a motor-driven syringe such as used in the Precision-Dov- titrator (16) or the one used by Lingane (8).
E
RI
PI
TO RECORDER
EXPERIMENTAL
Apparatus. A simple bridge circuit for the thermistor and recorder is shown in Figure 1. The sensitivity, exprrssed in centimeters of chart per degree centigrade, is adjusted by the potentiometer, PI. With PI set at its maximum resistance (to the left of Figure l), the 2-mv. recorder had a full-scale deflection correspondiy to a change of about 5.5' C. (The reciprocal of the sensitivity, C./cm. is linear with the settings of PI.) Since, in a thermometric titration, it is the change of temperature and not the actual temperature itself which is of interept, exact calibration is unnecessary. I n order to compensate for slight differences in the initial temperature in going from sample to sample, it was desirable to incorporate a means of suI!pIying a bucking voltage. This voltage, about zt6 mv., was available through the zero adjustor (Figure 1). Ordinary radio resistors and potentiometers rated a t 0.28 watt v i t h &IO% tolerance are adequate. The thermistor is a Western Electrlc Co. l4B having a resistance of about 2000 ohms a t 25" C. The recording potentiometer is a Leeds and Northrup Speedomax Model G, 0-2 mv. range. When the thermistor circuit was connected to the recorder, the horizontal axis of the chart became a function of temperature and since the chart was driven a t 2.G1 ern per minute with a constant speed motor, the vertical axis xvaq, oi npcessitv, time. A higher speed recorder was tried but offered no particular advantage in most cases. In order to relate volume of titrant to motion of the recorder chart, a constant flow buret wis built. This buret, shown in Fig-
Figure 1. Bridge Circuit for Thermometric Titrations Rj. 3900 ohms Rz, Rd. 2000 ohms
Rz. 1500ohms Ra. 500 ohms P I , P2. 1000-ohm potentiometers E . 1.5-volt dry cells S . SPST toggle switch T. Terminals for thermistor, Western Electric 14B
Table I. V a t e r Jacket Temp., C . 14.5 23 2 28.6
Calibration of Constant-Flow Buret Grams of 1.032 N HCl Delivered in 3 RIin. =k 0.2 Sec.a
Standard Deriation,
Replicates so. of
70 b
7.265 9.316 10.063
0.083 0.118 0,026
4
7 3
0 Tiiiied with stopwatch graduated t o 0.2 sec. Buret tip submerged in distilled water in collecting beaker. b Standard deviation expressed in per cent is equal t o standard deviation, o ,divided by the mean, 5, and multiplied by 100.
404
V O L U M E 25, NO. 3, M A R C H 1 9 5 3 Table 11. Substance Titrated
XaOH
50
SaOH NaOH NaOH Sa013 Sad202 Agll'02
Titrations with 1.032 A' Hydrochloric Acid
__
SaOEI SaOH NaOH
Solvent a,) ml. Hi0 611 nil. H20 5 3 !$.,3 .Jf
405
KCI id.
ernulsionb l e 5 nil. H90 a4 ml. Hz0 3 3 iiil. HrO 52 nil. H20 60 ml. €120 GO rnl. H i 0
S o . of Replicates 22 5 2
A v . Length of C h a r t t o E n d Point, Cni. 4.121 8 21 4.12
-4mount of Amount of Reactant Reactant Added, Found, Meq. Meq. 4.902 4.902 9,77 9.804 4 902 4.90
0.17 0.12 0.57
Ratio: N e q . Found .___ l l e q . Added 1.000" 0 997 1.00
c, R
3
4.14
4.902
4.93
0.il
1.01
.i
4.13 3.29 2.44 1 65 8 40 4.20
4902 3 922 2 941 1.961 10,000 5,000
4.92 3.91 2.90
0.62 0.78 O,l$
1.004 0,997 0.985 1.02 0.999 1.000
2
.!
1 96
9.99 5.00
3.6 0.28 0.31
a r s e d as standard solution. b Emulsion used was a milky licluid composed of 230 ml. of distilled water. 100 ml. of n-h1ityl alcohol, 3 nil. of Tergitol 7 wetting agent, 5 nil. of lubricating oil, and 5 ml. of ethyl alcohol a n d shoired no titratable basicity. C This large variation is probably result of a cornhination of the 1% error in using 2-1111. pipet and the measusenlent of the short length of chart.
Le., by allowing the buret to run vhile 12.69 em. of chart (10 divisions) passed the pen. The samples vere then titrated to a phenolphthalein end point with 0.9804 N sodium hydroxide and were found to contain an average of 15.100 meq. of acid (u = 0.Oi8%). This same volumetric buret was then used to measure five similar portions of the 0.9804 N sodium hydroxide to be titrated t h e r r n o m e t r i c a 1 I y . These thermometric titrations required an average of 12.732 em. of chart ( u = 0.1637,), a difference of 3 p.p.t. RESULTS
TYith this assurance, the authors proceeded n-ith thermometric titrations of various substances Tvith standard hvdrochloric acid. Table I1 gives the reproTable 111. Titrations with 1.032 .V Hydrochloric Acid of Hydroxide and ducibility of titrations of sodium hyCarbonate Dissolved in .4bOUt 60 311. of Distilled Water droxide a t various concentrations and in \Ieq. Found No. SazCOs, N e q . Ratio: l: l e q . Ad+& various media. I n addition to the data ~ ~of ~ l i N -a O K Rferi. cates Added Found 0 , '7' Added Found a, 70 KaOH Sa9COa given there, several titrations of sodium 4.902 4 90 0 60 5 000 4.99 0.84 1.000 0.998 hydroxide were made in solutions con4 10 000 9.99 0.14 1.000 0.999 3 0.080 0.98 6 4 taining varying amounts of filter-paper 3 4.902 4 87 0.43 1 000 1 05 1.3 0,994 1.050 pulp. Even when these suspensions n-ere thick slurries, there was no significant change in the end point. The results of the titrations of sodium carbonate (the salt of a veak acid) and silver nitrate (precipitation) are also given in Tahlc 11. Table I11 shoivs that it is possible to tit.rate mixtures of sodium TITRANT hydroxide and sodium carbonate with a good degree of accuracy. The titrations of Tables I1 and I11 are shown in Figure 3 as they n-ere plott,ed hy the recorder.
170 cm
+ DEWAR FLASK
Figure 2.
Titration .4pparatus
A glass stopcock conncctcd the end of the capillary to the delivery tip of the buret. This tip was held in a rubher stopper along with the thermistor and a g l a ~ ssleeve for the stirrrr shaft. The stirrer was made of glass and driven by a constant speed, 600r.p.m. motor to ensure uniform mixing. The placement of the tip, stirrer, and thermistor is not critical except that they should all be submerged and not too close together. In order to minimize the heat losses from the solution, the titrations were performed in a Dewar flask. Titrations have been done in ordinary glass flasks but the heat loss& from the system were about five times as great, caused excessive deviation from linearity i n the titration curves, and tended to obscure the end point. Reagents. All of the chemicals used in this work were of reagent grade. The solutions and all apparatus were kept in a thermostatically controlled room (21' i 2" C.) and all titrations were performed in this room. Calibration of Buret. I n order to ensure that the buret flow LYas indeed proportional to distance along the chart, six samples of 1.008 N hydrochloric acid were allowed to run into Erlenmeyer flasks which contained enough water to cover the delivery tip of the buret. These samples were timed with the recorder chart-
In Figure 3, A is the point where the recorder chart drive was started, and line A B is a record of the temperature of the solution a t the start of the titration. At point B the flow of titrant was started. the1ineBCshow-sthe gradualevolution of the heat of reaction, and point C is the end point. The line CD slopes downn-ard because in this instance the titrant was slightly cooler than the titrated solution. At point D the titration Tvas stopped. (Sens. iq the fractional settings of the sensitivity adjustment, P I , in Figure 1.) S o curves are shown for the titrations of silver nitrate (or for mercuric nitrate) with hydrochloric acid because these curves have the same shape as those of sodium hydroxide titrated Jvith hydrochloric acid (Figure 3). The reproducibility and accuracy obtained in a variety of representative reactions are shown in Table IV. This tabulation includes reactions involving complex formation and precipitation in addition to titrations of weak bases, weak acids, and salts of weak bases. Titrations of base and of silver nitrate at vaiious dilutions (0.02 to 0.005 N ) are also illustrated. The curves for these titrations are shown in Figures 4 through 6. Under ordinary conditions, one can expect a precision of a few parts per thousand. DISCUSSION
The limits of applicability of the method n-ill apparently be bet by a number of different factors. The reaction must be rapid or serious curvature will appear and the end point may be displaced. The adequate and rapid mixing of large volumes of solution is a real problem and heat loss due to evaporation becomes serious for very small titration volumes. If the solutions are sufficiently dilute, the amount of heat generated will be difficult to measure. The titration of 1 meq. of sodium hydroxide in 200 ml. of water, with a temperature rise of only about 0.07" C., will give an indication as to this limit. This temperature rise would correspond to
ANALYTICAL CHEMISTRY
406 Table IV. Substance Titrated KaOH BgNOs H g ( xo3)2 SHs HC1 H3P04b 2nd H,' 3rd H NHhC1 HC1 C XHhClC CHsCOOH
Other Titrations
KO.of Titrant 1 . 0 0 8 A' HC1 1.008 N HC1 1.008 N HC1 1.008 HC1 0.9804 A' N a O H 0.9804 N N a O H 2%'
Replicates 6 8 5 5
16 4
0.9804 X 0.9804 K 0,9804 S 0.9804 A' 0.9804 A' 0.1147 N 0.1147 N 0.1147 K 0.1147 V .
Amount Added, Meq.
Amount Found, Rleq.
9.804
9.804 4.98 10.01
5,000 10.000 8.490 9.540 1.029
8.51
9.54 0.342 0.342 0.373 10.01 4.78
u,
%
Ratio: Meq. Found Meq. Added
0.11 0.25 0.35 0.56 0.38 2.8 2.1 0.85 0.19 0.18 1.0 0.99 0.38 0.04 0.92 0.77 4.7
NaOH 4 10.000 KaOH 2 4.770 NaOH 2 5,000 5.08 KaOH 4 9.880 9.88 KaOH 4 10.00 10.24 HCl 4 0.954 0.936 NaOH HCl 4 0.954 0.942 NaOHd 3 0.500 0,500 AgN03 HC1 7 1.186 1.14 CaHsNe HCl All reactants dissolved in 50 t o 60 ml. of water unless noted. a Standard solution. b Potentiometrically standardized against sodium hydroxide t o second hydrogen. C Hydrochloric acid a n d ammonium chloride were in same solution (see Figure 5 ) . d Dissolved in 200 ml. of water. e Dissolred in 30 ml. of water.
1.oooa 0,996 1.001 1.006 l.OOOQ 0.997 0.997 1.09 1.001 1.002 1.02 1.000 1.024 0.981 0.987 1.000a 0.96
small in comparison with the heat of reaction. With the present apparatus and conditions, about 0.002 -V would appear to be the lorer limit of concentration of strong acid or base which could be determined to 1k2 to 3% accuracy without extraordinary precautions. I n the titration of weak acids and bases, not only the heat of neutralization of the hydrogen ion-hydroxide ion reaction, - 13.6 kcal. per mole, must be considered but also any heat effect involved in the ionization of the weak electrolyte. This may be either positive or negative, and is not dependent upon the ionization constant alone but a130 upon the entropy of ionization. .4s a rule, weak acids evolve less heat on neutralization than do the strong mineral acids, but hydrofluoric acid is an exception, yielding 2.7 kcal. per mole more than hydrochloric acid ( 1 7 ) . Boric acid and the ammonium ion have nearly identical acid strengths (pK 9.2 and 9.3, respectively) ( 7 ) but the former evolves 10.0 I.0.C kcal. per mole (19)on neutralization with a strong base while the latter releasesamere 1.3 kcal. per mole ( 1 7 ) . The heat of ionization of a weak electrolyte may be estimated with the aid of the relation
1 I ?
\
*TIME
Figure 3. Titrations of Bases in 50 $11. of Solution with 1 i Y Hydrochloric Acid 1. NaOH, 10 meq. (sens. = 0.5) 2. IYaOH, 5 meq. and Na2C08, 5 meq. (sens. = 3.
0.5) SasCOa. 10 meq. (sens. = 0.5)
AH = T A S
- RT
In K
but, as a rule, the entropy values are not well known. Most of the commonlyapplied titrations of analytical chemistrv involve sufficient heat effects to make thermometric determination of theendpoint worth consideration. For reasons similar to those mentioned above, hou ever, heats . 4 of reaction cannot be predicted from equilibrium constants alone. Figure 4. Titrations of Acids in 60 Ml. of Since no current need flow Solution with 0.954 N Sodium Hydroxide through the solution in a ther1. HPOi, 10 meq. (sens. = 0.2) mometric titration and also 2. HCl, 10 meq. (sens. = 0.2) since many organic solvents 3. CHaCOOH, 10 meq. (sens. = 0.2) 4. HsBO8, 10 meq. (sens. = 0.2) have heat capacities less than 5. Blank (heat of dilution of sodium hydroxide and heat added by warmer titrant); (sens. = 0.2) half that of water, thermometric titrations appear to be very well suited tononaqueous work. Indeed, it was for this reason that these investigations were started. I n working with mixtures of solvents, attention
Figure 6, which shows the titration of 0.005 lVsodium hydroxide, about 0.50 C. warmer the titrant, 0.1N hydrochloric acid, is than the titrated solution yet the slope after the end point caused by its addition is almost as great as the slope caused by the heat of reaction. In all of the titrations tried, the heat of dilution was
reaction.
The following brief review of thermometric titrations done by earlier works will give some idea as to the scope of the method: Acid-Base Titrations. Mixtures of brominated phenol and cresols in aqueous alcohol with base (16); arsenious acid with
V O L U M E 25, NO. 3, M A R C H 1 9 5 3
407
W
in concentrated acids by titration 71-ith fuming acids; “free anhydrides” in fuming acid; aniline in aniline .salts by acetylation (18).
I-
ACKNOW L E D G
W (L
3
l-
a (L
t5 a
-
\IENT h-I
I
Min. -4
+ TIME
Figure 6. Titration of 0.005 IV Sodium Hydroxide with 0.1147 iV Hydrochloric .4cid 1. NaOH, 1 m e q . (sens.
-
P-lhlin.+
TIME
LITERATURE CITED
h 3
Figure 5 . Titrations of Hydrochloric -kcid, immoniuni Chloride, and Mixtures of Hydrochloric Acid and rlmmonium Chloride in 60 Ml. of Solution with 0.994 A’ Sodium Hydroxide 1. HCI, 5 m e q . (sens. = 0.3) HCI, 5 m e q . a n d ”4C1, 5 m e q . (sens. = 0.3) NH4C1, 10 m e q . (sens. = 0.6) ( m u l t i p l y t e m p e r a t u r e
2. 3.
= 1.0)
The authors are indebted t o the Atomic ComEnergy mission for partial support of this work.
s c a l e by two)
base ( 1 1 ) ; various acids of phosphorus with base (13, 1 4 ) ; trisodium phosphate with acid ( 6 ) ; aprotic acids (aluminum chloride) and bases (dioxane, ethyl acetate) in benzene (20). Precipitation Titrations. Zinc, lead, and magnesium with hydroxide (6); calcium, strontium, and mercury(1) and (11) with oxalate (9). Complex-Formation Titration. Cobalt(11),copper, and nickel n-ith ammonia (6);niercury(I1) with iodide; nickel, zinc, and cobalt(I1) with cyanide (11). Redox Titrations. Arsenite with bromate and with hypochlorite; oxalate, hydrogen peroxide, iron( 11),and ferrocyanide Kith permanganate (9). Miscellaneous Titrations. Acetic anhydride in acetic acidsulfuric acid acetylating baths by reacting the anhydride 11-ith aniline: acetyl nuniber.and iodine number in fat analysis; 11-ater
(1) Becker, J. il., Green, C. B., and Pearson, G. L., Bell System Tech. J., 26, 170 (1947). (2) Dean, P. A i . , and Sewcomer, E., J . Ana. Chem. Soc., 47, 64 (1925). (3) Dean, P. JI., and Watts, 0. O., Ibid., 46, 855 (1924). (4) Dowell, K. P., Elec. X f g . , 42, No. 2, 84 (1948). (5) Dutoit, P., and Grobet, E., J..chim.phys., 19, 324 (1921). (6) Grobet, E., Ibid., 19, 331 (1921). (7) Kolthoff, I. M.,and Stenger, 5’. R., “T’olumetric .halysis,” Vol. I, Ken. York, Interscience Publishers, 1941. ( 8 ) Lingane, J. J., ASAL. CHEW,20, 285 (1945). (9) hlayr, C., and Fisch, J., 2. anal. Chem., 76, 418 (1929). (10) Alondain-hlonval, P., and Paris, R., Bull. SOC. chim. France, 5, Ser. 5,1641 (1938). (11) Mondain-Monval, P., and Paris, R., Compt. rend., 198, 1154 (1934); 207,335 (1938). (12) Aiiiller, R. H., Ax.4~.CHEM., 21, 108 (1949). (13) Paris, R., and Robert, J., Compt. rend., 223, 1135 (1946). (14) Paris, R., and Tardy, P., Ibid., 223, 1001 (1946). (15) Paris, R., and Vial, J., Chim. anal., 34, 3 (1952). (16) Robinson, H. A , , T r a n s . Electrochem. Soc., 92, 445 (1947). (17) Roth, W. A., and Scheel, K., “Landolt-Bornstein PhysikalischChemische Tabellen,” 5th ed., Berlin, J. Springer, 1923. (18) Somiya, T., J . SOC.Chem. I n d . , J a p a n , 51, 135T (1932). (19) Thomsen, J., “Thermochemische Untersuchung,” 1‘01. I, Leipzig, Barth, 1882. (20) Trambouae, Y., Compt. rend., 233, 648 (1951). RECEIVED for review July 18, 1962. Accepted December 2 , 1952.
Differential Titration of Amines JA3IES S. FRITZ, Iowa State College, Ames, Iowa
S
EF’ERAL recent papers have dealt with the titration of
organic bases in acetic acid, dioxane, and other solvents (1, 2, 6, 7 , 9, 10). These are excellent general methods but do not wrve to differentiate various types of amines. The use of acetic aiihydride permits the convenient determination of tertiary :imines in the presence of primary and secondary amines (12). TIeatment of a mixture with salicylaldehyde followed by titration in benzene-2-propanol (13) or in ethylene glycol-2-propanol ( 1 1 ) has been used to determine primary amines. It is now proposed that differential titration in nonaqueous solvents be used to
distinguish quantitatively between amines of different basic strength. THEORY
Although it has been widely and successfully used as a solvent for titration of amines of all types, acetic acid cannot be used to differentiate aliphatic and aromatic amines. This is illustated by titrating a mixture of pyridine and butylamine in acetic acidacetonitrile (Figure 1). This curve shows only a single break despite the considerable difference in basic strength of these two amines (in water the p K values differ by 5.5 units). An explana-
