Specific heat of binary liquid mixtures near the critical mixing point

Klein, H.; Woermann, D.

doi:10.1002/bbpc.19750791203

Cited by 32 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As a consequence, the composition of the mixture of isobutyric acid + water is uniquely determined by specifying the mass fraction, w , of water; hence, one density variable is held fixed. This view is consistent with the experimental behavior of the isobaric heat capacity, C P ,w = T (∂ S /∂ T ) P ,w , which in the case of both acidic and basic binary liquid mixtures has been observed to diverge weakly as a function of temperature in the critical region. Here, S is the entropy, which is a density .…”

Section: Resultssupporting

confidence: 89%

Reaction Kinetics and Critical Phenomena: Iodination of Acetone in Isobutyric Acid + Water near the Consolute Point

Baird

2009

J. Phys. Chem. A

View full text Add to dashboard Cite

The rate of iodination of acetone has been measured as a function of temperature in the binary solvent isobutyric acid (IBA) + water near the upper consolute point. The reaction mixture was prepared by the addition of acetone, iodine, and potassium iodide to IBA + water at its critical composition of 38.8 mass % IBA. The value of the critical temperature determined immediately after mixing was 25.43 degrees C. Aliquots were extracted from the mixture at regular intervals in order to follow the time course of the reaction. After dilution of the aliquot with water to quench the reaction, the concentration of triiodide ion was determined by the measurement of the optical density at a wavelength of 565 nm. These measurements showed that the kinetics were zeroth order. When at the end of 24 h the reaction had come to equilibrium, the critical temperature was determined again and found to be 24.83 degrees C. An Arrhenius plot of the temperature dependence of the observed rate constant, k(obs), was linear over the temperature range 27.00-38.00 degrees C, but between 25.43 and 27.00 degrees C, the values of k(obs) fell below the extrapolation of the Arrhenius line. This behavior is evidence in support of critical slowing down. Our experimental method and results are significant in three ways: (1) In contrast to in situ measurements of optical density, the determination of the optical density of diluted aliquots avoided any interference from critical opalescence. (2) The measured reaction rate exhibited critical slowing down. (3) The rate law was pseudo zeroth order both inside and outside the critical region, indicating that the reaction mechanism was unaffected by the presence of the critical point.

show abstract

Section: Resultssupporting

confidence: 89%

Reaction Kinetics and Critical Phenomena: Iodination of Acetone in Isobutyric Acid + Water near the Consolute Point

Baird

2009

J. Phys. Chem. A

View full text Add to dashboard Cite

show abstract

“…Especially in the vicinity of the critical temperature the turbidity change 6a/6T is big enough that in principle it is possible to work with smaller temperature-jump amplitudes than 6T Y 0.05 K. For the calculation of 6T approaching T, closely (T -T, < 0.1 K) it is necessary to take into account that the critical part of specific heat of the mixture has a logarithmic singularity [20]. show the phenomenon of electro-luminescence.…”

Section: Resultsmentioning

confidence: 99%

Temperature‐Jump Experiments with a Binary Critical Mixture Near the Critical Temperature

Woermann

1976

Ber Bunsenges Phys Chem

Self Cite

View full text Add to dashboard Cite

The time course of turbidity of critical isobutyric acid/water mixtures is measured after perturbing the internal equilibrium of the mixture by a small temperature jump (e.g. 6T z 0.05 K). The experiments are carried out as function of the temperature distance from the critical temperature (0.1 K < T -T, < 0.6 K). A mechanism for the relaxation of turbidity change is proposed having a relaxation time of the order of 5'D-l with < = SO^-" and D = DocY (< = correlation length of concentration fluctuations, D = mutual diffusion coeficient, v = 213, E = (T* -T,)/T,, T* = T + 6T/2). The experimental data are in qualitative agreement with the proposed mechanism.Die zeitliche Anderung der Turbiditat von Isobuttersaure/Wasser-Mischungen kritischer Zusammensetzung wird untersucht, nachdem das innere Gleichgewicht der Mischung durch einen kleinen Temperatursprung (z. B. 6T z 0,05 K) gestort wurde. Die Experimente werden als Funktion der Temperaturdifferenz von der kritischen Temperatur (0,l K < T -T, < 0,6 K) durchgefiuhrt. Es wird ein Relaxationsmechanismus fur die Turbiditatsanderung vorgeschlagen, der eine Relaxationszeit in der GroBenordnung <' D-' ergibt mit ( = tot-" und D = DocY (5 = Korrelationslange der Konzentrationsfluktuation, D = wechselseitiger Diffusionskoeffizient, v = 213, E = (T* -T,)/T,, T* = T + &T/2). Die experimentellen Ergebnisse sind in qualitativer obereinstimmung mit dem vorgeschlagenen Mechanismus.I n measuring the specific heat of binary liquid mixtures of critical composition in the vicinity of the critical temperature of phase separation it is of interest t o know the relaxation time for reestablishing the internal equilibrium of a mixture after perturbing the equilibrium by a small change of temperature. To study this question temperature-jump experiments with a binary liquid mixture with an upper critical point are carried out. A mixture of critical composition is kept a t a temperature T slightly above its critical temperature T,(T -T, < 1 K) at which the system shows critical opalescence. Then the temperature of the mixture is increased by a small temperature j u m p ST(0.05 K 5 6T 5 0.21 K). This is accomplished by applying a high voltage heating pulse to the mixture. The temperature j u m p causes a delayed decrease of critical turbidity which is observed as function of time.The experiments are carried out with the system isobutyric acid/water which has enough electrical conductivity so that temperature jumps with a heating time constant of less than 50 ps can be produced. This time is small compared with the time of relaxation of the critical turbidity. Temperature-jump experiments under pressure have been used t o study the kinetics of phase separation in ternary liquid mixtures with miscibility gap [l]. Theoretical SectionThe critical turbidity of a binary critical liquid mixture near its critical temperature in the one phase region is caused by large local concentration fluctuations with long-range correlation. Away from the critical temperature the correlation length < of concentrati...

show abstract

“…For the mixtures in this work, (UCST, LCSP) case, (dT/dp) c > 0 and then B + will be positive for all of them. Available literature values of x þ 0 for the (MeOH + n-C 7 ) 42 and (EtOH + n-C 12 ) 27 mixtures were combined with their T c and (dT/dp) c (see Tables 2 and 5) to yield their A + , B + , and C + . The results thus obtained are listed in Table 6.…”

Section: Test Of Prigogine and Defay's Equationmentioning

confidence: 99%

Two ways of looking at Prigogine and Defay's equationElectronic supplementary information (ESI) available: Sources of vE(x,T) and hE(x,T) data. See http://www.rsc.org/suppdata/cp/b2/b200292b/

Rebelo

Najdanovic‐Visak

Višak

et al. 2002

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

In the search for understanding of several types of abnormal thermodynamic behaviour in the vicinity of critical lines of binary liquid mixtures, we have revisited an apparently forgotten relationship between the pressure dependence of the critical temperature and the second derivatives with respect to the composition of the volumetric and enthalpic properties of the mixture. We refer to an equation originally developed in the fifties by Prigogine and Defay and soon afterwards analysed by others. Under some restrictive assumptions, the T-p slope of the critical locus can simply be inferred from the ratio between v E and h E . The interest and usefulness of this approximate relation is self-evident. Values for any one of the three properties involved,(dT/dp) c , v E or h E , can be assessed based on the availability of the other two. Moreover, the amplitude of the divergence of thermodynamic response functions to criticality are intimately associated with the slope of the critical locus. A link between critical behaviour and solution excess properties is thus established. For instance, double critical points tend to occur if one of the excess properties changes its sign as the temperature or pressure is varied. In this work, we have started a detailed study of the practical limits of validity of the approximate relation. Five binary liquid mixtures were tested, all of them sharing a UCST/LCSP-type of phase transition. Although, from a theoretical perspective, the original second-derivatives approach should perform better, in practice, the direct ratio of the excess properties constitutes a superior strategy for obtaining (dT/dp) c values. The underlying reasons for this are discussed in detail. The T-p critical slope is normally found to play a secondary role in assessing the critical amplitudes of diverging thermodynamic functions.

show abstract

Specific heat of binary liquid mixtures near the critical mixing point

Cited by 32 publications

References 17 publications

Reaction Kinetics and Critical Phenomena: Iodination of Acetone in Isobutyric Acid + Water near the Consolute Point

Reaction Kinetics and Critical Phenomena: Iodination of Acetone in Isobutyric Acid + Water near the Consolute Point

Temperature‐Jump Experiments with a Binary Critical Mixture Near the Critical Temperature

Two ways of looking at Prigogine and Defay's equationElectronic supplementary information (ESI) available: Sources of vE(x,T) and hE(x,T) data. See http://www.rsc.org/suppdata/cp/b2/b200292b/

Contact Info

Product

Resources

About