IOSIZATION OF TRIMETHYLAMINE-& IN WATER
1559
The Secondary Deuterium Isotope Effect in the Ionization of Trimethylamine-& in Water by D. Northcott and R. E. Robertson Publication N o . 10747 from the Division of Pure Chemistry, National Research Council, Ottawa, Canada (Receiced November 7, 1 9 6 8 )
The temperature dependence of the ionization constant of trimethylamine and trimethylamine-dg have been determined in water at 5' intervals over the temperature range 0-45' by a conductance method. The total isotope effect is shown to be due to &AH-a result consistent with a simple zero point energy explanation. The temperature coefficient of the heat capacity of ionization was shown to be small and positive. Many examples of secondary deuterium isotope effects have been reported for since Lewis and Boozer4 and Shiner6 recognized this effect. A lesser number of examples are available involving equilibria. By far the greater number of secondary isotope effects have been defined in terms of rate ratios or equilibria ratios determined a t one temperature only. Thus, although the sources of such effects were variously attributed to hyperconjugative inductive eff ects,1,8and nonbonded interaction^,^ in each of these proposals the secondary deuterium isotope effect could be related to an explanation based on differences in zero point energies. It follows that experimental confirmation of such a source should be evident in enthalpy differences where these could be measured with sufficient accuracy. It was something of a surprise, therefore, to find that rate change caused by the secondary @-deuterium isotope effect associated with the hydrolysis of 2-bromo- and 2-methanesulfonatepropane could be accounted for, largely, by a change in the entropy of activation, The corresponding effect in the hydrolysis of t-butyl chloride-ds1l was found to be almost entirely in the enthalpy of activation &AH*-a result conforming to normal expectations. Wolfsberg and Stern12 showed that it was possible to postulate a combination of reasonable frequency changes for the 2-X-propane system which would give a secondary isotope effect essentially temperature independent but still based on accepted theory.l3 Whatever the explanations it was clear that a determination of the temperature dependence of such isotope effects could provide evidence of previously unsuspected complexities associated with kinetic processes. It was natural to question whether similar apparently anomalous results would be obtained for secondary deuterium isotope effects associated with unambiguous equilibria. The work reported here was undertaken to determine whether in a simple acid-base equilibrium, where identifiable species are involved (as opposed to the transient species of the kinetic process) the secondary deuterium isotope effect could be accounted for in terms of zero
point energy differences alone or whether some appreciable entropy effect would be observed. As the aim was to determine the difference in the derived terms AH and A S for the deuterated and undeuterated species, respectively, the absolute value of the isotope effect was of importance. For this reason the methylamine series was chosen for study because it seemed likely' that larger effects could be obtained in that series compared with the corresponding effect in the carboxylic acid series. While suitable methods were being developed for the amine problem, the careful work of Gary, Bates, and Robinson provided a partial answer to the above speculation for the acetic acid systerns.l4
Experimental Methods and Results Economic considerations required that a system be designed which would permit the determination of the requisite values of AH and A S over the available range of temperatures using 5-10 g of the amine. At each temperature, a sufficient number of determinations were required over a range of concentrations to permit a determination of the ionization constant at infinite dilution. All determinations must be made in a closed system. I n our view, these limitations predicated the determination of the ionization constant by a con(1) E.A. Halevi, Progr. Phys. Org. Chem., i, 109 (1963). (2) E. R. Thornton, Ann. Rev. Phys, Chem,, 17, 349 (1966). (3) P.Laszlo and Z . Welvart, Bull. SOC.Chim. Fr., 2412 (1906). (4) E. 8. Lewis and 0.E. Boozer, J . Amer. Chem. Soc., 74, 6306 (1952). (5) V. J. Shiner, Jr., ib$d., 75, 2925 (1953). (6) E.8. Lewis, Tetrahedron, 5 , 143 (1959). (7) V. J. Shiner, Jr., ibid., 5 , 243 (1959). (8) E.A. Halevi, ibid., 1, 174 (1957). (9) L. 8. Bartell, J . Amer. Chem. Soc., 8 3 , 3667 (1961). (10) K. T. Leffek, R. E. Robertson, and 8 . E. Sugamori, Can. J. Chem., 39, 1989 (1961). (11) L. Haaka. A. Queen, and R. E. Robertson, J. Amer. Chem. SOC., 87, 161 (1965). (12) M.Wolfsberg and M. J. Stern, Pure Appl. Chem., 325 (1964). (13) J. Bigeleisen and M. Wolfsberg, Advan. Chem. Phys., 1, 15 (1958). (14) R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 69, 2750 (1965). Volume 75,Number 6 Mag 1969
D. NORTHCOTT AND R. E. ROBERTSON Table I: Values of A. for Trimethylamine Hydrochloride in H 2 0 for a Series of Temperatures Temp, "0
Ao(TMA.HCl), cms ohm-] mol-1
0.119 0.126 1.600 1 607 2.825 2.824 10.174 IO. 178 20.377 20.384 30.130 30.143 40.172 40.172 45.532 45.527
65.90 65.74 69.05 68.78 71.55 71.40 87.33 87.31 111.6 111.5 136.5 136.5 163.9 163.7 177.9 177.8
I
Table 111: Calculated Values of the Thermodynamic Functions"from the Temperature Dependence of Kb for the Ionization of Trimethylamine and Trimethylamine-d9in Water Temp, OC
a
+
0.022 0 024 5.163 5.164 10 063 10.064 15.032 15.037 20.304 20 305 25.131 25.153 30.145 I
I
I
35.17 40.184 40.187 45.582
0
4.149 4.155 5.173 5.177 6.234 6.234 7.424 7.423 8.638 8.638 9.763 9.756 10.938 10.98 12.047 12.093 13.210 13.339 14.291
7 R a N = trimethvlamine-T , oc
0,108 0.114 2.821 2 823 5.086 I
10.178 15.104
The Journal of Physical Chsmialry
kb
x
108
2.599 2.578 2.943
AG,
calimol
0 25 50
5732i2.2 6936f76 5722 f 2 4680 f 25 5901 rt 4 2424 f 104
0 25 50
5476f2 5469 rt 1 5648 f 4
4 . 4 f 0 . 2 7 -90rt3.5 -3.50 f0.08 -90 f 3.5 -10.8 f0 . 3 -90 f 3.5
6617f56 4415 rt 22 2212 f 83
4.17f0.2 -3.54 z t 0.07 -10.6 f0 . 3
-88f2.7 -88 =!z 2 . 7 -88 + 2.7
Concentration, molality units.
purified nitrogen and introduced into the reservoir under a positive pressure of nitrogen. (The details of making up the solution and the manipulation and construction of the conductance cell and the measuring system are given in a recent publication.16) The conductance cell was likewise filled with a known amount of distilled water and thermostated (A!!' = O.O0lo), and a connection was established with the titrimeter. When thermal equilibrium was attained, successive known increments of the amine solution were introduced and corresponding values of the conductance were determined. The usual precaution of checking earlier data at the end of a series was taken. Details of the apparatus, the calculations, and ancillary information are given in full in the paper by Van der Linde, Northcott, Redmond, and Robertson16 and need not be repeated here. Eastman grade trimethylamine hydrochloride was recrystallized twice from ethanol giving long white needles which were dried under vacuum for 7 hr a t 75'. The trimethylamine was released with KOH under purified nitrogen and subjected to bulb-to-bulb distillation, the center cut being used to make up the master solution. Mass spectral analysis showed that this sample and the corresponding one made from the -ds analog, as supplied by Merck Sharp and Dohme of Montreal, to be pure. Because it was not found satisfactory to determine A. and Ki simultaneously16using the Ives" or Shedlovsky method,18 A0 values for trimethylamine hydrochloride were determined in a preliminary experiment for a
i..: {z; 4.776 4.780
20.311 25.025
!.E6.363 :
30.036 30.038 35.040 35.044 40.383 40.358 45.014
7.189 7.178 7.985 7.979 8.838 8.831
Concentration units are moles per liter.
As,
cal/(mol deg)
Trimethylamine-&
Table 11: Ionization Constant for the Equilibrium0 RaN HzO $ RaNH+ OHc.-R IN = trimethylamine-dn T,"0 K b X 10s
AH, cal/mol
Trimethylamine
ductance method. The restriction of a closed system implied some kind of a dilution technique. The system finally usedlS8 consisted of a modified double stirred cell of about 180-ml capacity joined by a capillary t o a precision syringe of about 10-ml capacity,16J6 the latter being alternately filled from a reservoir or discharged into the cell incrementally. Sufficient amine solution for the complete determination (about 100 ml of 0.2 M ) was made up in carefully distilled water (conductance < 5 X 10+ ohms at 10') under
+
AG, cal/mol
(15) (a) Preliminary results published by Van der Linde and Robertson1Sb and unpublished results on trimethylamine by I. Ross and R. E. Robertson were determined in a conductance cell which differed in important details from the Anal design.16 (b) W. Van der Linde and R . E. Robertson, J. Amer. Chem. SOC.,8 6 , 4505 (1964). (16) W. Van der Linde, D. Northcott, W. A. Redmond, and R. E. Robertson, Can. J. Chem., 47, 279 (1969). (17) D.J. (3. Ives, J. Chem. Soc., 731 (1933). (18) T. Shedlovsky, J . Frankl6n Inst., 2 2 5 , 739 (1968).
IONIZATION OF TRIMETHYLAMINE-& IN WATER
1561
Table IV: A Comparison of the Values of Thermodynamic Constants from the Temperature Dependence of &, in Terms of Different Concentration Units at 25”
Kba
AGO,cal/mol AHo, cal/mol
AS, cal/(mol deg) ACD, cal/(mol deg)
Molarity ( c )
Molality ( m )
Mole fraction ( N )
6.381 x
6.375 X 10-6
1.150 x 10-6 8101.7 f 1 . 7 4680 f25 -11.48 f 0 . 0 8 -90 f3 . 5
5722.0 f 1.7 4680 f 25 -3.5 f 0.08 -90 f 3.5
5723.8 f 1 . 7 4641 f 26 -3.63 f0.08 -92 f 3 . 6
Kb values are related as follows pKb(c) = pKb(m) pKb(m) = pKb(N) where
- log do
- log 0.001w,
W. = molecular weight of H20.
series of temperatures using the same system but substituting in the reservoir a solution of a known concentration of the amine salt. The resulting values of A0 obtained from an A us. extrapolation are given in Table I. By combining these values with the corresponding A0 terms for C1- and OH- according to the Kohlrausch equation,lg the corresponding values of A. for trimethylammonium hydroxide for each temperature were obtained as required for the calculation of Ki. These data can be fitted to an equation of conventional form
di
Ao(TMA+ OH-)
= 149.979
+ 2.0724(T - 25)
+ 0.009541(T - 25) * - 0.00009384 ( T - 25)3 thus permitting interpolation of values a t other temperatures.
Determination of Kb
R l n K b = - - AGe + A H o ( ~ - ~ )
After the necessary values of A0 for the trimethylammonium hydroxide were obtained, the syringe was cleaned, dried, and reloaded as before with the amine solution, taking the usual precautions to exclude COz. A new series of concentration-resistance readings was determined, and these data were fitted to the Shedlovsky-Kay equa,tion20 1
-
AS(z)
1 A0
where X(2)
straight line, the slope of which is 1/KbAo2 and the intercept l/Ao, the value of ho being that determined in the previous experiments. Values of the classical dissociation constant, Kb for trimethylamine and the -ds analog calculated by the above method are given in Table 11. The data in Table I1 are reported in terms of the conventional concentration units of moles per liter. This raises difficulties2I when an attempt is made to interpret temperature derivatives; hence, these values were converted into corresponding values in terms of molality according to the relation pKb(c) = pKb(m) - log do where (c) and ( m ) refer to molarity and molality, respectively, and do is the density of pure water at the particular temperature. The data for Table I1 converted into molal concentration units were fitted a t reference temperature 0 by a least-squares method to an equation of the form
= 1
-k
CAb’(z)f” KAo2
+ + 2
*22
0
following the technique given by Clarke and GlewZ2and Table v: Valuesa of PKbh for Trimethylamine and Trimethylamine-d, (Molality Scale)
Temp,OC
0 25 50
and a
-Iogf=a+i;
a =
3.649 x 106 (DT)8‘2
and
x = AX(Z)/A~ A linear least-squares analysis of these data gives a
--TrimethylaminePKb PKbh
4.5888 4.1952 3.9824
r-Trimethylamine-dp-7
10.3547 9.8013 9.2793
PKb
PKbh
4.3825 4.0098 3.8128
10.5610 9.9867 9.4489
From four-constant equation, below.
(19) H. 9. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” 3rd ed, Reinhold Publishing C o . , New York, N. Y., 1958, p 233. (20) T. Shedlovsky and R . L. Kay, J. Phys. Chem., 60, 151 (1956). (21) R . A. Robinson, private communication. (22) E. C. W. Clarke and D. N . Glew, Trans. Faraday SOC.,62, 539 (1966). Volume 78, Nnmbsr 6 May 1069
D. NORTHCOTT AND R. E. ROBERTSON
1562 Table VI: Derived Parameters" from the Four-Constant Equation Log K b = A / T AG
AH
5477 f 1.3 5455 f0.9 5555 1
6835 f 90 4774 f 32 3255 f 72
5735 f 2 5707 f 1 5809 f 2
7317 f 110 5004 f 35 3541 f 71
+ B log T + C + DT22
AS
ACP
dAC,/dT
Trimethylamine-& 0
20 40
4.97 f0.33 -2.32 f 0 . 1 -7.34 1 0 . 2
-117 f 10 -90 f 2 -62 f 10
1 . 3 f0 . 5 1.3 f 0 . 5 1.3 f 0 . 5
-136 f 12 -94f2.4 -52 f 10
2.1 f0 . 5 2.1f0.5 2 . 1 f0 . 5
Trimethylamine 0
20 40 a
5 . 8 f0 . 4 -2.4 k 0 . 1 -7.2 f0 . 2
Molality scale.
the assumption that dAC,/dT = 0. Corresponding values of AH, AX, and AC, are given in Table 111. The agreement of the values of AC, for the two amines provides an internal check on the consistency of the data. It was gratifying to find that this value of AC, was in agreement with that determined by an emf method by Everett and Wynne-Jone~.~~ Because in all cases our values of Kb were determined from a series of concentrations varying from to 10-3 M and extrapolated to infinite dilution, the suggestion made by the above authors to account for the difference between values of Kb ( A = 0.006) determined by emf and conductive methods cannot apply here. Rather the fault may lie in the tendency of the emf method to give low values, as they recognize. However, the fact that the values of AC, derived from data by the two methods are the same within experimental error suggests that the discrepancy is probably constant with temperature. For interpolative purposes, it is more convenient to give the results of the above analysis in the form of the following equations. Trimethylamine in HZ0 : log Kb = -6902.885/T - 45.41187 log T
+ 131.32688
Trimethylamine-& in HzO : log Kb = -6705.421/T - 44.33428 log T
+ 128.18334
In Table IV we compare the values of AH, AX, and AC, at 2;' where K b is expressed in concentration units of molarity, molality, and mole fraction for trimethylamine. Values of the corresponding acid dissociation constant (Kbh) for the dissociation (CH3) 3NH+
~
(CHB)3N
+ N+
can be calculated from the relation Kb = Kw/Kbh. A series of values of PKH, are given in Table V for the two amines under discussion using values of K , determined by Harned and Robinson.24 If the assumption is made that dAC,/dT # 0 but The Journal of Physical Chemistry
rather that dzACi,/dT2 = 0 then the same procedureaa leads to the following equations where T = OK. Trimethylamine : log Kb
=
-27079'278 - 360.7242 log T T
+ 910.03952 + 0.2320247T Trimethylamine-& : log Kb =
- 19495.273/T - 244.82033 log T
+ 623.04884 + 0.14798186T
From these the corresponding thermodynamic constants can be derived. These are given in Table VI, without prejudice. The well-established hypothesis that deuterium appears to be more electron donating than protium is borne out here, the pKD > ~ K by H 0.206 pH unit a t 0' and KH/KD N 1.61 at 10'. This value may be compared to the corresponding value of 2.5 for the kinetic ratio l e H / k D for the hydrolysis of t-butyl chloride and the dganalog the inference being that the net change in the differences of { Y (C-H) - v (C-D) 1 over 9H (D) is much greater in the latter case, pointing to a considerable defect from a full charge on the quasication a t the transition state. Batts and Spinner's recently cited a body of evidence supporting the hypothesis that a strongly electrondemanding environment tends to reduce the normal secondary deuterium isotope effect and enhance the inverse one, ie., increase rather than decrease the net double difference in frequencies. It would seem that the trend in K H / K Dfor the acid dissociation of the methylamines is a t least formally consistent with this observation, the respective values 4.5%/D; dimethylamine, being methylamine: 5.3%/D,15band trimethylamine 6.l%/D. (23) D. H. Everett and W. F. K. Wynne-Jones, Proc. Roy. SOC., A117, 499 (1941). (24) H. S. Harned and R . A. Robinson, Trans. Faraday SOC., 36, 973 (1940). ( 2 5 ) S. D. Batts and E. Spinner, J . Chem. Soc., 789 (1968).
HYDRATION NUMBERSOF ELECTROLYTES
1563
From Table 111it is reasonably certain that the major, initial indications obtained for the mono- and dimethif not the entire change is accounted for by the differylamines.I5b ence, &AH, which may be set equal to the zero point The agreement of the values of ACp for the protium energy difference. This conclusion is the same as was and deuterium analogs confirms the absence of signifireached from the temperature dependence of k ~ / k ~cant solvation differences accompanying the secondary for the solvolysis of l-butyl chloride but differs from deuterium isotope effect in this system (ref 1, p 158).
Nuclear Magnetic Resonance Determination of Hydration Numbers of Electrolytes in Concentrated Aqueous Solutions by R. W. Creekmore and C. N. Reilley Department of Chemistry, University of North Carolina,, Chapel Hill, North Carolina
27514
(Received November 1.2, 1968)
Total effective hydration numbers have been determined for a number of alkali metal salts and alkaline earth metal salts by studying the temperature-dependent proton chemical shifts of their aqueous solutions. The hydration numbers obtained for the alkali metal halides were rationalized by assuming that the cation was coordinated to four waters whereas the anions contributed little if any to the hydration number obtained. The hydration numbers for the alkaline earth metal halides were found to include both primary and secondary waters which was attributed to their larger charge-size ratio. Also studied was the effect of several anions (Cl-, Br-, C104-, and p-toluenesulfonate-) on the effective hydration number of their sodium salts. Both NaC104 and Na p-toluenesulfonate gave hydration numbers lower than NaCl and NlaBr. The decrease in the effective hydration number was explained in terms of ion pairing, which was further supported by 23Na relaxation times.
taoduction I n the past decade nuclear magnetic resonance (nmr) has proved to be valuable in studying electrolyte solutions; an excellent review has been given by Hinton and Amis.’ Proton chemical shifts of electrolyte solutions have revealed information about solvent structuring and hydrogen bonding in these solutions. Of recent interest, however, have been the studies of solvation numbers by nmr. For ions which form rather strong coordination with water such 8s Ala+, ]Be2+,and Ciaa+,the exchange of solvation water with bulk water is sufficiently slow so that separate resonances for both types of water may be observed using either “0 r e ~ o n a n c e ~ or, - ~ a t low temperature, using proton resonan~e.~ By ~ ~the addition of acetone to aqueous solutions of Mg (Clod) and Mg (NO3)2, Matwiyoff and Taube? were able to decrease the exchange rate of solvation waters, thus distinguishing the proton signals of Mg (H2O)2’+ ion from those of the bulk water st temperatures below - 70°. The exchange of solvation water for bulk waters is much faster in the case of alkali metals, and their study by the above direct methods is not feasible. However, Malinowski, et al., have shown $ha$ the temperature
effects on the proton shifts of aqueous electrolyte solutions are related to the degree of “effective” hydration.8J‘ Their method is based on the assumption that the hydration number and the chemical shift for the hydration waters do not change with temperature; hence, the observed chemical shift is a weighted average of the chemical shift of the hydration waters and the temperature-dependent shift of the bulk water. They have studied two systems [NaCl and Al(NQa)s] and report a total “effective” hydration number of 4.5 for NaCP and 13.4 for A ~ ( N Q ~ ) Since s . ~ the hydration number for the aluminum ion has been shown by direct (1) J. F. Hinton and E, 8. Amis, Chem. Reo., 67, 367 (1967),and references therein. (2) J. A. Jackson, J. B. Lemons, and H. Taube, J . Chem. Phys., 3 2 , 563 (1960). (3) R. E. Connick and D. N. Fiat, $bid., 39, 1349 (1963). (4) D. N. Fiat and 3%. E. Connick, J. Amer. Chem. Soc., 88, 4754 (1966). (5) R. E. Shuster and A. Fratiello, J . Chem. Phys., 47, 1554 (1967). (6) A. Fratiello, R. E, Lee, V. M. Nishida, and R. E. Shuster, (bid., 48, 3705 (1968). (7) N. A. Matwiyoff and H. Taube. 9.Amer. Chem. Soc.. 90, 2796 (1968). (8) E. R. Malinowski, P. S. Knapp, and B. Feuer. J. Chem. Phys., 45, 4274 (1966). (9) E,R. Malinowski ana P. 8 . Knagp, (Bid., 48, 4989 (1968).
Volume 7.9,Number 6 May 1069
