THE JOURNAL OF
PHYSICAL CHEMISTRY
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VOLUME 70, NUMBER 2 FEBRUARY 15,1966
Cryoscopic and Calorimetric Investigations of Betaine and Betaine Hydrochloride
by J. C. Ahluwalia, Frank J. Millero, Robert N. Goldberg, and Loren G. Hepler Department of Chemistry, Carnegie Institute of Technology, Pittsburgh, Pennsylvania (Received September 87, 1966)
16219
Results of cryoscopic, calorimetric, and conductometric investigations of betaine and betaine hydrochloride in aqueous solution are presented and used in subsequent thermodynamic calculations. For the ionization of aqueous [ (CHa)aN+CH2COOH] we find AGO = 2.50 kcal mole-', AHo = -0.08 kcal mole-', ASo = -8.7 cal deg-' mole, and -7 cal deg-' mole-'. A new freezing point apparatus utilizing thermistors is ACPo described.
Betaine [(CH3)3N+CH2COO-], betaine hydrate [ (CH3)~N+CHtCOO-.HzO],and betaine hydrochloride [ (CH&N +CH2COOH]C1-, abbreviated in this paper to B, BmH20, and BHCl, respectively, are of interest for a variety of reasons related to the dipolar character of the betaine species and also because of relevance to biological problems. This paper reports results of calorLnetric, cryoscopic, and conductance measurements undertaken to provide information about aqueous solutions of these compounds and the heat of hydration of betaine. Precise measurements of freezing points of aqueous solutions of betaine have yielded activity coefficients of aqueous betaine a t -0'. Similar measurements on solutions of betaine hydrochloride have yielded the acid ionization constant of [(CHa)aN+CH&OOH] Calorimetric (aq), abbreviated to BH+(aq), a t -0'. measurements have yielded the heat of hydration of B(c) and the heat of ionization of BH+(aq), both a t 25'. Conductance measurements have been made
to obtain the ionization constant of BH+(aq) a t 25'. These results have been used in several thermodynamic calculations.
Experimental Section A common method of determining freezing point depressions of solutions is the Beckmann procedure involving cooling curves. Even with the most sensitive temperature measuring device, it is likely that the uncertainties will be more than O.O0lo. The difficulties inherent in the Beckmann method can be largely overcome by proper use of the "equilibrium" method that has been developed and applied by Richards, Adams, Harkins, Scatchard, and others. An accuracy of deg has been claimed for this method, but deg is more usual and accuracy of the order of corresponds to what we have attained with the apparatus described below. Although most precise measurements of freezing point depressions have been made with multijunction
319
J. C. AHLUWALIA, F. J. MILLERO,R. N. GOLDBERG, AND L. G. HEPLER
320
thermocouples and a microvolt (pv) potentiometer with high-sensitivity galvanometer, we have used the thermistor bridge circuit shown in Figure 1 with a Rubicon Type B potentiometer and a Leeds and Northrup 98358 amplifier. A few measurements were made with a Wenner potentiometer. The apparatus itself consists of two identical 450-ml dewars (Fisher Scientific Co. 10-198A), unevacuated and unsilvered. These dewars were suspended by a wooden cover in a 2-1. silvered dewar flask which contained a slurry of ice and salt for cooling purpases. Both dewars were closed with tapered aluminum stoppers that were covered with rubber sleeves to assure snug fits. Three aluminum glide tubes through the stoppers were used for introducing thermistors, stirrers, and a platinum resistance thermometer. The Fisher Scientific Co. 14-515 stirrers were run by Variac-controlled electric motors. Closely matched thermistors with resistances of 1000 ohms at 25' and a negative temperature coefficient of about 4% were obtained from the Yellow Spring Instrument Co. Each of these thermistors was immersed in silicone oil contained in a 5-mm Pyrex tube. The leads of these thermistors were connected to the legs of a bridge circuit (see Figure 1) by means of shielded wire. A constant current (8.6 X amp) through the circuit was maintained by means of two 6-v batteries connected in series and a variable resistor adjusted so that the potential drop across a 1000-ohm resistor was constant as measured by a Rubicon potentiometer. In all experiments the water and solution were precooled to 0.8' below their respective freezing points, poured into the dewars, and seeded with ice crystals on a spiraled steel wire. The temperature of the bath in which the dewars were suspended was kept about 0.2' below the freezing point of the solution. The solution and pure water were allowed to stand for about 2 hrs to reach equilibrium with ice. For determination of the relation between measured potential ( V ) and difference between equilibrium freezing points (0) of the solution and pure water we used either of two platinum resistance thermometers, one of which had been calibrated in the Petroleum Research Laboratory a t Carnegie Institute of Technology. Measurements with the platinum resistance thermometers were made with a Leeds and Northrup G-2 Mueller bridge and HS galvanometer. It was found that the results of the calibration experiments could be fitted to an equation of the form
e = uv + Z I V ~
so that the calibration had to be checked periodically. and 2.8 X Typical values of a and b were 3.87 X respectively, with V expressed in microvolts. For small temperature changes we thus have a sensitivity of 0.0004'/pv, compared to the sensitivity of 0.0005'/pv obtained by Scatchard and Prentiss' with 48 thermocouple junctions. In application of the equilibrium method of determining freezing point depressions it is necessary to determine the concentration of solute in the solution in equilibrium with ice. Concentrations of KC1 and BHCl were determined conductometrically. A Leeds and Northrup Type 4666 Jones bridge with a General Radio Co. Type 1323A tuned amplifier and null detector and Type 1302A oscillator was used for the conductance measurements. A dipping-type conductivity cell was immersed in a bath whose temperature was held constant to within *0.005'. The absolute temperature was 298.15 rt 0.05'K. Because of the slight hydrolysis of betaine, concentrations of reasonably concentrated solutions could be determined conductometrically. Determinations of the same accuracy could be obtained from conventional chemical analysis of equilibrium solutions. For dilute solutions, however, neither conductivities nor chemical analysis for nitrogen yielded adequately determined concentrations. In some of our experiments with dilute solutions we separated the ice from the equilibrium solution immediately after measuring the potential leading to the desired 0. Since the concentrations and amounts of solutions put into the freezing point dewars were known, determination of
(1)
The values of a and b in (1) changed slightly with time, The Journal of Physical Chemistry
Figure 1. Circuit diagram for apparatus for determination of freezing point depressions. Each T represents a thermistor. One thermistor wm immersed in each freezing point cell.
(1) G. Scatchard and 9. S. Prentiss, J. Am. Chem. Sac., 55, 4355 (1933).
CRYOSCOPIC AND CALORIMETRIC INVESTIGATIONS OF BETAINE
the ma.sses of ice formed permitted calculation of the concentrations of the equilibrium solutions. It had also been noted earlier that equilibrium concentrations of all KC1, BHCl, and concentrated betaine solutions were 1.0 f 0.3y0 greater than the concentration of the corresponding initial solution. concentrations of some of the dilute eauilibrium solutions of betaine were obtained from initial concentrations by applying this factor. Concentrations obtained from mass of ice formed as described above were 1.0 It 0.2% greater than initial concentrations for dilute solutions of betaine. I n order to test our apparatus, we measured the freezing point depressions (e)for three solutions about 0.01 m and three solutions about 0.10 m in KC1 and compared our results with those interpolated from the data of Scatchard and Prentiss.' For the three 0.01 m solutions with 8 0.036', the largest discrepancy between our results and those of Scatchard and Prentiss was 0.00012°. The average discrepancy amounted to 0.00010~. For the three 0.10 m solutions with 8 g 0.348', the average discrepancy was 0.0007'. We conclude that uncertainties in our 8 values range from O.OO0lo for dilute solutions to 0.001' for more concentrated solutions. The calorimeter used is patterned after one previously described,2 except that a Mueller G-2 bridge and HS galvanometer have been used with a nickel wire resistance thermometer for temperature measurements. Also, the resistance thermometer and calibration heater are contained in a glass spiral filled with paraffin oil rather than wound on a silver cylinder. All of the calorimetric work reported here was carried out with 950 ml of water or solution in the calorimetric dewar a t 25.0 f 0.2'. Highest purity betaine hydrate and betaine hydrochloride were obtained from Fisher Scientific Co. Betaine was obtained from K & K Laboratories, Inc. Kjeldahl analysis of the betaine hydrate yielded 99.82% of the theoretical amount of nitrogen. Betaine hydrochloride was analyzed by precipitation of silver chloride and was found to contain 99.84% of the theoretical amount of chloride.
Results and Discussion The smoothed results of the freezing point depression measurements on solutions of betaine are given in I in the Of j = - e/1*860mfwhere e is the freezing point depression, m is the molality, and 1.860 is t h e value recommended by Pitzer a i d B r e ~ e r . The ~ activity coefficients of aqueous betaine have been calculated from the equation
321
-In y = j
+- fm
. n
fdm m
Contributions from higher order terms are negligible for solutions more dilute than 0.5 rnn3 We estimate that uncertainties (mostly due to uncertainties in Table I: Smoothed j Values and Activity Coefficients for Betaine in Aqueous Solution at oo Molality
-j
Y
0.005 0.010 0.025 0.050 0.075 0.100 0.200 0.300 0.400
0.003 0.006 0,012 0.021 0.027 0.031 0.046 0.058 0.064
1.007 1.011 1.025 1.048 1.061 1.076 1.120 1.160 1.185
equilibrium concentrations) in our reported y values range from a maximum of It0.03 at m = 0.4 to f 0.01 a t m = 0.1. The only other activity coefficients for betaine that we know of are those determined isopiestically at 25' by Smith and Smiths4 ~
Table 11: Freezing Point Depression Data for Betaine Hydrochloride in Water Moles of BHCl/kg of water
0.0100 0.0200 0,0250 0.0350 0.0500 0.0800
e, o c
Ks X 101
0,0486 0.0924 0.1142 0.1544 0.2127 0.3261
1.34 1.51 1.70 1.55 1.39 1.46
The smoothed freezing point depression data for aqueous solutions of betaine hydrochloride are given in Table 11. We interpret these data in terms of the equilibrium constant for the process represented by eq 3 BH+(aq) = H+(aq)
+ Bbq)
(3)
(2) W. F. O'Hara, C. H. Wu, and L. G. Hepler, J. Chem. Educ., 38, 519 (1961). (3) G. N. Lewis and M. Randall, "Thermodynamics," 2nd ed, revised by K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., I ~ ~ .N~~ . Yo&. N. y.. 1961. (4) P. K. Smith and E. R. B. Smith, J . Biol. Chem., 132, 57 (1940).
Volume 70, Number 2
Februarv 1966
J. C. AHLUWALIA, F. J. MILLERO, R. N. GOLDBERG, AND L. G. HEPLER
322
If solutions of betaine hydrochloride were ideal, the freezing point data could be used directly to obtain the degree of dissociation of BH+(aq) and thence the desired equilibrium constant. Since total concentrations of H+(aq) and CI-(aq) ions in the solutions for which data are given in Table I1 range from about 0.02 to 0.16 m, we know that the solutions are sufficiently nonideal that the simplest calculation cannot be used. We have calculated values of the equilibrium constant for reaction 3, designated K 3 , from the freezing point depression data in Table I1 by first assuming that
e = i . 8 6 0 ( ~ )+ ei
(4)
The first term on the right of this equation represents the contribution of B(aq) to the observed freezing point depression (0), on the assumption (supported by the results given in Table I) that the behavior of B (as) in these very dilute solutions is nearly ideal. Since we know the concentration of Cl-(aq) in the solutions, we also know the sum of concentrations of H+(aq) and BH+(aq). The contribution of all of these ions to the freezing point depression is represented by 0i and taken equal to the observed' evalues for KCl(aq) a t the same concentrations. Insertion of appropriate values of 0 and 8 i in eq 4 permits calculation of the concentration of B(aq), represented by (B). We see from (3) that (B) = (H+). Subtraction of (B) values from moles of BHCl/kg gives corresponding (BH+) values. Now, assuming that the ratio of activity coefficients for H + and BH+ is unity, we calculate Ka values from the simple relation (H+)(B)/ (BH+) with the results shown in Table 11. The average is K 3 = 1.49 (av dev = 0.08) X We estimate that the total uncertainty in this equilibrium constant is about twice the average deviation and take at273'K. K S = (1.5 f 0.2) X Conductivity measurements on solutions of BHCl lead to K 3 = (1.50 0.06) X lod2a t 298OK. Earlier work5led to K 3 = 1.46 X also a t 298'K. Heats of solution of betaine and betaine hydrate are reported in Tables 111 and IV. Uncertainties indicated in A H o values include estimated contributions from extrapolation to infinite dilution and from possible sample impurities. Combination of these heats yields AHbO = -0.58 f 0.1 kcal mole-' for
*
B(c)
+ HzO(liq) = B.HzO(c)
(5)
Table 111: Heats of Solution of Betaine Hydrate in Water Molea of B * Hz0/950 ml of HzO
0.00979 0.01137 0.01451 0.01766 0.02101 0.02279 0.03299 AH" = 1.76 k 0.06 kcal mole-'
Table IV:
The Journal of Physieol Chemistry
1.74 1.75 1.72 1.74 1.71 1.67 1.64
Heats of Solution of Betaine in Water Moles of betaine/95O ml of H20
k0a1
mole-'
0.01819 1.13 0.02504 1.20 0.03159 1.20 AH" = 1.18 k 0 . 1 kcalmole-1
Table V: Heats of Solution of Betaine Hydrochloride in Water Moles of BHC1/950 ml of H20
4H, kcal mole -1
0.00566 0.00985 0.01425 0.01714 0.02024 0.02366 0.02677 0.03301
6.23 6.23 6.22 6.23 6.21 6.20 6.20 6.19
represented by the following equations in which m and m' indicate concentrations
+ CI-(m') BHCl(c) = B(m) + H+(m) + Cl-(m) BHCl(c) = BH+(m')
AH6 AH,
(6)
(7)
Calculations similar to those carried out earlier6 for sulfamic acid permit separation of the total measured AH values into AH values for reactions 6 and 7. With the assumption that heats of dilution of (BH+ H+) C1- are the same as those' for H + C1- in dilute solu-
+
~
Heats of solution of betaine hydrochloride in water B'HC1 are presented in When dissolves in water, processes take place that may be
4H,
kcal mole -1
+
+
~~
(5) C. A. Grob, E.Renk, and A. Kaiser, Chem. Ind. (London), 1222 (1956). (6) H. P. Hopkins, Jr., C. H. Wu, and L. G. Hepler, J. Phya. Chem., 69, 2244 (1965).
CRYOSCOPIC AND CALORIMETRIC INVESTIGATIONS OF BETAINE
tions (0.005-0.033 m), we also obtain standard heats for reactions 6 and 7 for which we report AHBO = 6.37 kcal mole-' and AH7' = 6.28 kcal mole-'. Subtraction of AHeo from AHTO gives AH3' = -0.09 kcal mole-' a t 298OK for the ionization of BH+(aq) shown in (3). Heats of solution of BHCl(c) into dilute aqueous NaOH are presented in Table VI for the reaction BHCl(c)
+ OH-(aq)
+ Cl-(aq) + H2O
(8)
Combination of the data in Table VI with those in Table V as previously described6 leads to the heats of neutralization referring to the process
+ OH-(aq)
= B(aq)
+ H2O
AH,
(9)
and reported under AH, in Table VI. In order to obtain a standard heat of neutralization to be represented by AH,' we estimate heats of dilution from known ~~~
~~~~~~
AG30 = 2.50 kcal mole-' from the ionization constant to obtain AS3' = -8.7 cal deg-' mole-' for the entropy of ionization of BH+(aq) a t 298OK according to (3)* Combination of dAGo/dT = - A S o with dASo/dT = ACpo/T leads to
ACpo = (AGO298
- A G O 2 7 3 + 25As02ss)/ (25
=
B(aq)
BH+(aq)
323
~
Table VI: Heats of Solution of Betaine Hydrochloride in 0.0515 m NaOH Moles of BHC1/950 ml of s o h
koa1 mole -1
AH*, kcal mole -1
0.00892 0.01372 0.01387 0.01432 0.02614
7.18 7.24 7.23 7.25 7.20
-13.38 -13.50 -13.49 -13.53 -13.37
AHs,
heats for 1:l electrolyte^.^ The result is AH,' = -13.40 kcal mole-'. Combination of this value with the heat of ionization of waters gives AH," = -0.06 kcal mole-' for the ionization of BH+(aq) at 298OK as in (3). For the heat of ionization of BH+(aq) we adopt an average AH3' = -0.08 kcal mole-' and combine with
+ 273 In 273/298)
(10)
Inserting our data for the ionization of BH+(aq) as in eq 3 leads to ACpo Gi -7 cal deg-I mole-' for this process. Recent investigations by Ives and Marsdeng call renewed attention to the importance of ACpo data for understanding solute-water interactions. These workers and Kinglo have pointed out the difficulties and uncertainties associated with calculating ACpo values from equilibrium constants a t several temperatures. We suggest that extension of the method employed here to calorimetric determination of heats a t several temperatures along with determination of equilibrium constants a t several temperatures can reduce the uncertainties in derived ACpo values enough SO that it will prove possible to make definite statements about variation of ACpowith temperature.
Acknowledgment. We are grateful to Niss Willis Gelbart for help with the conductivity measurements and to both the National Science Foundation and the National Institutes of Health for financial support of this research. (7) "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. 5. Government Printing Office, Washington, D. C., 1952. (8) J. Hale, R. M. Iaatt, and J. J. Christensen, J . Phys. Chem., 67, 2605 (1963); C. F. Vanderzee and J. A. Swanson, ibid., 67, 2608 (1963). (9) D. J. G. Ives and P. D. Marsden, J . Chem. SOC.,649 (1965). (10) E. J. King, "Acid-Base Equilibria," Pergamon Press, New York, N . Y., 1965; see especially p 194.
Volume 70,Number 3 February 1966
