6
ANDRZEJ S. CUKROWXKI
I n a previous study,g it had been shown that a departure from normal kinetics in the reactions of certain bidentate chelating agents could be ascribed to sterically hindered chelate ring closure. The experimental evidence in support of this conclusion was that the effect mas exhibited by ions more labile than nicliel(111, namely, Co(I1) and Illn(II), but not by nickel(I1) itself. For the oligoglycines and glycylsarcosine the opposite is true; that is, reaction with cobalt(I1) is normal, while that with nickel(I1) is inhibited. The grounds for this behavior should therefore be found in the nature of the nickel(I1) chelate's structure. Without further experimental evidence, the details of this interaction remain an open question. However, the kinetic evidence leads us to the conclusion that the bonding model is somewhat different for the nickel complexes of these oligopeptides than for the cobalt complexes. It would appear that whereas bonding to the carboxyl oxygen might be of considerable importance in cobalt complexes, it plays a small role in the nickel complexes. From a molecular model of glycylsarcosine we learn that for effective bonding to the carboxyl oxygen the cobalt ion must be associated with
the peptide nitrogen rather than the carbonyl oxygen atom of the dipeptide. This model is consistent with the observation that the methyl group bound to the peptide nitrogen atom more effectively influences the rate of the formation of the bis complex for cobalt(I1) than for nicliel(I1). The kz value for niclrel(I1) is about the same for the 7 X lo3 M - 1 oligoglycines and glycylsarcosine (Icz sec-I), while for cobalt(I1) the glycylsarcosine value is significantly larger than the oligoglycine value. One further bit of kinetic evidence for a difference between the bonding in nickel peptides and cobalt peptides involves the lc2/k1ratios. This ratio is greater than unity for nicliel(I1) and the oligoglycines but less than unity for cobalt(I1) and thcse same ligands. The degree of enhancement ( k 2 / I c l ) has been shown to be strongly dependent on the nature of the ligand bonding. l 3 Aclcnotcleilgment, The authors gratefully acknowledge partial support from the Public Health Service Research Grant GAISS93-06 from the National Institute of General AIedical Sciences, Public Health Service (IC.IC.),and from the Petroleum Research Fund for Grant 29S2B (R. F. P.) N
The Diaphragm Cell Method for the Investigation of Thermal and Self-Thermal Diffusion in Liquid Electrolyte Solutions1 by Andrzej S. CukrowskP Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland Accepted and Transmitted by The Faruday Society
(November 6, 1967)
The diaphragm cell method with a magnetically operated stirring system has been adapted for the time-dependent and the stationary-state measurements of thermal and self-thermal diffusion in liquids. The phenomenological equations derived here describe the rate of change of concentrations. Formulas which allow the calculation of the activation energy from the average for the diaphragm values of diffusion and self-diffusion coefficients in polythermal and isothermal conditions have been given. Experiments with dilute aqueous solutions of NaC1, KCl, '%aCl, and Z2Na in KCl have been carried out. Diffusion and self-diffusion coefficients under polythermal conditions, activation energies, the Soret coefficients, and heats of transport are evaluated. The Soret coefficient and the heat of transport of NaCl in extreme dilution have been measured. Comparison with other experimental and theoretical results is given.
I. Introduction The method discussed here makes it possible to investigate thermal diffusion as well as self-thermal diffusion, i,e., the transport of a small amount of a labeled tracer ion under polythermal conditions, in liquid electrolyte solutions. Contrary to widely investigated T h e Journal of Physical Chemistry
thermal diffusion, 3 self-thermal diffusion in liquid electrolyte solutions has not been investigated yet. (1) This work comprises part of the P h D . dissertation of A. S.CUI+ rowski, Institute of Physical Chemistry, Polish Academy of Sciences, Warsav. (2) Institute of Basic Technical Problems, Polish Academy of Scienoes, Tvarsaw.
THERMAL AND SELF-THERMAL DIFFUSION IN LIQUIDELECTROLYTE SOLUTIONS I n the theoretical section we present the equations which describe the concentrations as functions of time and which allow us to study a polythermal process at any instant, contrary to the measurements4J performed under stationary conditions. I n the Experimental Section self-thermal diffusion as well as thermal diffusion data are presented. The apparatus used enabled us to investigate the stationary states of thermal and self-thermal diffusion as well as the rate of attainment of these states. For this reason we could use only those methods in which it is possible to measure the concentrationof radioactive ions. That is why the conductometric and optical methods and those methods in which the thermoelectric powers are measured could not be used.3 The thermogravitational method3 also is not suitable here because it is not possible to investigate the transport of the radioactive ions in the stationary state of thermal diffusion. Also electrothermal diffusion,7bs which is especially convenient for the measurements of thermal diffusion in electrolyte solutions, cannot be applied here to measure the self-lhermal diffusion of a radioactive ion in pure water because the voltage needed is too high. The diaphragm cell method seems to be the most suitable for the investigations of thermal and self-thermal diffusion. It has already been applied for thermal diff u ~ i o n , ~but J the laminar layer, which always exists in the vicinity of the diaphragm and directly affects transport processes, has not been reduced in the papers mentioned to such an extent as it has been under isothermal conditions by Stokes.6~9 That is why we tried to adapt the Stolics method to polythermal conditions.
11. The Time Dependence of Concentrations during Thermal Diffusion in the Diaphragm Cell Method The derivations will be limited to thermal diffusion in binary electrolyte solutions. The discussion of the self-thermal diffusion equations, which can be performed in a similar manner, will be given in section IV. The electrolyte discussed consists of solvent 0 and ions 1 and 2 . In the derivations to be given, the scheme of the diaphragm cell method as presented in Figure 1 will be adopted. The apparatus contains two vessels which are separated by means of a porous diaphragm. JAetthe effective cross section of the diaphragm be A and the effective average length along the diffusion path be 1. The quantities connected with the lower and upper vessels mill be denoted by the subscripts L and U, respectively. We assume that the mixing is sufficient to maintain, in each vessel, constant temperatures T L and TU and molar concentrations c t r L and c d , u (i = 0-2). In other words, temperaure and concentration gradients exist in the diaphragm only. We assume that the temperature gradient is stationary; i.e., TI, and TU are constant during the experiment. It means that the relaxation time for the temperature
7
Figure 1. Scheme of the diaphragm cell method.
change is much smaller than for diffusion processes. We want to determine now the concentrations of components in both vessels as a function of time. We shall take into account suitable boundary conditions. If we assume that the volume of the liquid in porous diaphragm is negligible
+
+
c ~ , A ( V L Vu> (i = 0-2) (1) where C ~ , A denotes the average concentration of ith C ~ , L ~ Lc t , u v u
=
component for both vessels. For molar fractions eq 1 can be presented in the form
(i = 0-2)
(2)
where
(3) where c denotes the sum of the concentrations of the ions and solvent and A is used for the average quantities for both vessels. From eq 3 we see that for dilute solutions, for which CA = CL = CU, V,’ and VU‘ are equal to VI, and VU, respectively. It is sufficient to discuss the thermal diffusion of one ion only because in binary-electrolyte solutions the two ions move together owing to electroneutrality.*O Therefore, let us further discuss ion 1 only. We assume, as Robinson and (3) H. J. V. Tyrrel, “Diffusion and Heat Flow in Liquids,” Butterworth & Co., London, 1961. (4) I
