Yo

W 0.441 - rw V& 3) (12-6.9) where is defined by Eq. (12-6.5) and pw, po are the superficial bulk volume fractions of water and organic material, i.e., Number of carbon atoms One less than the number of carbon atoms Number of carbons times ratio of molal volume of halogen derivative to parent fatty acid Acetic acids, q 2 Acetone, q 2 _ ,, Vt (chloroacetic acid) ' Vb (acetic acid) io I0 (12-6.10) where *w, bulk mole fraction of pure water and pure organic component VWj Vo molal volume of pure...

Y i y2n y2 yin

Where t m viscosity of the mixture Vu V2 pure component viscosities y,, y2 mole fractions TABLE 9-4 Comparison of Calculated and Experimental Low-Pressure Gas Mixture Viscosities Percent deviationf calculated by method of TABLE 9-4 Comparison of Calculated and Experimental Low-Pressure Gas Mixture Viscosities Percent deviationf calculated by method of

10

0.286+ (188)(0.714)(1.237 X KT3)(3 + (2)(86.469) 28.013 29.71 and K (CHC1F2) 107.9. Substituting into Eq. (9-5.8), v (29.71) 1 + (1.237 X 10 3)2(107.9)2 + (107.9) 1 + (2)(1.237 X 10-3)(29.71) + (1.237 X 10-3)2(29.71)2 146.2 iP Error 146'2 145 x 100 0 8 145 In a further simplification of the kinetic theory approach, Wilke 221 neglected second-order effects and proposed < t> ji is found by interchanging subscripts or by For a binary system of 1 and 2, with Eqs. (9-5.13) to (9-5.15),

W2g21 ui Y w2 wg12i yV

Y When the Rowley correlation is written in the form of Eq. (10-12.12), it is clear that the entire nonideal effect is included in the R parameter, and the form is quite similar to the Filippov and Jamieson et al. relations described earlier. To employ this technique, values for the liquid thermal conductivities of all pure components are required. In addition, from data sources or from regressing vapor-liquid equilibrium data, the NRTL parameters, G,- and Gji must be found. The concept of...

Variation of Surface Tension with Temperature

In Fig. 12-1, log a is plotted against log (1 Tr) with experimental data for acetic acid, diethyl ether, and ethyl acetate. For the latter two, the slope is close to 1.25 for a value of n 0.31 for acetic acid, the slope is 1.16 or n 0.29. For most organic liquids, this encompasses the range normally found for n, although for alcohols, n may be slightly less. The corresponding states correlation predicts a slope of 1.22, giving n 0.305. For values of Tr between...

V

Where M' molecular weight, kg mol 77 viscosity, N-s m2t p molar density, mol m'1 D diffusion coefficient, m2 s Most early theories selected D to be equivalent to the molecular self-dif-fusion coefficient, and fml is then the reciprocal of the Schmidt number. With Eqs. (9-3.9) and (11-3.2) it can be shown that nt 1.32 and is almost independent of temperature. With this formulation, Eq. (10-3.2) becomes Equation (10-3.5), often referred to as the modified Eucken correlation, was used by Svehla...

1

R (Bi y) 1 - exp (-B4y) + BtGx exp (R,y) + fi3G, --B,B4 + B2 + Bs ( 5'8) The coefficients Bt to S7 are functions of the acentric factor w, the reduced dipole moment pr as defined in Eq. (9-4.11) , and the association factor k. Some values of k are shown in Table 9-1. Bi a, + 6,co + cm* + diK (10-5.9) with a bit c and d, given in Table 10-4. The relation for high-pressure thermal conductivities is quite similar to TABLE 10-4 Values of B, in Eq. (10-5.9) TABLE 10-4 Values of B, in Eq. (10-5.9)

Theory of Thermal Conductivity

In Sec. 9-3, through rather elementary arguments, the thermal conductivity of an ideal gas was found to be equal to vLCvn 3 Eq. (9-3.7) , where v is the average molecular velocity, L is the mean free path, Cu is the heat capacity per molecule, and n is the number density of molecules. Similar relations were derived for the viscosity and diffusion coefficients of gases. In the case of the last two properties, this elementary approach yields approximate but reasonable values. For thermal...

The Effect of Pressure on the Binary Diffusion Coefficients of Gases

At low to moderate pressures, binary diffusion coefficients vary inversely with pressure or density as suggested by Eqs. (11-3.1) and (11-3.2). At high pressures, the product DP or Dp is no longer constant but decreases with an increase in either P or p. Note that it is possible to have a different behavior in the products DP and Dp as the pressure is raised, since p is proportional to pressure only at low pressures, and gas nonidealities with their concomitant effect on the system density may...

T

We now determine r 0, the low-pressure viscosity of the reference fluid (methane), with T0 from Eq. (10-5.17) and Eq. (10-3.27), where the constants Cn were given below this latter equation. 5. With 7o, the first component of the thermal conductivity is found from Eq. (10-5.19). which is identical with the form of Eq. (10-3.28). 6. The second component for X is calculated by where T0 and p0 are given in Eqs. (10-5.17) and (10-5.18) and the coefficients bn are 6, 2.5276 E 4 bo 3.3433 -4 bs 1.12...

SvCiv Cjm

1 k - (vjf + yi 3)3 (49'6) Mixing rules recommended 22 for the Hankinson-Brobst-Thomson equation are V* i z *iVT + 3 Z x,vr2 3J z x vtmj V jTc (V*Tc VJTcj)m (4-9.9) > srkm Z XVSRKi (4-9.10) Pcra (0-291 - 0.080.SRKJfiTCm (4 9 n) In the HBT compressed liquid correlation Eq. (3-11.5), Pvp , for a mixture is calculated by PCm is from Eq. (4-9.11), and Prm is calculated from the generalized Riedel vapor pressure equation logio Prm + auuPii (4-9-13) P 5.8031817 log,0 Trm + 0.07608141a (4-9.14) P<...

Surface Tensions of Nonaqueous Mixtures

The surface tension of a liquid mixture is not a simple function of the surface tensions of the pure components because, in a mixture, the composition of the surface is not the same as that of the bulk. In a typical situation, we know the bulk composition but not the surface composition. The surface tension of a mixture am is usually but not always 2, 77 less than that calculated from a mole fraction average of the surface tensions of the pure components. Also, the derivative dojdx usually...

Surface Tensions of Aqueous Solutions

Whereas for nonaqueous solutions the mixture surface tension is often approximated by a linear dependence on mole fraction, aqueous solutions show pronounced nonlinear characteristics. A typical case is shown in Fig. 12-5 for acetone-water at 353 K. The surface tension of the mixture is

Scope

Thermal conductivities of both gases and liquids are considered in this chapter. Some background relevant to the theory of thermal conductivity is given in Sees. 10-2 and 10-3 (for gases) and in Sec. 10-8 (for liquids). Estimation techniques for pure gases at near ambient pressures are covered in Sec. 10-4 the effects of temperature and pressure are discussed in Sees. 10-4 and 10-5. Similar topics for liquids are in Sees. 10-9 to 10-11. Thermal conductivities for gas and for liquid mixtures are...

Rt

M (57.14H100) (83.14X398.15) 0.48 + 1.574 - 0.176 2 0.703 4274g 1 + 0.703(1 - 1.091 2) 2(83.14)2(364.9)2 46.0 (0.42748X8.03 X 106) (83.14)(0.703) (l 09)(46 Q) If Eq. (3-6.2) is solved for Z, the result is Z 0.4470, V 148.0 cm3 mol. 0.4470 - 0.1726 , 148.0(1) 15,281 , 0.4470 S - S -83.14 In- --83.14 In (83 14)(398 15) 0.4470 + 0.1726 56.91 56.91 9.89 X 104 bar cm3 mol 9.89 X 104 8.314 _ H 42.081 83.14 235 J g

References

Physical Properties of Molecular Crystals, Liquids and Glasses, Wiley, New York, 1968. 2. Din, F., (ed.) Thermodynamic Functions of Gases, vol. 3, Butterworth, London, 1961. 3. Maxwell, James Clerk Atoms, Encyclopaedia Britannica, 9th ed., A. & C. Black, Edinburgh, 1875-1888. 4. Slater, J. C. Modern Physics, McGraw-Hill, New York, 1955. 5. van Krevelen, D. W. Properties of Polymers Their Estimation and Correlations with Chemical Structure, 2d ed., Elsevier, Amsterdam, 1976....

R2n6i loVn

The meaning of Cj and C2 is clear from Eq. (9-5.4). Finally, with (T T y 2 and Mr,2 (vnVr2)2 (M,M2 32)' 2 1 + 0MTn2(Tm - l) l 6 (A , + M2)3 2 (T )1 _ yir iYA u , I J rijWtii + J OCIOI 12 ,. ,, , , > 3 2 T IS-D.IZJ 2 ns2 4- (10M 2)7 T 1 + (10Mn2)7 To employ Reichenberg's method, for each component one needs the pure gas viscosity at the system temperature as well as the molecular weight, dipole moment, critical temperature, and critical pressure. The...

R

Figure 11-1 Diffusion across plane RR'. bution x (2VA + iVB). For equimolar counterdiffusion, iVA + A B 0 and Jf NA. One other flux is extensively used, i.e., one relative to the plane of no net volume flow. This plane is less readily visualized. By definition, and if J a and are vectorial molar fluxes of A and B relative to the plane of no net volume flow, then, by definition, where VA and VB are the partial molar volumes of A and B in the mixture. It can be shown that where V is the volume...

R V

H - H (A - A) + T(S - S ) + RT(Z - 1) (5-3.8) U U (A A) 4- T(S - S ) (5-3.9) G - G (A - A) + RT(Z - 1) (5-3.10) Also, although not strictly a departure function, the fugacity-pressure ratio can be expressed in a similar manner Therefore, from any pressure-explicit equation of state and a definition of the reference state (P or V ), all departure functions can readily be found. Example 5-1 Derive the departure functions for a pure material or for a mixture of constant composition by using the...

R A

V*0' PCVQ) RTC, and the constants are given in Table 3-7 for a simple fluid. With V*0), the simple fluid compressibility factor is calculated. Next, using the same reduced temperature and pressure as determined above, Eq. (3-7.1) is again solved for V*0' but with the reference fluid constants in Table 3-7 call this value V< S). Then

Q

Qp parameter in Eq. (12-3.8) r parameter in Eq. (12-5.2) R gas constant T temperature, K Tc, critical temperature Tb, normal boiling point, T reduced temperature T Tc Tbr, Tb Tc TCm, pseudocritical mixture temperature V liquid molal volume, cm3 mol V, for the surface phase Vc critical volume, cm3 mol x, liquid mole fraction xf, in the bulk phase x , in the surface phase y, vapor mole fraction 7, activity coefficient of component i yf, in the bulk liquid phase y , in the surface phase V liquid...

Pr

(v - V )Zt 1.656pJ111 pr < 0.1 (9-6.12) (v - V )Zt 0.0607(9.045pr + 0.63)1739 0.1 < pr < 0.9 (9-6.13) log 4 - log (j, - 7, ) r 0.6439 - 0.1005pr - A 0.9 < pr < 2.6 (9-6.14) where A 0 when 0.9 < pr < 2.2 A (4.75 X 10-4)(p - 10.65)2 when 2.2 < pr < 2.6 (9-6.15) and (ri - v ) t 90.0 and 250 at pr 2.8 and 3.0, respectively. The notation used in Eqs. (9-6.12) to (9-6.15) is defined under Eq. (9-6.11). Note that the parameter is not the same as defined earlier in Eq. (9-4.14). An...

Pf loof irrti

Where fx is the calculated fugacity of the more volatile component in the vapor phase and f is that in the liquid phase. When the binary parameter is obtained by minimizing DP P, the other deviation functions are usually close to their minima. However, for a given set of data, it is unavoidable that the optimum binary parameter depends somewhat on the choice of objective function for minimization. Minimizing DP P is preferred because that objective function gives the sharpest minimum and...

O

TAlthough Eq. (8-13.3) is based on the simple two-suffix (one-parameter) Margules equation, similar calculations can be made using other expressions for gE. See, for example, Ref. 111. Stability analysis for ternary (and higher) systems is, in principle, similar to that for binary systems, although the mathematical complexity rises with the number of components. (See, for example, Refs. 14 and 103.) However, it is important to recognize that stability analysis can tell us only whether a system...

N

Where nT, the total number of moles, is equal to YL ni- Individual activity coefficients can be obtained from GE upon introducing the Gibbs-Duhem equation for a multicomponent system at constant temperature and pressure. That equation is The activity coefficient yf is found by a generalization of Eq. (8-5.3) where nj indicates that all mole numbers (except n,) are held constant in the differentiation. The key problem in calculating multicomponent vapor-liquid equilibria is to find an expression...

N 584 556 536 7812 0236n

-213.14+ 18.330N -213.14 + 18.330N - 338.01+25.086N -338.01+25.086N -213.14 + 18.330N Phenylacetic acid Ethyl valerate Benzyl benzoate Methyl n-butyl ketone Acetophenone Ethyl hexyl ether Propyl phenyl ether Propylamine Benzylamine Ethyl propylamine 7.56 545.01 243.44 12.70 790.47 328.36 8.69 605.44 265.53 8.57 442.82 263.28 10.48 567.43 296.33 Calculate AB as for straight-chain acid calculate AN for straight-chain acid but reduce AN by 0.24 for each methyl group in iso position If hydrocarbon...

M

Figure 8-6 Vapor-liquid equilibria for carbon monoxide (1)-methane (2) at 90.7 K. (From Ref. 97.) Figure 8-6 Vapor-liquid equilibria for carbon monoxide (1)-methane (2) at 90.7 K. (From Ref. 97.) difference between and 82 is small. To illustrate, suppose T 300 K, Vx 100 cm3 mol, 5i 14.3, and b2 15.3 (J cm3)I 2. At infinite dilution 1) we find from Eq. (8-10.8) that yf 1.04 when 12 0. However, if el2 0.01, we obtain yf 1.24, and if tn 0.03, yf 1.77. These illustrative results indicate that...

Lb

Equation (7-11.2) has been widely employed to make rapid estimates of AHub usually, in such cases, AZVb is set equal to unity. In this form, it has been called the Giacalone equation 32 extensive testing of this simplified form indicates that it normally overpredicts AHUb by a few percent. Correction terms have been suggested 30, 52 to improve the accuracy of the Giacalone equation, but better results are obtained with other relations, noted below. TABLE 7-4 Comparison between Calculated and...

L

0.010 -0.006 0.00* 0.003 -0.003 -0.002 0.002 0.002 0.001 -0.001 8.781 -6.532 -4.916 -3.730 -2.841 0.020 0.013 0.009 0.007 -0.005 0.004 -0.004 -0.003 -0.003 0.003 8.785 -6.536 -4.919 3.734 2.845 0.043 -0.028 -0.018 0 013 -0.011 0.009 -0.008 -0.007 -0.006 0.005 -8.797 -6.551 -4.937 -3.750 2.861 -2.184 -1.664 -1.258 -0.940 0.688 -0.487 -0.327 0.039 I -0.199 0.029 -0.048 0.023 -0.037 8.790 -6.544 -4.929 -3.742 -2.853 0.018 0.016 0.014 0.012 -0.010 -0.029 0.025 -0.021 -0.018 0.016 -8.804 -6.559...

K

With Tb as the normal boiling point (at 1 atm) in kelvins. Note, for systems in which one component is air, a (air) 3.62 A and e k (air) 97.0 K. We illustrate this method in Example 11-3. These authors modified Eq. (11-3.2) to Uab PAfl& Ue )i'3 + (e )b3 2 u ' where the terms have been defined under Eq. (11-4.1) and is found for each component by summing atomic diffusion volumes in Table 11-1 69 , These atomic parameters were determined by a regression analysis of many experimental data, and...

J

That is, ACp is the sum of the heat capacities of the compound and the constituent elements, each element in its standard state, and each multiplied by the appropriate stoichiometric multiplier vj. For most elements, there is no difficulty in obtaining Cp. As examples, oxygen at 298 K has a standard state as an ideal gas and Cp (02) is then the heat capacity of diatomic oxygen as an ideal gas. Or, for carbon, one would need the heat capacity Cp ( -graphite) as a function of temperature....

Nlq

No. C atoms 1 for acetone. tNo. C atoms 1 for methylformate. No. C atoms 1 for acetone. Constants C C , and C(, are restricted to monofunctional, primary alkanes. Not enough information is available to predict the effects of mul-tifunctionalities, secondary or tertiary positioning of the functional group, chain branching, and cyclic or aromatic backbones. Like any model for mixture properties, MOSCED has both advantages and disadvantages 1. Good overall...

Introduction

The boundary layer between a liquid phase and a gas phase may be considered a third phase with properties intermediate between those of a liquid and a gas. A qualitative picture of the microscopic surface layer shows that there are unequal forces acting upon the molecules i.e., at low gas densities, the surface molecules are attracted sidewise and toward the bulk liquid but experience less attraction in the direction of the bulk gas. Thus the surface layer is in tension and tends to contract to...

Info

Where aci 0.45724R2T2C PC and a, is given in Table 3-5 k j is symmetric, but dy is not. That is, dtJ dji, but ky Also, kti du O Thus, in the above formulation, there are three parameters per binary, ku, dl2, and ( 21- Local composition mixing rules as applied by other authors vary in the number of parameters used and in the equation of state to which the mixing rules are applied. Some forms do not reduce to a quadratic mixing rule at low densities as is required by the virial equation. Equation...

Ijqiy ka k

For a bubble point calculation, a useful objective function F( T) is where K, In this calculation, the important unkown is T (rather than y) because P pi is a strong function of temperature, whereas < j> , is only a weak function of y. A suitable program for these iterative calculations uses the Newton-Raphson method, as discussed in Ref. 99 . This program requires initial estimates of T and y. The calculated bubble point temperature is 335.99 K. At this temperature, the second virial...

Ii

Figure 11-3 Takahashi correlation for the effect of pressure and temperature on the binary diffusion coefficient. Figure 11-3 Takahashi correlation for the effect of pressure and temperature on the binary diffusion coefficient. As an illustration of this technique, in Fig. 11-4, we have plotted the data of Takahashi and Hongo 201 for the system carbon dioxide-eth-ylene. Two cases are considered, one with a very low concentration of ethylene and the other with a very low concentration of carbon...

I

ZL is the compressibility factor for the pure saturated liquid. The coefficients Ai and are given in Table 3-6. Morris and Turek 70 have used the vapor pressure and volumetric data over a range of pressures (at a fixed temperature) to determine optimal values of a and b for eight sub- TABLE 3-6 Coefficients for Eqs. (3-6.7) and (3-6.8) TABLE 3-6 Coefficients for Eqs. (3-6.7) and (3-6.8)

Xoo

And the correction factors FP and Fq, i + (Fp i) y-3 1 + (F - l) y-' - (0.007)(In y)* Pa -- where Ff> and Fq are low-pressure polarity and quantum factors determined as shown in Eqs. (9-4.17) and (9-4.18). Finally, the dense gas viscosity is calculated as where is defined in Eq. (9-4.14). At low pressures, Yis essentially unity, and FP 1, Fq 1. Also Z2 then equals so t) tj , as expected. The Lucas method is illustrated in Example 9-10, and calculated dense gas viscosities are compared with...

Gnc

- CH2 - N - CH.,--CH2 - N - (CH3)2 2.94 After calculating C for an amine as noted above, any methyl substitutions for a hydrogen on a side chain increase C by 4.56 (the same as shown for fourth and successive methyl substitutions in paraffinic hydrocarbons). Nitriles. Only three AC contributions are shown they were based on thermal conductivity data for acetonitrile, propionitrile, and acrylic nitrile. On methane 5.43 CH3-CH3 - CH3-CH2-CN 7.12 Halides. Suggested contributions are shown below...

H

Where Nt, Nj total number of carbon atoms in molecules l and 2, respectively N, number of paraffinic carbon atoms in solute N number of aromatic carbon atoms, including C , CH , ring-juncture naphthenic carbons C H, and naphthenic carbons in the a position to an aromatic nucleus N number of naphthenic carbon atoms not counted in N r number of rings Butyl decalin N 4 N 2 N 8 N, 14 r 2 Butyl tetralin N, 4 N. 8 N 2 N, 14 r 2 solution First we find for ethanol. Subscript 1 stands for ethanol, and...

Estimation of Low Temperature Liquid Viscosity

Estimation methods for low-temperature liquid viscosity often employ structural-sensitive parameters which are valid only for certain homologous series or are found from group contributions. These methods usually use some variation of Eq. (9-10.1) and are limited to reduced temperatures less than about 0.75. We present two such methods in this section. We also describe a technique which employs corresponding states concepts. None of the three methods considered is particularly reliable, and we...

Enthalpy of Sublimation Vapor Pressures of Solids

Solids vaporize without melting (sublime) at temperatures below the triple-point temperature. Sublimation is accompanied by an enthalpy increase, or latent heat of sublimation. This may be considered to be the sum of a latent heat of fusion and a hypothetical latent heat of vaporization, even though liquid cannot exist at the pressure and temperature in question. The latent heat of sublimation AHs is best obtained from solid vapor pressure data. For this purpose, the Clausius-Clapeyron equation...

Enskog densegas theory

One of the very few theoretical efforts to predict the effect of pressure on the viscosity of gases is due to Enskog and is treated in detail by Chapman and Cowling 40 . The theory has also been applied to dense gas diffusion coefficients, bulk viscosities, and, for monatomic gases, thermal conductivities. The assumption is made that the gas consists of dense, hard spheres and behaves like a low-density hard-sphere system except that all events occur at a faster rate due to the higher rates of...

Effect of Temperature on the Thermal Conductivities of Liquids

Except for aqueous solutions, water, and some multihydroxy and multi-amine molecules, the thermal conductivities of most liquids decrease with temperature. Below or near the normal boiling point, the decrease is nearly linear and is often represented over small temperature ranges by where A and B are constants and B generally is in the range of 1 to 3 X 10 4 W (m-K2). In Fig. 10-10, we show the temperature effect on L for a few liquids. Over wider temperature ranges, the correlation suggested...

E8 3162e8 6661e8 6665e8 3398e8

1.457E+5 7.787E+4 1.055E+5 1.444E+5 7.578E+4 -2.093E+4 -2 . 809E+4 -3.178E+4 -3.634E+4 -4.258E+4 2.106E+5 1.468E+5 1.704E+5 2.104E+5 1.460E+5 7.917E+4 7.189E+4 6.996E+4 6.565E+4 5.970E+4 278 C5H6N2 2-methyl pyrazine 289 C5H802 ethyl acrylate 3 293C5H10 2-pentene, trans 1 298 C5H100 methyl n-propyl ketone 3 299 C5H100 methyl isopropyl ketone 3 300 C5H100 diethyl ketone 1

E8 3162e8 4099e9 3808e8 2339e8

-1.172E+5 -7.461E+5 8.792E+4 -9.000E+4 5.234E+4 -3.894E+4 -1.300E+5 -1.298E+5 -4.940E+5 -1.644E+5 -5.267E+4 -4.351E+5 -3.500E+5 -6.406E+4 -1.118E+5 -2.617E+5 -8.370E+3 -8.474E+4 -1.842E+5 -2.350E+5 -3.896E+5 -4.614E+4 -3.756E+4 -4.605E+4 -1.880E+4 -1.060E+4 -7.314E+4 -7.390E+4 -4.365E+5 -1.334E+5 -1.310E+4 -3.769E+5 -2.974E+5 -2.633E+4 -6.004E+4 -2.097E+5 2.135E+4 -3.295E+4 -1.130E+5 -1.684E+5 -3.047E+5 -4.670E+3 6.950E+3 3.730E+4 6.800E+4

E8 1272e8 2453e8 1715e8 2673e8

-2.420E+5 -2.018E+4 1.825E+5 -4.572E+4 -4.815E+5 -2.211E+5 -2.847E+5 -1.005E+5 -8.830E+4 -9.337E+5 -1.106E+5 -1.385E+5 -3.938E+5 1.171E+5 -2.288E+5 -3.308E+4 1.578E+5 -1.616E+4 -4.425E+5 -2.069E+5 -2.455E+5 -5.828E+4 -5.954E+4 -8.890E+5 -1.374E+5 -1.658E+5 -3.946E+5 6.695E+4

E8 0791e9 1101e8 3559e9

-5.238E+4 -5.393E+4 -4.765E+4 -5.447E+4 -6.653E+4 -6.222E+4 -6.314E+4 -5.748E+4 -6.150E+4 -6.636E+4 7.628E+4 7.649E+4 8.307E+4 7.767E+4 7.126E+4 7.327E+4 7.134E+4 8.219E+4 7.967E+4 7.90 9E+4 354 C6H12 methyl cyclopentane 1 369 C6H120 ethyl propyl ketone 3 370 C6H120 methyl butyl ketone 371 C6H120 methyl isobutyl ketone 1 372 C6H1202 n-butyl acetate 1 373 C6H1202 isobutyl acetate 1 374 C6H1202 ethyl butyrate 1 375 C6H1202 ethyl isobutyrate 1

E

-0.15 -0.10 -0.05 0 0.05 0.10 0.15 (Est value of & Ge RT-Y) Y Figure 6-1 Effect of errors in AG RT on the equilibrium constant. molecule. Although exact for molecular weights and even reasonable for a few other properties, e.g., the liquid molar volume at the normal boiling point, such methods are completely inadequate for the properties discussed in this chapter. Only slightly more complicated are methods which assign contributions to various chemical bonds. Such techniques are easy to use...

E iS

Where N+, diffusion flux densities of the cation and anion, respectively, g-equiv cm2-s c+, c. corresponding ion concentrations, g-equiv cm3 dE dz gradient in electric potential The electric field gradient may be imposed externally but is present in the ionic solution even if, owing to the small separation of charges which result from diffusion itself, there is no external electrostatic field. Collision effects, ion complexes, and activity corrections are neglected. One equation for each cation...

DNj

The subscripts on the partial derivative indicate that the temperature, total system volume, and all mole numbers (except i) are to be held constant. Thus, one may take the Helmholtz energy function for a particular equation of state, as shown in Table 5-1, and find n, by differentiation. Since the functions so given are expressed as the difference in specific Helmholtz energy between the real state and the chosen reference state, one must multiply the entire expression by N, the total moles,...

Discussion

The quantity of accurate liquid viscosity data at temperatures much above the normal boiling point is not large. In addition, to test estimation methods such as those of Chung et al. or Br l and Starling, one needs accurate liquid density data under the same conditions as apply to the viscosity data. This matching makes it somewhat difficult to test the methods with many compounds. However, Br l and Starling developed their technique so that they would be coupled to a separate computation...

Diffusion in Electrolyte Solutions

When a salt dissociates in solution, ions rather than molecules diffuse. In the absence of an electric potential, however, the diffusion of a single salt may be treated as molecular diffusion. The theory of diffusion of salts at low concentrations is well developed. At concentrations encountered in most industrial processes, one normally resorts to empirical corrections, with a concomitant loss in generality and accuracy. A comprehensive discussion of this subject is available 159 . For dilute...

Diffusion Coefficients

In Sec. 11-2 we discuss briefly several frames of reference from which diffusion can be related and define the diffusion coefficient. Low-pressure binary gas diffusion coefficients are treated in Sees. 11-3 and 11-4. The pressure and temperature effects on gas-phase diffusion coefficients are covered in Sees. 11-5 and 11-6, respectively. The theory for liquid diffusion coefficients is introduced in Sec. 11-8, and estimation methods for binary liquid diffusion coefficients at infinite dilution...

Delgf

7.134E+4 6.590E+4 6.301E+4 1.101E+5 5.81 IE+4 230 C4H602 vinyl acetate 1 231 C4H603 acetic anhydride 1 232 C4H604 dimethyl oxalate 235 C4H602 methyl acrylate 3 242 C4H80 i sobutyraldehyde 1 243 C4H80 methyl ethyl ketone 1 245 C4H80 vinyl ethyl ether 1 246 C4H802 n-butyric acid 1 247 C4H802 isobutyric acid 2 249 C4H802 ethyl acetate 1 250 C4H 802 methyl propionate 1

Dab 781

Where is the viscosity of the solvent and rA is the radius of the spherical solute. Equation (11-8.1) is the Stokes-Einstein equation. Although this fixed relation was derived for a very special situation, many authors have used the form as a starting point in developing correlations. Other theories for modeling diffusion in liquids have been based on kinetic theory 10, 18, 31, 33, 48, 52, 91, 114, 148 , absolute-rate theory 45, 62, 73, 78, 124, 127, 161, 176 , statistical mechanics 17, 18, 111...

C Cj2 x X M 956

Is found from Eq. (9-5.5) with TV, replaced by 7Y and m, by xni (M Mr,)1 2. For a binary gas mixture of 1 and 2, these equations may be written as r,m 1 + tf yel) + X2(l + 2HUKX + H 2K ) (9-5.8) Kl y. + . y2 i.2 3 + (2 m2 M,) (95'9) y2r)2 K2 y2 + i i.2 3 + (2M, M2) (95'10) i + o.36rn(Tfl - i) ' 6 n5 + ioy,

Bp

B is given in Eqs. (3-5.3) and (4-4.1)_ a , 2Z + B*(u - Vu2 - 4w) Z B* V A - A , , In-, . - RT In----RT In bVu2 - 4w 2Z + B*(u + Vu2 - 4w) Z _ Z B* , V 1 da 2Z+ B*(u - Vu2 - 4w) S - S R n-- + R In --, , n-, , Z V bVu- - 4w dT 2Z + B*(u + Vu2 - 4w) For the Soave Equation fa 0.480 + 1.574 , - 0.176 fa 0.37464 + 1.54226 , - 0.26992 Q 0.45724 Note u, w, ah a, and b are given in Table 3-5 and Eqs. (4-5.1) and (4-5.2). Next, using the same Tr but V R) and Z R recompute Eq. (5-4.1) using the reference...

Hv at the Normal Boiling Point

A pure component constant that is occasionally used in property correlations is the enthalpy of vaporization at the normal boiling point AHub. Any one of the correlations discussed in Sees. 7-8 to 7-10 can be used for this state where T Tb, P 1.01 bar. We discuss some of the techniques below. In addition, several special estimation methods are suggested. AW 0 from vapor pressure relations In Table 7-3, we show equations for p AHJ(RTC AZ ) as determined from a number of the more accurate vapor...

Ah

7.08(1 - T,.)0354 + 10.95oo(l - Tr)0'456 (7-9.4) The effect of temperature on AHv is similar to that suggested by Watson (see Sec. 7-12). Nath 68 has presented an equation similar to Eq. (7-9.4) for 0.5 < Tr < 0.7. To use the Lee-Kesler method to obtain values for AS ,0' and AS ,1', the vapor pressure is determined with Eq. (7-2.6) and H H is evaluated for both liquid and vapor. The difference in these two enthalpy departure functions is AHv. Gupte and Daubert 38 report good results with...

Uzy

Om *a< ta + xBaB - (cta < tb)2*a*b (12-5.5) where the terms are as defined above (with xA, xB bulk mole fractions) and A is an average surface area for the molecules constituting the system. This simplified form clearly indicates that < rm is less than a mole fraction average. Example 12-4 Repeat Example 12-3 by using the simplified (ideal) form of the thermodynamic correlation. solution Let subscript A stand for diethyl ether and subscript B for benzene. Then zA 0.423, < rA 16.47, xB...

A m Q QSJfl TfflV V

A 4 0.291 - 0.04(a), + ajy) (5 The interaction parameter ky usually ranges from 0.1 to 0.01. Values for a large number of binary systems have been tabulated 12 . Spencer et al. 74 have reported that the average deviation between PCT estimated from the Chueh-Prausnitz correlation and experimental values was 2 bar unless methane was one of the components. In such cases, the deviation was often much larger. Other techniques for estimating PCm for systems containing methane have been suggested 2,...

[i MvJWMj1

Equation (9-5.13), with from Eq. (9-5.14), has been extensively tested. Wilke 221 compared values with data on 17 binary systems and reported an average deviation of less than 1 percent several cases in which 7jm passed through a maximum were included. Many other investigators have tested this method 4, 28, 42, 51, 78, 161, 176, 177, 191, 214, 223 . In most cases, only nonpolar mixtures were compared, and very good results obtained. For some systems containing hydrogen as one component, less...

Mutual solubilities of liquids

When two liquids are only partially miscible, experimental data for the two mutual solubilities can be used to estimate activity coefficients over Figure 8-12 Activity coefficients in the system ethyla-cetate-ethanol. Calculated lines from azeotropic data (indicated by x) at 1.01 bar. Points are experimental 39, 43 . (From Ref. 123.) Figure 8-12 Activity coefficients in the system ethyla-cetate-ethanol. Calculated lines from azeotropic data (indicated by x) at 1.01 bar. Points are experimental...

Effect of Pressure on the Thermal Conductivities of Liquids

At moderate pressures, up to 50 to 60 bar, the effect of pressure on the thermal conductivity of liquids is usually neglected, except near the critical point, where the liquid behaves more like a dense gas than a liquid Figure 10-10 Thermal conductivity of a few organic liquids as functions of temperature. Figure 10-10 Thermal conductivity of a few organic liquids as functions of temperature. (see Sec. 10-5). At lower temperatures, Aj, increases with pressure. Data showing the effect of...

Property Data Bank

The listing of compounds is by the total carbon number. Within each carbon number class, subgroups are indexed by the number of hydrogens and, further, by additional atoms in alphabetical order. The symbols and equations used are shown below. The enthalpy and Gibbs energy of formation at 298.2 K (DELHF and DELGF) are for the ideal-gas state. The reference states chosen for the elements are as follows Ideal gases at one atmosphere Ar, Cl2, D2, F2, He, H2, Kr, Ne, 02, Rn, T2, and Xe. A1 (crystal)...

Thermodynamic Properties of Ideal Gases

Methods are described to estimate the enthalpy and Gibbs energy of formation as well as the entropy for organic compounds in the ideal-gas state. The reference temperature is 298.15 K, and the reference pressure is one atmosphere. In addition, ideal-gas heat capacity estimation techniques are presented to allow one to determine C as a function of temperature. The enthalpy of formation is defined as the isothermal enthalpy change in a synthesis reaction from the elements in their standard...

Ethyl Chloride Thermal Conductivity

Vinyl fluoride 1,1,1-trifluoroethane acetonitrile methyl isocyanate ethylene 1.2-dichloroethane 1,1-difluoroethane acetaldehyde ethylene oxide acetic acid methyl formate ethyl bromide ethyl chloride ethylene glycol ethyl mercaptan dimethyl sulfide ethyl amine dimethyl amine

Excess thermal conductivity correlations

Many investigators have adopted the suggestion of Vargaftik 169, 170 that the excess thermal conductivity, X X , be correlated as a function of the PVT properties of the system in a corresponding states manner. (Here X is the low-pressure thermal conductivity of the gas at the same temperature.) In its simplest form, where p is the fluid density. The correlation has been shown to be applicable to ammonia 49, 134 , ethane 20 , n-butane 22, 73 , nitrous oxide 133 , ethylene 122 , methane 21, 91,...

Kwm

To determine UD, T* kT e (MC-SD) 323 398 0.811. With Eq. (11-3.6), fiD 1.60. Then with Eq. (11-3.7), (0.19)(0.490)2 a 1JS0 + (0.811) 165 With Eq. (11-3.2) and M (MC) 50.49, M (SD) 64.60, and Mab (2) (l 50.49) + (1 64.60) -' 56.68 MC SD (l)(56.68)1 2(3-84)2( 1.65) 84 Cm S The experimental value is 0.078 cm2 s and the error is 8 percent. A comprehensive review of the theory and experimental data for gas diffusion coefficients is available 138 . There have been many studies covering wide...

Volumetric Properties of Mixtures

In Chap. 3 we reviewed methods for calculating the PVT properties of gases and liquids. To extend the methods to mixtures, they must be modified to include the additional variable of composition. In essentially all cases, the inclusion is accomplished by averaging pure component constants to obtain constants which hopefully characterize the mixtures. Equations which do this are called mixing rules. Many algebraic relations have been suggested, although it can be shown (Sec. 4-2) that...

Jl

Figure 10-3 Eucken factors as functions of temperature (a) hydrogen, (6) nitrogen, (c) carbon dioxide. (From Ref. 14.) Eucken relations. In Fig. 10-3, the Zrot shown is that which gave the best fit to the experimental data. Zrot was assumed temperature-independent. Although Eq. (10-3.8) is probably the best theoretical equation available for estimating the thermal conductivity of a nonpolar polyatomic gas, without some a priori knowledge of ZTOt, it is not of much practical value. ZTOt values...

Sh

Furanose ring Pyranose ring Furanose ring Pyranose ring -0.64 1.049 -+0.546 +0.524 - +0.12 2 -0.60 -0.65 -0.69 2 -0.303 -0.327 2 TABLE 6-5 Cardozo Correction Factors for the Enthalpy of Combustion (Continued) Examples of the Cardozo Method to Estimate the Enthalpy of Combustion TABLE 6-5 Cardozo Correction Factors for the Enthalpy of Combustion (Continued) Examples of the Cardozo Method to Estimate the Enthalpy of Combustion

Gases Liquids

A comprehensive and critical survey of the most reliable estimating methods in use today plus property values for more than 600 pure chemicals. This highly regarded reference has been completely revised to bring you the latest developments in estimating the properties of gases and liquids. An invaluable aid to engineers and scientists, it is the only book in the field to give you a critical analysis of existing estimating methods as well as instantly usable practical recommendations for...

S

H (for formic acid, formates, hydrogen cyanide, etc.) 15 tAdd 18.8 for any carbon group which fulfills the following criterion a carbon group which is joined by a single bond to a carbon group connected by a double or triple bond with a third carbon group. In some cases a carbon group fulfills the above criterion in more ways than one. In these cases 18.8 should be added each time the group fulfills the criterion. The following are exceptions to the 18.8 addition rule 1. No 18.8 additions for...

B

Figure 7-1 shows that the linear form of In Pvp versus l T is not satisfactory for associating materials. Equation (7-2.3) generally overpredicts vapor pressures below Tb (see Fig. 7-1 or Table 7-2). Figure 7-1 Comparison of the simple Clapeyron equation with experimental vapor pressure data. (Adapted from Ref. 2.) Figure 7-1 Comparison of the simple Clapeyron equation with experimental vapor pressure data. (Adapted from Ref. 2.) Equation (7-2.4) is a two-parameter corresponding states equation...

Z Thermal Conductivity

DZ _ (dA* dT)(B* - Z) - B*(A* + Z + 2B*Z) T dT 3Z2 2Z + (A* - B* - B*2) d In < > , _ bj dZ (dZ dP) - (B* P) (8 1229) where a a, blt A*, B*, and fwt are given on pages 42 and 43 and in Eqs. (4-5.1) and (4-5.2) da dT is given in Table 5-1 5, is given in Table 5-13. Example 8-13 Use the Soave equation to calculate the dew point temperature at 40 bar for a 26.54 ethane-73.46 heptane mixture. solution By using the pure component properties in Example 8-12, dew points may be calculated at 5-bar...

Method of Ely and Hanley [40

An extended corresponding states procedure, the method of Ely and Hanley was developed to estimate the viscosities and thermal conductivities of nonpolar fluids, pure or mixtures, over a wide range of densities and temperatures. As illustrated in this section, the procedure has been simplified to treat the thermal conductivity of low-pressure, pure gases. Later we shall extend the approach to handle fluids at high densities. The estimation technique is based on Eucken's proposal to separate the...

E8

101 CHC1F2 chlorodi fluoromethane 1 105 CHN hydrogen cyanide 2 110 CH202 formic acid 3 111 CH3Br methyl bromide 1 112 CH3C1 methyl chloride 1 113 CH3F methyl fluoride 1 114 CH3I methyl iodide 1 118 CH4S methyl mercaptan 1 119 CH5N methyl amine 1 120 CH6N2 methyl hydrazine 3 122 C2Br2ClF3 1,2-dibromo-l-chlorotrifluoroethane 1 124 C2C1F3 chl orotri fluoroethene 1

Ycc

Substituting into the equation of equilibrium and noting that x + x2 1 and x + x'i 1, we obtain exp M1 tX )2 x' exp M1-tX' 2 (8-13.7) and (1 - x ) exp (1 - x' ) exp (8-13.8) Equations (8-13.7) and (8-13.8) contain two unknowns (x and x), which can be found by iteration. Mathematically, several solutions of these two equations can be obtained. However, to be physically meaningful, it is necessary that 0 < x < 1 and 0 < x < 1. Similar calculations can be performed for ternary (or higher)...

Przezdziecki and Sridhar method [160

In this technique the authors propose using the Hildebrand-modified Bat-schinski equation 15, 99, 217 . and the parameters E and V0 are defined below. 12.94 + 0.10M - 0.23pc + 0.0424T, - U.58(Tf Tc) (9-11.10) v0 0.0085cotc - 2.02 + q + q (9-11.11) where Tc critical temperature, K Pc critical pressure, bar Vc critical volume, cm3 mol M molecular weight, g mol 7) freezing point, K to acentric factor Vm liquid molar volume at 7), cm3 mol Thus, to use Eq. (9-11.9), one must have values for Tc, Pc,...

Rt Conductivity

In these equations x, is the mole fraction of component i and the summations in Eqs. (8-10.50) and (8-10.51) are over all components, including component i, 6, is the area fraction, and < i> , is the segment fraction, which is similar to the volume fraction. Pure component parameters r, and q,-are, respectively, measures of molecular van der Waals volumes and molecular surface areas. In UNIQUAC, the two adjustable binary parameters ry and r i appearing in Eq. (8-10.51) must be evaluated...

Yivi

Xi is the mole fraction of component i, and lt t gt , is the superficial volume fraction of i. V, is the molar volume of the pure liquid. For a binary system of 1 and 2, Eq. 10-12.17 becomes Xm 0 X, 2 lt t gt lt t gt 2 2 lt t gt 22X2 10-12.20 The harmonic mean approximation for X1 was chosen over a geometric or arithmetic mean after extensive testing and comparison of calculated and experimental values of Xm. Also, it was found that the V, terms in Eq. 10-12.19 could be replaced by critical...

Estimation of Liquid Viscosity at High Temperatures

Low-temperature viscosity correlations as covered in Sec. 9-10 usually assume that In rn is a linear function of reciprocal absolute temperature. Above a reduced temperature of about 0.7, this relation is no longer valid, as illustrated in Fig. 9-10. In the region from about Tr 0.7 to near the critical point, many estimation methods are of a corresponding states type that resemble or are identical with those used in the first sections of this chapter to treat gases. For example, Letsou and...

Index

Table, 656-732 Activity coefficients from ASOG group contribution method, 313-314 from azeotropic data, 307-309 correlations for, 254-257 definition of, 248 estimation of, 283-332 at infinite dilution, 290-307 from mutual solubilities, 309-311 one-parameter correlations for, 255-259 from UNIFAC group contribution method, 314-332 Ambrose estimation method for critical properties, 12-14 Amoco Redlich-Kwong equation of state, 44, 346 Andrade'correlation for liquid viscosity, 439 Antoine vapor...

Low pressure

This region extends from approximately 10 3 to 10 bar and includes the domain discussed in Sees. 10-3 and 10-4. The thermal conductivity increases about 1 percent or less per bar 68,174,175,176 . Such increases are often ignored in the literature, and either the 1-bar value or the zero-pressure extrapolated value may be referred to as the low-pressure conductivity. TABLE 10-3 Thermal Conductivities of Some Gases at About 1 Bar1 X A BT CT- DT3 X in W m K and T in keivins TABLE 10-3 Thermal...

Recommendations for estimating lowtemperature liquid viscosities

Three estimation methods have been discussed. In Table 9-11 calculated liquid viscosities are compared with experimental values for 35 different liquids usually of simple structure . Large errors may result, as illustrated for all methods. The method of van Velzen et al. is not recommended for first members of a homologous series, and the method of Przezdziecki and Sridhar should not be used for alcohols. The method of van Velzen et al. assumes that log in is linear in T l, whereas the Orrick...

A

Alkanes Boiling Point Nomogram

Thus, all the A terms in Eqs. 5-6.31 and 5-6.32 are second derivatives of the total Helmholtz energy A with respect to moles at constant temperature and total volume V. The determinants expressed by Eqs. 5-6.31 and 5-6.32 are solved simultaneously for the critical volume and critical temperature. The critical pressure is then found from the original equation of state. Peng and Robinson 61 used their equation of state to calculate mixture critical points later Heidemann and Khalil 32 ,...

Notation

A group contribution sum Eq. 9-4.21 b0 excluded volume, 2 3 7rN0 lt T3 B viscosity parameter in Eq. 9-11.2 C heat capacity at constant volume, J mol-K C,-, structural contribu D diffusion coefficient, cm2 s or m2 s Fc shape and polarity factor in Eq. 9-4.10 FP, low-pressure polar cor rection factor in Eq. 9-4.17 Fq, low-pressure quantum correction factor in Eq. 9-4.18 FP, high-pressure polar correction factor in Eq. 9-6.8 Fq, high-pressure quantum correction factor in Eq. 9-6.9 Glt Go...

Chueh And Sswansons Method

Errors for the Chueh-Swanson method rarely exceed 2 to 3 percent and those for Missenard's method 5 percent. Example 5-7 Estimate the liquid heat capacity of 1,4-pentadiene at 20 C by using the Chueh-Swanson group contribution method. CpL 20 C 2 CH2 2 CH -CHj corrections noted in Table 5-10 2X21.8 2X21.3 30.4 10.5 18.8 146 J mol K Tamplin and Zuzic 78 indicate that CPL 147 J molK at 293 K. Example 5-8 By using Missenard's group contribution method, estimate the liquid heat capacity of isopropyl...

Roy and Thodos estimation technique

In the same way that the viscosity was nondimensionalized in Eqs. 9-4.12 and 9-4.13 , a reduced thermal conductivity may be expressed as In SI units, if R 8314 J kmol-K , N0 Avogadro's number 6.023 X 1026 kmol -1, and with Tc in kelvins, M' in kg kmol, and Pc in N m2, T has the units of m K W or inverse thermal conductivity. In more convenient units, where F is the reduced, inverse thermal conductivity, W m-K Tc is in kelvins, M is in g mol, and Pc is in bars. TABLE 10-1 Recommended f Tr...

Method of Chung et al [27

Chung et al. employed an approach similar to that of Mason and Mon-chick to obtain a relation for X. By using their form and a similar one for low-pressure viscosity Eq. 9-4.9 , one obtains where thermal conductivity, W m K M' - molecular weight, kg mol r low-pressure gas viscosity, N-s m2 C heat capacity at constant volume, J mol-K R gas constant, 8.314 J mol-K 1 a 0.215 0.28288a - 1.061 3 0.26665Z 0.6366 pZ P 0.7862 - 0.7109a 1.3168a 2 Z 2.0 10.5T2 The term is an empirical correlation for t 1...

Method of Grunberg and Nissan [87

In this procedure, the low-temperature liquid viscosity for mixtures is given as since Gu 0. In Eqs. 9-13.1 and 9-13.2 , x is the liquid mole fraction and Gij is an interaction parameter which is a function of the components i and j as well as the temperature and, in some cases, the composition . This relation has probably been more extensively examined than any other liquid mixture viscosity correlation. Isdale 107 presents the results of a very detailed testing using more than 2000...

MlJM l

The method of Lucas does not necessarily lead to the pure component viscosity tji when all yj 0 except y, 1. Thus the method is not inter-polative in the same way as are the techniques of Reichenberg, Wilke, and Herning and Zipperer. Nevertheless, as seen in Table 9-4, the method provides reasonable estimates of rim in most test cases. Example 9-7 Estimate the viscosity of a binary mixture of ammonia and hydrogen at 33 C and low pressure by using the Lucas corresponding states method. solution...

Ebs 200 Thermal Conductivity

Prediction of Transport Properties of Dense Gases and Liquids, UCRL 14891-T, University of California, Berkeley, Calif., May 1966. 2. Alder, B. J., and J. H. Dymond Van der Waals Theory of Transport in Dense Fluids, UCRL 14870-T, University of California, Berkeley, Calif., April 1966. 3. Alder, B. J., D. M. Gass, and T. E. Wainwright J. Chem. Phys., 75 394 1971 . 4. Amdur, I., and E. A. Mason Phys. Fluids, 1 370 1958 . 5. American Petroleum Institute, Selected Values of Physical...

Liquid Mixture Viscosity

Essentially all correlations for liquid mixture viscosity refer to solutions of liquids below or only slightly above their normal boiling points i.e., they are restricted to reduced temperatures of the pure components to values below about 0.7. The bulk of the discussion below is limited to that temperature range. At the end of the section, however, we suggest approximate methods to treat high-pressure, high-temperature liquid mixture viscosity. At temperatures below Tr 0.7, liquid viscosities...

Phase envelope constructiondew and bubble point calculations

Calculations at low pressures present little difficulty, but high-pressure calculations can be complicated by both trivial root and convergence difficulties. Trivial root problems can be avoided by starting computations at a low pressure and marching toward the critical point in small increments of temperature or pressure. When the initial guess of each calculation is the result of a previous calculation, trivial roots are avoided. Convergence difficulties are avoided if one does dew or bubble...

Gqh

CpL 0 C 2 CH3 -1- -CH -OH 2X40.0 23.8 33.5 137.2 J mol K The experimental value is 135.8 J mol K 25 . Several corresponding states methods for liquid heat capacity estimation have been cast in the form of Eq. 5-5.4 . For example, with Tables 5-8 and 5-9, one can estimate the heat capacity departure function CPL Cp for liquids as well as for gases. Good results have also been reported by using an analytical form of the Lee-Kesler heat capacity departure function 47 for calculating liquid heat...

Viscosity of Gas Mixtures at High Pressures

Sae Viscosity Temperature

The most convenient method to estimate the viscosity of dense gas mixtures is to combine, where possible, techniques given previously in Sees. 9-5 and 9-6. In the pure dense gas viscosity approach suggested by Lucas, Eqs. 9-6.4 to 9-6.10 were used. To apply this technique to mixtures, rules must be chosen to obtain Tc, Pc, M, and m as functions of composition. For Tc, Pc, and M of the mixture, Eqs. 9-5.18 to 9-5.20 should be used. The polarity and quantum corrections are introduced by using...

Aay12i f yK yAi

In Eq. 4-8.1 , there are three parameters per binary in Eq. 4-8.2 there are two. Both of these equations make kijt as defined in Eq. 4-5.1 , a linear function of composition. The composition dependence expressed by Eq. 4-8.2 is obtained from Eq. 4-8.1 if is set equal to minus Burcham et al. 7 have examined the case when one of the two d parameters in Eq. 4-8.1 is set equal to zero. Several authors have added a second binary interaction parameter in the b constant 8, 15, 49, 55 , i.e. See also...