Entropy values

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

The entropy value of gaseous HCl is a sum of contributions from the various transitions summarized in Table 4. Independent calculations based on the spectroscopic data of H Cl and H Cl separately, show the entropy of HCl at 298 K to be 186.686 and 187.372 J/(mol K) (44.619 and 44.783 cal/(mol K), respectively. The low temperature (rhombic) phase is ferroelectric (6). SoHd hydrogen chloride consists of hydrogen-bonded molecular crystals consisting of zigzag chains having an angle of 93.5° (6). Proton nmr studies at low temperatures have also shown the existence of a dimer (HC1)2 (7). 

Available data on the thermodynamic and transport properties of carbon dioxide have been reviewed and tables compiled giving specific volume, enthalpy, and entropy values for carbon dioxide at temperatures from 255 K to 1088 K and at pressures from atmospheric to 27,600 kPa (4,000 psia). Diagrams of compressibiHty factor, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, velocity of sound in carbon dioxide, viscosity, and thermal conductivity have also been prepared (5). 

Pressure and volume values converted, and entPalpy and entropy values reproduced, from Hust and Stewart, NBS TecP. Note 202, 1963. TPis source gives values at and above 72.373 K at closer pressure intervals, c = critical point. Tbe notation 1.268.-3 signifies 1.268 x 10" ... 

A thermodynamic analysis regarding the relation between enthalpy and entropy values on the one hand and non-bulk electrostatic contributions on the other leads to the same result144). 

Thermodynamic parameters have been obtained from kinetic HNMR spectroscopic studies of the thermal decomposition of ethyl 2,7-di-to7-butyl-5-methylthiepin-4-carboxylaten and two 1-benzothiepin compounds.12 The activation parameters for sulfur extrusion are AH = 93.7 kJ mol - 1 and AS = — 112.6 J Kmol-1 (in [2H18]Decalin) for the thiepin derivative,11 and AH = 75.3 and 87.9 kJ mol1 and AS = —100.4 and —104.6J Kmol-1 (in [2Hs]toluene) for the benzothiepin compounds.12 The large negative activation entropy values are consistent with a high degree of order in the anticipated thianorcaradiene transition state of the sulfur extrusion reaction. 

Fig. 37. Dependence of the thermodynamic parameters AH and AS of triple-helix formation on the imino acid content of the peptides (obtained by cleavage of calf skin-type I collagene with cyanogene and subequent isolation by column chromatrography)3) and of the native neutral salt-soluble skin collagene of various animals. The entropy values are denoted by dotted lines...

Integrating to successively higher T gives Sm values as a function of T. Sm.r also depends upon p, especially if the substance is in the gas phase at the temperature. The entropy values are usually calculated and tabulated at a... 

K. (b) 0 kj. (c) The discrepancy arises because the enthalpy and entropy values calculated from the tables are not rigorously constant with temperature. 

The contribution of this lack of regularity to the entropy of ice is thus R In 3/2 = 0.805 E. U. The observed entropy discrepancy of ice at low temperatures is 0.87 E. U., obtained by subtracting the entropy difference of ice at very low temperatures and water vapor at standard conditions, for which the value 44.23 E. U. has been calculated from thermal data by Giauque and Ashley,7 from the spectroscopic value 45.101 E. U. for the entropy of water vapor given by Gordon.8 The agreement in the experimental and theoretical entropy values provides strong support of the postulated structure of ice.9... 

C14-0064. Without doing calculations or looking up absolute entropy values, determine the sign of A S ° for the following processes ... 

The connection between the multiplicative insensitivity of 12 and thermodynamics is actually rather intuitive classically, we are normally only concerned with entropy differences, not absolute entropy values. Along these lines, if we examine Boltzmann s equation, S = kB In 12, where kB is the Boltzmann constant, we see that a multiplicative uncertainty in the density of states translates to an additive uncertainty in the entropy. From a simulation perspective, this implies that we need not converge to an absolute density of states. Typically, however, one implements a heuristic rule which defines the minimum value of the working density of states to be one. 

If the stability constant measurements are coupled with enthalpy determinations, then entropy values (as well as the corresponding free energy values) may be calculated ... 

Thermochemical data from the compilation of Stull et at., 1969. Entropy values are based on a 1 M standard state. The asterisk denotes symmetry-corrected quantities. Symmetry numbers were chosen as follows 18 for the n-alkanes, cis-3-hexene, dibuthyl sulphide, diethyl ether, and diethyl amine 2n for the cycloalkanes and 2 for all of the remaining ring compounds 3 for the alkanols, alkanethiols and alkyl amines 9 for the methyl alkyl sulphides... 

The need for entropy values is bypassed when the van t Hoff equation (d In K/dT) =AH/RT2 is used. This can be integrated, either assuming AH is temperature-independent, or by incorporating a specific heat-temperature variation. This is the so-called second law method which contrasts with the third law method. In the latter method, the standard enthalpy is obtained from each equilibrium constant using free-energy functions of all the species present, for example... 

To begin the problem, we need the standard entropy values for each of the reactants and products. These are the values we ll be using to complete this problem ... 

A Unlike heats of formation and Gibbs free energies of formation, the standard entropy values for elements are not zero. 

The loss of symmetry which occurs after deprotonation leads to bigger T AS0 values and the gain in degrees of freedom in internal rotation leads to bigger entropy values, as shown in reaction 7. 

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