Pure liquid heat capacity

There are a number of reliable estimating techniques for obtaining pure-component hq uid heat capacity as a function of tem )erature, including Ruzicka and Dolmalsld, Tarakad and Danner, " and Lee and Kesler. These methods are somewhat compheated. The relatively single atomic group contribution approach of Chueh and Swanson for liquid heat capacity at 29.3.15 K is presented here ... 

The specific heats of liquid mixtures can be estimated, with sufficient accuracy for most technical calculations, by taking heat capacities as the mass (or mole) weighted sum of the pure component heat capacities. 

Viscosities, thermal conductivities, liquid density, and pure component heat capacities have been estimated at the temperature and composition in the respective bulk phases. These properties are assumed constant for this example. In view of the small temperature changes that are encountered here, this is a reasonable assumption. 

We express the difference Hi(T) - H,(T) using the liquid heat capacity of pure component,... 

For the material and energy balances, pure-component heat capacity and density data are needed. These are among the most widely measured data and are available on process simulators for more than a thousand substances. (See Chapter 13 for details of process simulators.) There are also reasonably accurate group-contribution techniques for use when no data are available [8]. The enthalpies of mixtures require an accurate equation of state for gases and nonionic liquids. The equations of state available on process simulators are accurate enough for these systems. However, additional heat of solution data are needed for electrolyte solutions, and these data may not be as readily available. For these systems, care should be taken to use accurate experimental data, because estimation techniques are not as well defined. 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

In this book we have decided to concentrate on purely synthetic applications of ionic liquids, just to keep the amount of material to a manageable level. FFowever, we think that synthetic and non-synthetic applications (and the people doing research in these areas) should not be treated separately for a number of reasons. Each area can profit from developments made in the other field, especially concerning the availability of physicochemical data and practical experience of development of technical processes using ionic liquids. In fact, in all production-scale chemical reactions some typically non-synthetic aspects (such as the heat capacity of the ionic liquid or product extraction from the ionic catalyst layer) have to be considered anyway. The most important reason for close collaboration by synthetic and non-synthetic scientists in the field of ionic liquid research is, however, the fact that in both areas an increase in the understanding of the ionic liquid material is the key factor for successful future development. 

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

There are two steps in the calculation. First, calibrate the calorimeter by calculating its heat capacity from the information on the first reaction, Cca) = qc, /AT. Second, use that value of Cc-1 to find the energy change of the neutralization reaction. For the second step, use the same equation rearranged to gcal = Cca AT, but with AT now the change in temperature observed during the reaction. Note that the calorimeter contains the same volume of liquid in both cases. Because dilute aqueous solutions have approximately the same heat capacities as pure water, assume that the heat capacity is the... 

C06-0067. When 10.00 mL of a solution of a strong acid is mixed with 100.0 mL of a solution of a weak base in a coffee-cup calorimeter, the temperature falls from 24.6 °C to 22.7 °C. Determine q for the acid -base reaction, assuming that the liquids have densities of 1.00 g/mL and the same heat capacity as pure water. 

Let us now consider the effect of a difference between the heat capacity of pure liquid i and pure solid i on the enthalpy and entropy of fusion and subsequently on the phase diagram. This effect is easily taken into consideration by using eqs. (1.24) and (1.54). Ais now given as... 

Evaluations of Rd and Y necessitate a knowledge of certain physical properties of the two liquids and the mixtures. The variation of refractive index with concentration is measured readily by refractometry, if I nT, — n21 is large. The coefficient of isothermal compressibility of a mixture t2 requires specialised equipment. Alternatively, it can be determined from the heat capacity and the coefficient of isentropic compressibility87, 88, the latter being yielded from velocity of sound data88. However, provided and 02 for the pure compounds are known, j312 is evaluated most conveniently on the basis of additivity, thus ... 

A critically evaluated compilation of the heat capacities of pure liquid organic and some inorganic compounds. It covers data published between 1993 and 1999 and some data of 2000 as well as some data from older sources. This paper is an update of reference [24]. 

A comprehensive collection of evaluated heat capacities of 1624 pure substances in the liquid state. This was updated in reference[19]. 

No adequate theoretical treatment has been developed that might serve as a guide in interpreting and correlating data on the heat capacities of liquids, but a critical review and recommended values are available for several hquids [18], However, it has been observed that the molar heat capacity of a pure hquid generally is near that of the sohd, so if measurements are not available we may assume that Cvm is 25 J mol K However, the heat capacities of solutions carmot be predicted reliably from the corresponding properties of the components. Empirical methods of treating solutions will be considered in later chapters. 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

Constant volume heat capacities for liquid oiganic compounds were estimated with a four parameter fit (219). A 1.3% average absolute error for 31 selected species was reported. A group contribution method for heat capacities of pure solids and liquids based on elemental composition has also been provided (159). 

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