Heat capacity standard state values

In equations (18.91) and (18.92), C° 2 and V are the partial molar heat capacity and partial molar volume of the surfactant in the infinitely dilute solution (standard state values). 

For nonisothermal processes, the change of energy functions contains a change of standard state. The standard-state values need to be known. The ideal-gas standard-state values are given in standard tables. These have to be looked up or, alternatively, heat capacity data are employed instead of the standard-state values. Consider the change of enthalpy the difference is found by integrating the heat capcity. 

According to Reichelt and Hemminger (144), the values of the calibration constant of a DSC apparatus obtained by means of heat of fusion standards are different from those of well-known heat capacity standards. Varying the container geometry, they were able to show that there was no influence of the disturbance of steady-state conditions of heat flux on the calculated value of the enthalpy of fusion of indium. An error of 20% in the enthalpy may result if incorrectly closed containers are employed. 

Our analysis using standard state values implies dP = 0, and under that constraint, the second term in Equation 6.44 is zero. The remaining partial derivative is the constant-pressure heat capacity of the fth substance, Cp. To evaluate the enthalpy (or other thermodynamic state functions) at a temperature, call it T2, different from a temperature Ti for which there are known enthalpies, we invoke Hess s law, treating the temperature changes of reactants and products as reaction steps. Here is an example ... 

The interpretation of AC is that it is the difference in the standard molar heat capacities of the transition state and the reactants. Values of AC for the solvolysis of neutral molecules lie in the range 0 to -400 J mol-1 K l. The need for high-precision determinations of k (and 77) is emphasized by these values. 

The value of this standard molar Gibbs energy, p°(T), found in data compilations, is obtained by integration from 0 K of the heat capacity determined by the translational, rotational, vibrational and electronic energy levels of the gas. These are determined experimentally by spectroscopic methods [14], However, contrary to what we shall see for condensed phases, the effect of pressure often exceeds the effect of temperature. Hence for gases most attention is given to the equations of state. 

References (20, 22, 23, 24, 29, and 74) comprise the series of Technical Notes 270 from the Chemical Thermodynamics Data Center at the National Bureau of Standards. These give selected values of enthalpies and Gibbs energies of formation and of entropies and heat capacities of pure compounds and of aqueous species in their standard states at 25 °C. They include all inorganic compounds of one and two carbon atoms per molecule. 

For a Gas. The procedure for the calculation of the entropy of a gas in its standard state is substantially the same as the that for a solid or liquid except for two factors. If the heat capacity data have been obtained at a pressure of 1 atm (101.325 kPa), the resultant value of Sjj, is appropriate for that pressure and must be corrected to the standard state pressure of 1 bar (0.1 MPa). This correction is given by... 

The standard state for the heat capacity is the same as that for the enthalpy. For a proof of this statement for the solute in a solution, see Exercise 2 in this chapter. This choice of standard state for components of a solution is different fixjm that used by many thermodynamicists. It seems preferable to the choice of a 1-bar standard state, however, because it is more consistent with the extrapolation procedure by which the standard state is determined experimentally, and it leads to a value of the activity coefficient equal to 1 when the solution is ideal or very dilute whatever the pressure. It is also preferable to a choice of the pressure of the solution, because that choice produces a different standard state for each solution. For an alternative point of view, see Ref. 2. 

We have seen in chapter 2 that the heat capacity at constant P is of fundamental importance in the calculation of the Gibbs free energy, performed by starting from the standard state enthalpy and entropy values... 

Standard state entropy values and Maier-Kelley coefficients of heat capacity at constant P, with respective T limits of validity, are listed for the same components in table 5.13. The adopted polynomial expansion is the Haas-Fisher form ... 

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

The integration of Equation (11.22) to determine the equilibrium constant as a function of the temperature or to determine its value at one temperature with the knowledge of its value at another temperature is very similar to the integration of the Clausius-Clapeyron equation as discussed in Section 10.2. The quantity AHB must be known as a function of the temperature. This in turn may be determined from the change in the heat capacity for the change of state represented by the balanced chemical equation with the condition that all substances involved are in their standard states. 

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of liquid hydrocarbons into water. The first of these, 7h is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of liquids. The second universal temperature is Ts, where the standard-state entropy change is zero and, as noted, Ts is about 140°C. The standard-state free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance... 

Thermo chemical tables list values of the standard enthalpy of formation, Af H° (formerly called heats of formation) the standard Gibbs energy of formation, Af G° the standard entropy, S° the heat capacity at constant pressure, C° m for substances in defined physical states (e.g. solid (s) or crystalline (c), liquid (1), aqueous (aq) or gas (g)). In much of this frame we shall be assuming that the heat capacities, C°m, are temperature independent. 

The quasi-stationary state approximation consists of setting Rj = 0 for very reactive and short-lived intermediates such as free radicals. The result is that molar enthalpies of these intermediates do not appear in the calculation of H. Therefore, it is necessary to know neither their standard heats of formation, nor their heat capacities, values of which are not as well known as those of stable species. 

Property values in the standard state are denoted by the degree symbol (°). For example, C°P is the standard-state heat capacity. Since the standard state for gases is the ideal-gas state, C% for gases is identical with Cj , and the data of Table 4.1 apply to the standard state for gases. All conditions for a standard state are fixed except temperature, which is always the temperature of the system. Standard-state properties are therefore functions of temperature only. 

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23 Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technolo, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Magee, J. W., Outcalt, S. L., and Ely, J. F., Molar Heat Capacity C(u), Vapor Pressure, and (p, Rho, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for ChlorotrifluorometEiane (R13), Int. J. Thermophys. 21(5) 1097-1121, 2000. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. 

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