Enthalpy estimating temperature effects

Example 8.3 Temperature effect on equilibrium conversion Consider the elementary reversible reaction B P with no initial product P, while the initial concentration of B is B0. The standard Gibbs energy and standard enthalpy of the reaction are AG° (298.15K) = -14.1kJ/mol and A//" (298.15K) = -83.6kJ/mol. Assume that the specific heats of solutions are equal to that of water. Estimate the equilibrium conversion of B between 25°C and 120°C. 

Vapour pressure measurements have led to heats of sublimation of octafluoro-naphthalene and decafluorobiphenyl of 79.3 2.4 and 85.2 2.3 kJ mol , respectively, and the enthalpy of fusion and heat capacity of octafluorotoluene have been obtained from adiabatic calorimetry at 10—365 K the last study yields a triple-point temperature of 207.69 K, and the standard entropy of the ideal gas is 462.6 J K mol i at 298.15 K. Adiabatic calorimetry has also been used to obtain the heat capacities of the three tetrafluorobenzenes at 11— 353 K, and the entropies of the liquids at 298.15 K are 256.1,257.3, and 250.4 J mol- for the 1,2,3,4-, 1,2,3,5-, and 1,2,4,5-isomers, respectively 1,2,3-trichlorotrifluorobenzene fcry-stals) has an entropy of 243.3 J mol at 298.15 K. . Liquid densities from 293 to 490 K have been determined for eight polyfluoroarenes (CeFe, CeFsH, 1,2,3,4-F4C H2, CsFsa. l,3.5-F3C6Cl3, CsFs CFa, CeFsMe, and CeFsOH) and densities up to the critical temperatures have been estimated the effects of dissolved... 

Adiabatic flame temperatures agree with values measured by optical techniques, when the combustion is essentially complete and when losses are known to be relatively small. Calculated temperatures and gas compositions are thus extremely useful and essential for assessing the combustion process and predicting the effects of variations in process parameters (4). Advances in computational techniques have made flame temperature and equifibrium gas composition calculations, and the prediction of thermodynamic properties, routine for any fuel-oxidizer system for which the enthalpies and heats of formation are available or can be estimated. 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

The heat requirements in batch evaporation are the same as those in continuous evaporation except that the temperature (and sometimes pressure) of the vapor changes during the course of the cycle. Since the enthalpy of water vapor changes but little relative to temperature, the difference between continuous and batch heat requirements is almost always negligible. More important usually is the effect of variation of fluid properties, such as viscosity and boiling-point rise, on heat transfer. These can only be estimated by a step-by-step calculation. 

Reasonably reliable pATbh+ values for the protonation of weak bases or of weakly basic substrates can be obtained via equation (17), together with m slope parameters that can be used to classify basic molecules as to type, and for an estimate of the solvation requirements of the protonated base. Measurements at temperatures other than 25°C can be handled using equation (22), and enthalpies and entropies for the protonation can be obtained. Protonation-dehydration processes are covered by equation (26). Medium effects on the... 

Free energy variations with temperature can also be used to estimate reaction enthalpies. However, few studies devoted to the temperature dependence of adsorption phenomena have been published. In one such study of potassium octyl hydroxamate adsorption on barite, calcite and bastnaesite, it was observed that adsorption increased markedly with temperature, which suggested the enthalpies were endothermic (26). The resulting large positive entropies were attributed to loosening of ordered water structure, both at the mineral surface and in the solvent surrounding octyl hydroxamate ions during the adsorption process, as well as hydrophobic chain association effects. 

In addition to the activity and osmotic coefficients at room temperature, the first temperature derivatives and the related enthalpy of dilution data were considered for over 100 electrolytes (26, 29). The data for electrolytes at higher temperatures become progressively more sparse. Quite a few solutes have been measured up to about 50°C (and down to 0°C). Also, over this range, the equations using just first temperature derivatives have some validity for rough estimates in other cases. But the effects of the second derivative (or the heat capacity) on activity coefficients at higher temperatures is very substantial. 

In a more trivial sense, small isotope effects may appear temperature-independent simply because the expected isotopic difference in enthalpies or energies of activation is small. It is thus, of course, important to compare the apparent isotopic temperature dependences and their error estimates with the semiclassical expectations. 

We are at a loss to explain the discrepancy in the BF3 enthalpies of interaction with the sulfur donors. Steric effects may be operative, but this is far from the whole story for the BCI3 interaction is much larger than BF3 with these donors. Furthermore, using the tentative ( 113)3 parameters to estimate those of ( 2115)3 , we calculate an enthalpy from E and of 11.1 k.cal mole- for the BF3-P( 2H6)3 adduct compared to a measured value of 9.5 k.cal mole i. The authors report much difficulty with the sulfur donor system, but their error estimates could not possibly account for the difference between our calculated and the observed result. The behavior of ( 2115)35 compared to ( 2115)3 is clearly inconsistent with the behavior of these two donors toward ( 2H5)sAl where both enthalpies are correctly predicted with our parameters. It may be that the BF3-( 2115)25 system has an even lower equilibrium constant than reported and is completely dissociated over the temperature range studied. (This would require a very different entropy if the — AH predicted by E and were correct.) A slight impurity (reported to be less than 0.1%) or decomposition product could interact appreciably with BF3 and changing pressure contributions from this adduct with temperature could be attributed incorrectly to the sulfur donor adduct. The actual BF3-sulfur donor adduct would then be a very common example of an adduct which cannot be studied by the vapor pressure technique because it is completely dissociated at the temperatures at which one of the components has appreciable vapor pressure. We have examined the reaction of BF3 ( 2Hs) 2O with large excess of ( H2) 4S in dichloroethane solution at 25 ° and have found the equilibrium constant to be too low to be measured calorimetrically. 

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