Temperature dependence of molar

Figure 5.30 Temperature dependence of molar ellipticity at 218 nm for liposomes prepared from L-DMPC, L-DPPC (39), and L-POPC (40). Reprinted with permission from Ref. 134. Copyright 1997 by the American Chemical Society.

Temperature Dependence of Molar Absorption Coefficient of Iodine Vapor at 520 nm... 

The temperature dependence of molar conductivity, calculated from ionic conductivity determined from complex impedance measurements and molar concentrations, and the VFT fitting curves are shown Figure 5.8. The VFT equation for molar conductivity is... 

The [Fe(phen)3]3+ complex dissolved in water is known to behave as a hydrophobic ion, as demonstrated by the ion association with o- and m-benzenedisulfonate and 2,6- and 2,7-naphthalenedisulfonate ions, which was investigated by the conductivity method. Similar hydrophobic properties were also observed for trivalent [Co(phen)3]3+ and [Co(bpy)3]3+ complexes.2 In the present study, the temperature dependence of molar conductivities of [Fe(phen)3]2+, [Co(phen)3]3+, and [Co(bpy)3]3+ as well as the ion association with chloride and perchlorate ions were examined in order to elucidate the effect of the ionic charge on the hydrophobic interactions. 

The general equation of the temperature-dependence of molar specific heat is ... 

Figure 7.5 Temperature dependence of molar heat capacity at constant pressnre (p I bar) of H2O, N2, and C(graphite).

This method has the disadvantage that calculation of AG° values for temperatures different from those for which the data have been tabulated makes it necessary to employ empirical relations for the temperature dependence of molar heats, the precision of which varies — with the use of three constants — between 0.5 and 1%, which is usually insufficient for accurate work. Moreover such calculations are time-consuming. 

Fig. 186. H[Fe 2,5-0(Cl)C6H3 CH=NN=C(NH2)S- 2]. Temperature dependence of ( ). Molar heat capacity (o) measured [74S30].

Fig, 20. Temperature dependence of molar magnetic susceptibility x(T) and its inverse X (T) for the CUO3 array of Lai-xNdxCuOs. The small difference between field-cooled and zero-field-cooled data below room temperature appears to be due to a lateral displacement of the sample in the bore of the SQUID on thermal cycling after [94]... 

Fig. 4 Temperature dependence of molar conductivity of AMPS, PAMPS, and a PAMPS gel.

Suppose we prepare a solution at 20 °C by using a volumetric flask calibrated at 20 °C. Then suppose we warm this solution to 25 °C. As the temperature increases from 20 to 25 °C, the amount of solute remains constant, but the solution volume increases slightly (by about 0.1%). The number of moles of solute per liter—the molarity—decreases slightly (by about 0.1%). This temperature dependence of molarity can be a problem in experiments demanding a high precision. That is, the solution might be used at a temperature different from the one at which it was prepared, and so its molarity is not exactly the one written on the label. A concentration unit that is independent of temperature, and also proportional to mole fraction in dilute solutions, is molality (m)—the number of moles of solute per kilogram of solvent (not of solution). A solution in which... 

The ideal-gas-state heat capacity Cf is a function of T but not of T. For a mixture, the heat capacity is simply the molar average X, Xi Cf. Empirical equations giving the temperature dependence of Cf are available for many pure gases, often taking the form... 

Next we consider a molecular crystal composed of N2 molecules, (Vp = 0). Molecular N2 solids at low temperatures and low pressures are in the a structure (Pa3). Using PIMC simulations we studied the low temperature properties of N2 sohds [260] (B = 2.88 K, = 500). In Fig. 6 the temperature dependence of the molar volume is shown for our simulational as well as for experimental [289] data. We note that the classical simulations (corresponding to P = 1) lead to a nonzero slope of the volume at very low temperatures, which is in sharp contrast to the experimental behavior [289]. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

The last term in Eq. (6-32) describes the temperature dependence of the molar concentration in water, this contributes only about —45 cal mol to E at room temperature. In a strong mineral acid solution, the temperature dependence of the activity coefficient term contributes about —90 cal mol . These are small quantities relative to the uncertainty in E s-... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

There is an unfortunate consequence of replacing segment fraction by volume fraction. For given composition (weight or mole fraction), volume fraction is temperature dependent because molar volume is temperature dependent. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Figure 13.9 (a) Temperature dependence of p on the DMPC bilayer on glass (white) and silicon (black), (b) Dependence ofp on the molar fraction of a cationic DMTAP additive in the DMPC bilayer. Adapted from Ref [48] with permission. 

The temperature dependence of the molar susceptibility of a paramagnetic substance follows the Curie-Weiss law (if the magnetic field is not too strong) ... 

Temperature dependence of thermodynamic equilibrium composition of the products obtained from CH4 C02 = 1 1 (molar) mixture at atmospheric pressure. 

Fig. 15 Temperature dependence of the molar magnetic susceptibility (yM) ofCoII2MnII(PhCOO)6 (TTF—CH=CH—py)2 (white circle) with the best fitted curve full line)...

The temperature dependence of the molar magnetic susceptibility (x) of an assembly of paramagnetic spins without interaction is characterized by the Curie behavior with x = C/T where C = /Vy2( 2.S (.S + l)/3k. It is a very common situation in the organometallic chemistry of radical species when the spin density is essentially localized on the metal atom. Since, in most cases, this atom is surrounded by various innocent ligands, intermolecular interactions are very weak and in most cases are reflected by a small contribution described by a Curie-Weiss behavior, with x = C/(T 0) where 0 is the Curie-Weiss temperature. A positive value for 0 reflects ferromagnetic interactions while a negative value — the most common situation — reflects an antiferromagnetic interaction. 

Fig. 16 The temperature dependence of the inverse molar magnetic susceptibility, a, and the corresponding effective magnetic moment, b, of [Fe(HC(3,5-(CH3)2pz)3)2](BF4)2. Data obtained from [46]...

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

The effect of monomer concentration on the dependence of the DP on temperature. Further studies [12,52, 62] of the temperature dependence of the DP showed that the Arrhenius plot was approximately linear over the temperature range -5° to -78° for all concentrations of isobutene from about half-molar to undiluted monomer, and that the slope of the line increased with decreasing concentration in such a way that all the lines crossed at approximately the same temperature, -50°. This means that at -50°, the inversion temperature , the DP is independent of monomer concentration at lower temperatures it decreases, at higher temperatures it increases with increasing monomer concentration. This behaviour was found for polymerisation in methyl, ethyl and vinyl chloride as solvents. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

The contribution of the poly(Pro)II conformation to the ensemble of unordered peptides has been considered.1158 The temperature dependence of [0]222 for the peptide Ac-YEAAAKEAPAKEAAAKA-NH2 in 8 M guanidinium chloride and of poly(Lys) in water and in ethylene glycol/water (2 1) mixtures 156 was fitted to a two-state equation for a poly(Pro)II-unordered equilibrium with a temperature-independent AH and temperature-independent molar ellipticities for the two components. The peptide with a Pro at the central position is an unordered peptide, the spectrum of which has pronounced poly(Pro)II-like features at low temperatures. This fit yielded [0]222=- -9580 deg-cm2dmol 1 for the poly (Pro)II component and —5560 deg-cm2-dmol 1 for the unordered component. These values provide a method for roughly estimating the poly(Pro)II content, /Pn, of an unordered peptide from [0]222 ... 

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