Entropy versus temperature data

Entropy versus temperature data give values for 0S, so values for g can be obtained from Equation 10.3. These values depend on valence electron densities just as the elastic stiffnesses do. 

Make a rough, qualitative plot of the standard molar entropy versus temperature for methane from 0 K to 298 K. Incorporate the following data into your plot mp = —182°C bp = —164°C S° = 186.2 J/(K mol) at... 

Entropy versus temperature graphs such as Figure 19.12 can be obtained by carefully measuring how the heat capacity of a substance aoo (Section 5.5) varies with temperature, and we can use the data to obtain the absolute entropies at different temperatures. (The theory and methods used for these measurements and calculations are beyond the scope of this text.) Entropies are usually tabulated as molar quantities, in units of joules per mole-kelvin (J/mol-K). 

Figure 15. Plot of the excess entropy versus the reduced density for three different temperatures. The solid line represents the results from the BB approximation conjugated with the direct formula of Lee, while the open circles correspond to the Johnson et al. [34] data. The dash line stands for the pair contribution S to the excess entropy defined by Eq. (85). Taken from Refs. [69,70],...

Compute entropy change between 18.3 K andfusion temperature. Plot the given experimental data on the crystal heat capacity versus temperature in kelvins and evaluate the integral (the B term... 

The phase diagram of transition temperature versus a or alkyl chain length is shown in fig. 5.2.4. There is broad agreement with the trends in thermodynamic data, though the theoretical A-N transition entropy versus is somewhat higher than the observed values (fig. 5.2.5). To... 

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

To illustrate the type of analysis that is involved we exhibit a representative set of heat capacity data in Fig. 1.20.2 for oxygen, as a plot of CP versus log T this representation is useful for the direct calculation of the entropy of oxygen from the area under the curves. Note that the element exists in three allotropic modifications in the solid state, with transition temperatures near 23.6, 43.8, and 54.4 K, the last being the melting point of solid phase I. The boiling point of liquid oxygen is near 90.1 K. An extrapolation procedure was used below 14 K. 

Use the data in Table 6-9 to calculate the enthalpy and entropy of reaction for dissociation of acetic acid using (a) Equations (4) and (5) and (b) the temperature dependence of of Equation (7) by graphing In Kg versus 1/T. 

Typical variable temperature spectral data for ns.(5) and (6) are shown in Figure 2. This data can be used to calculate equilibrium constants and plots of In versus 1/T are shown in Figure 3. Enthalpies and entropies of binding csdculated from these plots are collected in Table I. 

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