Second virial coefficient value errors

Values of the second virial coefficient of ethylene for temperatures between 0° and 175°C have been determined to an estimated accuracy of 0.2 cm3/mol or less from low-pressure Burnett PVT measurements. Our values, from —167 to —52 cm3/mol, agree within an average of 0.2 cm3/mol with those recently obtained by Douslin and Harrison from a distinctly different experiment. This close agreement reflects the current state of the art for the determination of second virial coefficient values. The data and error analysis of the Burnett method are discussed. 

Despite the importance of mixtures containing steam as a component there is a shortage of thermodynamic data for such systems. At low densities the solubility of water in compressed gases has been used (J, 2 to obtain cross term second virial coefficients Bj2- At high densities the phase boundaries of several water + hydrocarbon systems have been determined (3,4). Data which would be of greatest value, pVT measurements, do not exist. Adsorption on the walls of a pVT apparatus causes such large errors that it has been a difficult task to determine the equation of state of pure steam, particularly at low densities. Flow calorimetric measurements, which are free from adsorption errors, offer an alternative route to thermodynamic information. Flow calorimetric measurements of the isothermal enthalpy-pressure coefficient pressure yield the quantity 4>c = B - TdB/dT where B is the second virial coefficient. From values of obtain values of B without recourse to pVT measurements. 

Before comparing theory and experiment let us discuss the convergence of the semiclassical expansion of the dielectric second virial coefficient. In Table 1-15 the classical dielectric virial coefficient the first and second quantum corrections, and the full quantum result are reported. An inspection of this table shows that the quantum effects are small for temperatures larger than 100 K, and /it(/) can be approximated by the classical expression with an error smaller than 2.5%. At lower temperatures the dielectric virial coefficient of 4He starts to deviate from the classical value. Still, for T > 50 K the quantum effects can be efficiently accounted for by the sum of the first and second quantum corrections. Indeed, for T = 50, 75, and 100 K the series (7) + lli 1 (7) + (7) reproduces the exact results with errors... 

Approximately what percentage errors are allowable in the measured variables if the maximum allowable error in calculated values of the second virial coefficient B is I percent Assume that Z — 0.9 and that values of B are calculated by Eq. (332). 

We now show predictions of the compressibility factor for pure carbon dioxide along two isotherms, one supercritical and the other subcritical. All results shown here used values of a and b computed from and P. Figure 4.14 shows the results for the supercritical isotherm, T = 350 K. Up to about 75 bar, the three equations are all in good agreement with experiment, indicating that, at least at this temperature, all three satisfactorily estimate the second virial coefficient. However, for P > 100 bar, errors in... 

T = 300 K, the second term contributes about 20 J mol to G (0.5). The third term contributes about 4 J mol, while the last term contributes generally less than 0.1 J mol k To obtain G (0.5) to an accuracy of 1 Jmol for the above conditions, it is necessary to know the second virial coefficients for the pure components and the mixture to within 20cm mol. For non-polar + polar gas mixtures and polar + polar gas mixtures the usual methods for calculating Sab are far from reliable. For example, if the calculated values of Sab for acetone + nitromethane at 300 K listed by Reid and Sherwood were used in equations (2) and (3) to calculate G (0.5) an error of approximately 30 J mol would be introduced. In circumstances where the second virial coefficients are not known and the prediction methods are unreliable, it is advisable that the coefficients for the pure components and the mixture be measured. It should be sufficient for Rab to be determined from one measurement at y 0.5. 

Ya=i In turn, Ui has been chosen by trial-and-error such as to make the threshold energy of the calculated excitation function similar to the experimental activation energy for the 0( P) -h 03( Ai) reaction see section 5. Finally, the optimum values of 6, U2, and were determined from a least-squares fitting procedure to the available information on the second virial coefficients of gaseous oxygen as it is described in section 4. Table 1 summarizes the final numerical values of all parameters. 

For each of the temperatures in Table A.4 at which a value of the second virial coefficient is given for argon, calculate the value of the second virial coefficient from the values of the van der Waals parameters. Calculate the percent error for each value, assuming that the values in Table A.4 are correct. 

To determine the second virial coefficients to the required acciu acy of about 100 ppm, one needs to know the helium dimer potential to a few mK at the minimum. Consider first the interaction of two hehum atoms in the nonrelativistic Born-Oppenheimer (BO) approximation. The best published calculations using the supermolecular method have estimated error bars of 8 mK [ 150,151]. More recently, improved calculations of this type reached an accuracy of 5 mK [ 158]. Also, the SAPT calculations have been repeated with increased accuracy, resulting in an agreement to 5 mK with the supermolecular method. Furthermore, the upper bound from four-electron exphcitly correlated calculations is 5 mK above the new supermolecular value [159]. All this evidence from three different theoretical models seems to show convinc-... 

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