S.
H.
F I S H T I N E
RELIABLE L A T E N T H E A T S OF V A P O R I Z A T I O N
n the two previous articles I have presented several
I reliable methods for calculating heats of vaporization
from vapor pressure data, critical data, or both. All of the methods discussed so far represent simplifications of the Clapeyron equation. I t is also possible to calculate latent heats when only the normal boiling point is known. No further d a t a are required, although a good knowledge of chemical structure may be needed. Heats of vaporization and boiling points are both functions of the forces of molecular attraction within the saturated liquid and vapor phases. I t is logical, then, that there be a direct relationship between these two properties. Kistiakowsky (75) developed a n equation, given below, expressing this relationship for nonpolar liquids. T h e Kistiakowsky equation can be used with complete confidence to calculate latent heats for most, but not all, nonpolar substances, organic or inorganic, at the normal boiling point. T h e aim of this article is to present methods which will enable the reader to apply the Kistiakowsky equation to most associated as well as normal liquids, with little or no loss in accuracy. Forces of Intermolecular Attraction
V a n d e r Waals’ Attraction. Even in nonpolar substances, electron motion gives rise to small, transient separations of charges within the molecule, resulting in temporary but ever-forming dipoles. Attraction between opposed dipoles of this type is called van der Waals’ force. T h e strength of the van der Waals’ force increases as the number and complexity of atoms in the molecule increases. Dipole-Dipole Attraction. Permanent electrical dipoles in molecules produce a force of attraction in addition to the van der Waals’ forces. I n polar substances the centers of density of the positive a n d negative charges within the molecule ( Z + a n d 2-) are separated by a distance d. Dipole moment ( p ) is a measure of this polarity, and is equal to the product Z X d.
For low molecular weight organic compounds, the attractive forces due to polarity are of the same order of magnitude as the van der Waals’ forces. But as the molecular weight of compounds in a homologous series increases, van der Waals’ forces begin to predominate in governing physical properties such as boiling point and the latent heat of vaporization. Also, as the normal boiling point within a polar homologous series increases, the molecules become more a n d more disoriented because of thermal agitation, a n d dipole-dipole attraction with its resultant molecular association decreases rapidly. H y d r o g e n Bonding. I n compounds where hydrogen is attached directly to atoms which are strongly electron attracting (such as oxygen, nitrogen, or fluorine) the hydrogen atom is stripped of its electron to a considerable extent. T h e electron deficient proton may approach the valence electrons of the electronegative atom in a second molecule, resulting in a chemical bond. T h e attractive forces between molecules due to hydrogen (proton) bonding are generally much more powerful than the forces of attraction resulting from dipole-dipole interaction or transient polarization. T h e high degree of association in compounds which form hydrogen bonds generally results in abnormally high boiling points a n d very high molal heats of vaporization. The Kistiakowsky Equation
Kistiakowsky found the following very simple relationship to be remarkably accurate for nonpolar substances at the normal boiling point : L a b = v b In v b (3.1) or L o b = p b v b In ( p b v b ) (3.2) T h e units of L o b are m1.-atm./g. mole, vbis the molal volume of the saturated vapor in ml., and Pb is the saturation pressure (one atmosphere). Applying the
Stanley H . Fishtine is a Consulting Engineer in Boston, Mass.
AUTHOR
VOL. 5 5
NO. 6
JUNE
1963
47
ideal gas law to the vapor converts this equation to its usual form: Lzb= Tb(8.75 4.576 log T o ) (3.3) Laois now in cal./g. mole and T,is in I-l benzenes). The possibility of calculating reliable heats of vaporization without vapor pressure data or critical data is a fascinating one. T o serve this end? I derived correction factors for a ivide variety of compounds which associate b y dipole-dipole interaction, by hydrogen bonding, or by both. The correction factor, K K ~may , be applied to Equation 3.3 to give the modified Kistiakowskjequation : L , ~ KKir, (8.75 4.576 log r,) (3.4) Methods of estimating K K are ~ discussed in the following paragraphs.
=
+
K K z Factors for Aliphatic and Alicylic Organic Compounds
For aliphatic and alicyclic compounds, K K % factors are listed in Table 3.1. The correction factors were derived from a combination of sources : -Experimental latent heat values from the literature. -The Haggenmacher equation, using vapor pressure data of Stull (29) and Rossini ( 2 6 ) . -The Giacalone equation. The experimental critical constants used in the Haggenmacher and Giacalone calculations were in most cases those recommended by Kobe and Lynn (77). LVhere experimental values of T , and P, were not available. they were 48
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
estimated by the Lydersen group contribution method (79). -The use of judgment, based on a consideration of molecular structure and a comparison with correction factors determined for similar compounds. The Klil factors for many of the hydrocarbons were calculated directly from A.P.I. latent heat data (26). Factors for other h>-drocarbons, the sulfides and mercaptans were calculated via the Haggenmacher equation, using Antoine constants also listed by Rossini. The factors for the halides were derived from 16 reliable experimental latent heat values, and from a consideration of the effect of dipole moment and boiling temperature on the compounds included. Experimental latent heats were available for 28 esters, three ketones and one aldehyde. Where experimental data were needed and not available, the Haggenmacher and Giacalone equations were used to calculate Lvb. Equal KKI values were assigned to corresponding members of the three homologous series containing more than 3 carbon atoms. Experimental latent heats were available for elcven alcohols containing 1 to 8 carbon atoms. Latent heats at the normal boiling point for 1-nonanol and undecane2-01 were calculated b>- means of the Haggenmacher and Giacalone equations. All latent heats for the polyhl-dric alcohols were calculated from the Haggenmacher equation alone. Values computed by means of the Giacalone equation using estimated critical constants appear quite unsatisfactory. For cyclohexanol, cyclohexyl methyl alcohol, and so forth, K K ( factors are lower than the correction factors for the aliphatic alcohols with the same number of carbon atoms. Cyclohexanol is believed to be fairly rigid in structure. Hence the -OH group is relatively immobile and is not so accessible for proton bonding a s the -OH group in the corresponding aliphatic alcohol. Where the alcoholic -OH group occurs on an alk>-l side chain of cyclohexane, I have shown K K to ~ increase in value as the length of the side chain increases. These ~ based on the increasing mobility of the values of K K are hydroxyl group and hence its greater availability for proton bonding. Note that the K K factors ~ for the primary amines are high, but not nearly so high as those for the alcohols. The secondary amines do not associate to a very large degree by proton bonding. In fact, K1ci values for many of the highly polar compounds listed in Table 3.1 ~ for the secondary amines are a s high as the K K factors containing the same number of carbon atoms. I n the case of the tertiary amines hydrogen bonding is no longer possible. Since the dipole moments of tertiary amines are relatively low, I have arbitrarily assigned a value, K K = ~ 1.01, for this class of compounds.
Alicyclic Compounds Which Undergo Hydrogen Bonding, Values of KKt for many of these substances are not listed directly in Table 3.1. However, Table 3.1 may be used as a basis for estimation. Here are some illustrations :
TABLE 3.1.
K K FACTORS ~ FOR A L I P H A T I C AND ALICYCLIC" O R G A N I C COMPOUNDS
n-Number of carbon atoms in compound, including carbon atoms of functional grouji 3 4 5 6 7 8 9 70 77
Comfiound T y f i e
Hydrocarbons n-AI kanes Alkane isomers Mono- and diolefins and isomers Cyclic saturated hydrocarbons Alkyl derivatives of cyclic saturated hydrocarbons
0.97
Halides (saturated or unsaturated) Monochlorides Monobromides Monoiodides Polyhalides (not entirely halogenated) Mixed halides (completely halogenated) Pe rfl uo roca rbons Compounds Containing the Keto Group Esters Ketones Aldehydes
Sulfur Compounds Mercaptans Sulfides Alcohols Alcohols (single-OH group) Diols (glycols o r condensed g Iyco Is) Triols (glycerol, etc.) Cyclohexanol, cyclohexyl methyl alcohol, etc. Miscellaneous Compounds Ethers (aliphatic only) Oxides (cyclic ethers)
1.01
1.01 1.00
1 .OO 0.99 1.01 1 .oo
1 .OO 0.99 1.01 1 .oo
1 .OO 0.99 1.01 1 .oo
1 .OO 0.99 1.01 1 .oo
1.00 0.99 1.01 1 .oo
1 .OO 0.99 1.01 1 .oo
1.09 0.99 1.01 1 .oo
1 .OO 0.99 1.01 1 .oo
1 .OO 0.99 1 .oo 1 .oo
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.99
1.04 1.03 1.02
1.03 1.03 1.02
1.03 1.03 1.02
1.03 1.03 1.02
1.03 1.03 1.02
1.03 1.02 1 .01
1.03 1.02 1.01
1.02 1 .02 1 .01
1.02 1.01 1.01
1.02 1.01 1.01
1.01 1.01 1 .01
1.05
1.05
1.05
1.04
1 .04
1.04
1.03
1.03
1 .03
1 .02
1 .02
1 .01
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.01 1 .oo
1.14
1.09 1.08 1.08
1 .08 1.07 1.08
1 .07 1.06 1.07
1 .Ob 1.06 1.06
1.05 1.05 1.05
1 .04 1.04 1.04
1 .04 1 .04 1.04
1 .03 1 .03 1.03
1 .02 1 .01 1 .02 1 .01 1.02 1.01
1.13. 1.12 1.09 1 .08 1.01 1.05 1.07 1.07 1.07
1.11 1.08 1.01 1.C6 1.06
1.10 1.07 1.01 1.06 1.06
1.10 1.07 1.01 1.05 1.05
1.09 1 .06 1.01 1.05 1.05
1.09 1.05 1.01 1.04 1.04
1.08 1.05 1.01 1.04 1.04
1.07 1 .04 1.01 1.03 1.03
1.06 1 .04 1.01 1.02 1.02
1.05* 1 .03b 1.01 1.01 1.01
1.05
1.03 1.03
1.02 1.02
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.01 1.01
1.22
1.31
1.31
1.31
1.31
1.30
1.29
1.28
1.27
1.26
1.25
1.24b
1.33
1.33 1.38
1.33 1.38
1.33 1 .38
1.33
1.33
1.33
1.20
1.20
1.21
1.24
1.26
1.16
1.07
'
1 .OO
1.05 1.04 1.03
-
Nitrogen Compounds Primary amines Secondary amines Tertiary amines Nitriles Nitro compounds
1 .OO
72-20
1.09
1.03 1.08
1.03 1.07
1.02 1.06
1.02 1.05
1.02 1.05
1.01 1.04
1.01 1.03
1.01 1 .02
1.01 1.01
1.01 1.01
1.01 1.01
(Continued on next page) VOL. 55
NO. 6
JUNE 1963
49
Cyclohexylamine: The correction factor for this compound would be expected to be ~ for the correlower than the K K value sponding aliphatic amine ( n = 6), due to H the relative immobility of the hydrogen I bonding group. For the aliphatic hexylamines K K = ~ 1. l o . For cyclohexylamine, I would use K K = ~ 1.07. Pif?eridine: Piperidine is a cyclic secondary amine. Once again the proton bonding group is relatively immobile. From Table ~ 1.07 for aliphatic secondary amines ( n = 5). 3.1, K K = I suggest using K K = ~ 1.05 for this compound. Aliphatic or Alicyclic Compounds Containing More Than One Functional Group. I n such cases, I recommend selecting che value from Table 3.1 with ~ For example, for chloroacetone: the highest K K factor. K K= ~ 1.08 for acetone, K K CHO
‘
-CHo
2.76
-
’NO2
3.98
+ = (4.752 + 3.452)1’2
Z p h = 2.76 (1/2)(3.98) = 4.75 Zpv = (3.98)(0.866) = 3.45 = 5.89 (calculated) No experimental value is available for comparison ( b ) p-chlorobenzaldehyde The -CHO group is a nonsymmetrical group and it lies para to the -C1 atom. For calculation purposes move the dipole vector for the -CHO group to the meta position. Then the vector diagram for p-chlorobenzaldehyde is the following: p
3.3 : Estimate the dipole moment of p-acetylacetophenone. Solution : We see from Table 3.2 that the axis of the dipole of the -COCHs group does not pass through the center of the benzene ring. Since the two groups lie para to each other, assume one of the groups is in the meta position for estimating purposes. Then the vector diagram may be shown as follows:
EXAMPLE
J
2.89
2.89 - (1/2)(2.89) = 1.45 Z p u , = (2.89)(0.866) = 2.50 p = (1.452 2.502)*/* = 2.89 (calculated) p = 2.71 (experimental) Zph =
+
The method described above is used in Examples 3.4, 3.5, and 3.6 to calculate latent heats of vaporization for polysubstituted benzenes. The illustrations selected show the applicability of the method in cases where basic data are lacking. Calculate Lobfor salicylaldehyde. OH Data: M = 122.1, To = 470°K. Solution : The calculation method described in Section B may only be used for compounds which do not associate by hydrogen bonding. From the structural formula shown above it would appear that the method may not be applied in this case, since phenols do associate by proton bonding. However, salicylaldehyde forms a hydrogen bond within the molecule itself (cheleate ring formation). The proton of the phenol group is tied up and cannot form intermolecular hydrogen bonds. Since the only forces acting on the molecules are those of dipoledipole interaction and van der Waals’ attraction, the method of Section B is applicable. Estimate p.
E X ~ M P L E3.4:
0“““
1.6
2.76
1.58 - (1/2)(2.76) = 0.28 Z p * = (2.76)(0.866) = 2.39 p = (2.392 0.282)1’2 = 2.41 (calculated) p = 2.03 (experimental) Zph =
+
Case C-The moments of more than one substituent group are not colinear with the axis of the benzene ring. When two lopsided functional groups lie ortho or meta to each other, calculate the resultant moment as if the two groups were colinear with the axis of the ring. When the two unsymmetrical groups lie para to each other, assume that one of the groups lies in the meta position. Then calculate the resultant moment as if the moments of all groups lie on the axis of the benzene ring. The treatment is exactly the same as in Case B.
-OH
T/ -CHO
Z p I L = (2.76)(@.866)
= 2.39 S p , = 1.6 (2.76)(0.5) = 2.98 = (2.3V 2.982)”2 = 3.82 p
+
2.76
- ----
+
Estimate K K %from Equation 3.5. K K= ~ 1 (2)(3.82)/10@ = 1.076 Calculate Lobfrom Equation 3.4. L t t = (1.076)(47@)(8.75 4.576 log 470)/(122.1) = 86.7 cal./g. (calculated)
+
+
EXAKPLE
3.5 : Calculate Lbbfor phthalic anhydride.
Data: M
=
148.1, To = 558
Solution : In order to estimate the dipole moment for this molecule, assume the following molecular structure for which the component moments are known. (Continued on next page) VOL. 5 5
NO. 6 JUNE 1963
51
Estimate
p
2.76 -CHO
I/ -CHO
2.76
-----
= 2.39 Zpn = (2.76) (0.866) Z p L i = 2.76 (2.76)(0.5) = 4.12 1.1 = (2.39' 4.122)"2 = 4.77
+
+
Estimate KKz from Equation 3.5. KIi, = 1 (2)(4.77)/100 = 1.095 Calculate Lcbfrom Equation 3.4. L,, = (1.096)(558)(8.75 4 376 log 558)/(148.1) = 87.9 cal. /g. (calculated) EXAMPLE 3.6: Calculate LLb for piperonal [Formula (a)]. Data: M = 150.1, T o = 536'K.
+
+
These values are recommended even when the benzene ring also contains other polarizing substituent groups. ~ 1.15 for 2,3-dichlorophenol. HowFor instance, K K = ever, the values listed for the phenols should not be used when the benzene ring contains more than one highly polar group. Resonance effects may radically alter the proton bonding ability of the phenolic -OH group. I n some cases the resultant dipole moments for polysubstituted benzene compounds containing the --T\;HR group will yield K K ~values greater than 1.06. For these cases use of the larger K K ,value is recommended. The K K i factor for phenols containing a single -OH group was derived by calculating Lobof phenol, o-cresol, m-cresol, and &cresol by the Haggenmacher and Giacalone equations. Values of the B and CAntoine constants used in the Haggenmacher calculations are those of Biddescombe and Martin (7). The other factors listed in Table 3.3 were also developed from calculated latent heats. K K %Factors for Naphthalene Derivatives
Solution : For calculation purposes assume the compound contains two methoxy groups [Formula (b) 1. The assumed compound has two asymmetric functional groups in para positions. As illustrated in Case C, the dipole vector for one of the groups will be moved to a meta position so as to give the maximum moment for the compound. This is accomplished by moving the dipole vector for the -CHO group to the 2 position. The \Tector diagram for piperonal, then, may be shown as below. Estimate ,u
-F2*76
+ 1.25)(0.866) 3.48 - 1.25 = 0.13 = (3.482+ 0.132)1/2 3.48
Z,un = (2.76
--3p--
=
Z,uL = (2.76)(0.5)
-0CHa
-OCH, 1-26
I.(.
=
1.25
Estimate K K %from Equation 3.5. Kit, = 1 (2)(3.48) = 1.070 Calculate Lobfrom Equation 3.4. LLb= (1.070) (536) (8.75 4.576 log 536) /(150.1) = 81.3 cal., g. (calculated)
+
+
For substituted naphthalenes which do not associate by hydrogen bonding. K K , may be estimated by the following equation : KK, = 1 /.4/100 (3.6) K K , values for substituted naphthalenes will be lower than the correction factors for the corresponding benzene derivatives. T o estimate ,u for naphthalene derivatives containing one or more substituent groups or atoms, use the moments listed in Table 3.2. For estimating purposes, assume naphthalene is shaped like an octagon (see diagram below). Of course this is not true, but the assumption will greatly simplify calculations for resultant dipole vectors. Thus. according to the diagram, 7@2' 1,4-dichloronaphthalene is polar, 6 \ whereas 1,5-dichloronaphthalene is - - _ 4_ 3 1 nonpolar. 6 K K ~factors for naphthols and naphthylamines are given in Table 3.4. X'alues have been determined from a bare minimum of data, using Giacalone and Haggenmacher equations to calculate Lzb.
+
TABLE 3.4.
KK; FACTORS FOR NAPHTHOLS AND NAPHTHYLAMINES Compound type
KK$ Factors for Benzene Derivatives Which Associate by Hydrogen Bonding
This class of compounds includes the phenols, anilines and N-substituted anilines. Table 3.3 gives recom~ for these compounds. mended K K values T A B L E 3.3. K K % FACTORS FOR BENZENE DERIVAT I V E S W H I C H ASSOCIATE BY H Y D R O G E N B O N D I N G
ComFound T y p e Phenols (single -OH group) Phenols (more than one -OH group) Anilims (single --?;H? group) Anilines (more than one -NH? group) N-substituted anilines (C6Hj-NH-R)
52
1
K K ~
I
1.15 1.23 1.09
,
1 I
1 .14
1.06
INDUSTRIAL AND ENGINEERING CHEMISTRY
Kaphthols (single -OH group) Naphthylamines (single -NHe group) N-substituted naphthylamines (Ci0H,---NHR) _ _ _
1 ~
KKi 1 09 106 1 .03 ~
K K ~Factors for Miscellaneous Aromatic Compounds
This Here judgment plays a part in estimating K K ~ . is illustrated in the following examples : Diphenyl Sulfide: This compound is not rigid in structure. It is unsymmetrical and hence is polar. K K ~= 1.026 for phenyl methyl sulfide, estimated from the dipole moment of that compound given in Table 3.2. K K t = 1.03 for the corresponding aliphatic sulfide
from Table 3.1 (n = 2). The two values are so close that either one may be used in Equation 3.4 to calculate Lob. Diphenylamine: KKt = 1.09 from Table 3.1 for secondary amines (n = 2), while K K ( = 1.06 from Table 3.3 for N-substituted anilines. I would use the latter value. Diphenylamine is an aromatic compound, and the value from Table 3.3 should be given greater weight. Triphenylamine: Select KKi = 1.01 from Table 3.1. Benzophenone: K K = ~ 1.09 from Table 3.1 (n = 3). = 1.058 estimated from the dipole However, moment of acetophenone listed in Table 3.2. I would use the latter value. K K i Factors for Miscellaneous Organic Compounds
Heterocyclic Compounds Which Are Aromatic in Nature. Several important heterocyclic compounds such as pyridine, furan, and thiophene possess conjugated double bonds and mobile electrons which characterize aromatic behavior. It is not difficult to estimate dipole moments for substituted pyridines, furans, and thiophenes once the moments and dipole orientations of the base compounds are known. Dipole vector diagrams for these three substances are given below. p =
2.23
p =
0.69
p =
0.54
T
t
T
pyridine
furan
thiophene
Once more, the arrow indicates the negative end of the dipole. Calculations for furan and thiophene derivatives may be simplified greatly by assuming that all bond angles are 60'. The next example illustrates the method ~ for of determining resultant moments and K K values this class of compounds. 3.7: Estimate K1ct values for (a) a-picolene, and (b) furfural.
EXAMPLE
Data: Use the base group moments shown above, and use the values listed in Table 3.2 for moments of substituent groups. Solution : (a) a-picolene The dipole vector diagram is the following:
jiH3
6
2.14 (calculated) K x 1 = 1.042 (from Equation 3.5) p =
CH3
-----_30'
0.4
(b) furfural For simplicity, all bond angles are assumed 0 O C H o to be 60'. The dipole vector diagram may then be represented in the following way:
0.69 p =
2.76
lo\
3.07 (calculated)
K K i = 1.061 (from Equation 3.5)
-CHO
All Other Nonaromatic Compounds Boiling Over 0' C. Which Do Not Associate by Hydrogen Bonding. Assume K K ( = 1.06. This heading is nearly all-
inclusive. Nevertheless, errors in calculated values of Lvb should not exceed 5y0. If the molecular structure of the compound indicates beyond any reasonable doubt that the substance is nonpolar, then, of course, a value of 1.00 should be used for K K ( . K K Factors ~ for Inorganic Compounds
Nonpolar Inorganic Compounds and the Elements. For all nonpolar compounds which do not undergo ~ 1.0. Thus, partial vapor phase association, use K K = the unmodified Kistiakowsky equation is quite accurate for substances such as the inert gases and the halogens. Equation 3.3 works equally well for metallic elements such as mercury, silver, and gold which have monatomic vapors. However, large errors result when this equation is applied to members of the alkali metal family. Sodium and potassium are both known to contain a mixture of monatomic and diatomic molecules in the vapor phase. It is assumed that Rb and Cs behave in a similar manner. Calculations by the author have also shown the Kistiakowsky equation to be quite inaccurate for members of the alkaline-earth family of metals-Ca, Sr, and Ba. No evidence is now available to show that these metals associate in the vapor phase, so the reason for the discrepancies in latent heat calculations is by no means apparent. Polar Inorganic Compounds Boiling Above 50". For polar inorganic compounds boiling in the range 50 " to 500° C. assume K K ~ = 1.06. For the temperature range 500Oto 1000' C., assume K K ~= 1.03. For all ionic salts, except the fluorides, boiling above 1000° C., use K K ( = 1.00. These factors do not apply to substances which associate by hydrogen bonding. Below 50' C. thermal agitation is not great enough to prevent a high degree of association even in compounds with relatively low dipole moments. For example, the K K factor ~ for SO2 is calculated to be 1.12. This factor is quite high, when we consider that the dipole moment of SO2 is only 1.6. Conclusion
I n many instances, no hard and fast rules are set down for estimating the factor. Judgment should be used. For organic compounds a good knowledge of chemical structure and its relation to physical behavior will be very helpful in minimizing errors. However, most of the calculation methods described can be utilized by people with little background in the organic field.
(Continued on next page) VOL. 5 5
NO. 6
JUNE 1 9 6 3
53
&
E V A L U A T I O N OF CALCULATION METHODS
I n the first two articles of this series several methods were discussed and illustrated for calculating latent heats of vaporization of pure liquids. \Ve already know that the Giacalone, Riedel, and modified Klein equations may be used with complete confidence when experimental values of critical temperature and critical pressure are available (Part I-April 1963). But can we expect the same high degree of accuracy when the critical data must be estimated3 The theoretical basis for determining latent heats from vapor pressure data is well established. However, use of the Haggenmacher latent heat equation (Part IIMay 1963) requires determination of the Antoine C constant and the correction factor, AZ, for nonideal gas behavior, both by empirical means. When using the Haggenmacher equation and the modified Othmer equation, we also depend on the accuracy of published vapor pressure data. How accurate, then, are latent heats calculated by these two methods? K K ~factors for the modified Kistiakowsky equation have, in effect, been predetermined for aliphatic organic compounds and inorganic salts. The modified Kistiakowsky equation may be used with confidence for these compounds, But what measure of reliability can we place on latent heat calculations for substituted aromatic and heterocyclic compounds? Finally, how accurate are published experimental latent heat values? The answers to these questions are demonstrated in Table 3.5 and in the discussion to follow. The table compares values of Loa calculated by the Haggenmacher, modified Othmer, Giacalone and modified Kistiakowsky equations. Heats of vaporization calculated by the Haggenmacher and modified Othmer equations are in all cases determined using the vapor pressure tabulations of Stull ( 2 9 ) . T h e R and C Antoine constants used in the Haggenmacher correlation are all estimated by the methods described in Part 11. I n most cases, calculations of the Haggenmacher AZ factor and calculations involving the Giacalone equation were made using estimated values of critical temperature and critical pressure. Few experimental latent heats are available in the literature for substituted aromatic and heterocyclic compounds. Thus, in many cases it is necessary to determine by calculation a “most probable value of Lva.” I n most instances this is accomplished by taking 54
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
an alerage of all calculated values. Where reliable experimental values of Labare available, these are used as the most probable values. Deviations from the \-slues which I consider to be most reliable are shown in Table 3.5 for each compound and for each calculation method tested. Since reliable estimates of T , and P,can only be made for organic compounds, the evaluation to follow will be restricted to organic substances. Accuracy of Calculation Methods
For the 43 substances studied (chloral hydrate excluded), the modified Kistiakowsky equation appears to qive the most accurate results. The ax’erage de\,iation from the most probable values of L a bis only 1.37,. It is true that K K factors ~ for all aliphatic compounds (except diethyl oxalate and dimethyl oxalate) were, in effect, Predetermined from other experimental or calculated latent heat values. But for 32 of the 43 ~ were not predetermined. substances listed, K K factors The average deviation for these substances is still only 1.67,. The average deviation for the Giacalone equation is 1.7%. This is quite remarkable when we consider that estimated values for the critical constants were used in nearly all cases. It is clear that very poor results can be obtained with the Haggenmacher and modified Othmer equations when we use published vapor pressure data which ha.ve not been completely evaluated for accuracy. Excluding diethyl oxalate, phthalic anhydride, and 2,4-xylaldehyde, the average deviation of the Haggenmacher equation is reduced from 2.67, to 1.8y0. Omitting diethyl oxalate and 2,4-xylaldehyde, the average deviation for the modified Othmer equation is 1.77,. Calculated latent heats agree within 5% for 30 of the 44 substances tabulated. Some of the larger discrepancies will now be discussed. Diethyl Oxalate: Lj-dersen’s group-contribution method for estimating the critical temperature and critical pressure has been found to be very accurate for esters (79). Consequently, the Giacalone L,, value for diethyl oxalate should be reasonably accurate ( f3%). For this reason we have selected the Giacalone value as the most probable value of LCb. Using this criterion, it appears that the high latent heats calculated by the Haggenmacher and modified Othmer equations can only result from poor vapor pressure data. It is interesting to note that agreement in calculated latent heats is reasonably good for dimethyl oxalate. The deviation of the Giacalone latent heat from the selected value for this compound is only - 1 .8y0. Phthalic Anhydride: Values of L,,determined by the Giacalone and modified Kistiakowsky equations are in close agreement, and are assumed to be approximately correct, The relatively large error of the Haggenmacher value may be attributed mostly to poor vapor pressure data, although uncertainty of the -4ntoine C correlation for high-boiling organic compounds ma); also be a contributing factor (see Table 2.1).
2,4-Xylaldehyde: The latent heats determined by the Giacalone and modified Kistiakowsky equations for this compound are in close agreement. From structural considerations we know that K K ( values for 2,4-xylaldehyde and benzaldehyde should be nearly the same. Deviations of the Giacalone and modified Kistiakowsky latent heats for benzaldehyde are only +0.2Oj, and - 1.1yo, respectively. Therefore, we must conclude that the Haggenmacher and modified Othmer values of L,, for 2,4-xylaldehyde are in error. Once again, this error can only come from poor vapor pressure data.
TABLE 3.5.
Experimental Data-How
RELIABILITY OF CALCULATION METHOD Lotent Heats at the Normal Boiliy
Compound Acetaldehyde
M
44.05
tb,
Llaggen- Modifred macher Othmer
Giacul-
Pc, atm.
one
Modified KisliuI;owshy
0.631
(55.3)
146.5
143.9
145.4
93.9 95.2 93.9 96.6 112.6 115.9 56.5 57.7 64.7 65.8 62.1 63.5 81.4 84.9 68.3 74.4 75.9 71.1 72.9 70.2 71.6 67.7 68.6 85.2 87.0 141.2 82.0 84.4 90.0 88.2 65.1 79.4 81.5 108.0 110.2 103.1 105.6 136.0 200.8 123.7 101.9 79.0 82.1
93.4 90 5 95.1 93.9 114 0 112.0 57.2 58.4 63.0 63.0 64.4 64.7 82.3 81.3 62.2 67.2 76.9 75.6 72.9 73.3 73.4 74.7 71.0 69.4 69.3 73.7 136.4 139.7 85.0 83.2 85.1 83.5 67.0 67.4 78.4 79.8 103.2 100.0 99.6 104.2 137.2 133.7 193.4 197.7 118.0 121.7 102.5 102.4 81.0 80.7
Input Datu Tb/Tc
C.
20.2
Reliable?
I n the April article we surveyed the sources and accuracy of published latent heat data in a general way. Now we can be more specific. From Table 3.5 we can see that heats of vaporization measured by the condensation method (see Part I) are often quite unreliable. The value for acetic anhydride is approximately 29y0 too low. For carvacrol the measured value of L,, is about 18% too low. The measured value for nitrobenzene is 11yo too low. For salicylaldehyde the error in the experimental latent heat is about - 13y0,
Acetic anhydride Benzaldehyde Benzyl alcohol Bromobenzene i-Butyl-i- bu tvra te i-Butyl-n-butyrate Carvacrol Chloral hydrate Chlorobenzene a-Chlorotoluene p-Chlorotoluene Di-&butylamine Diethyl oxalate Dimethylamine Dimethylaniline Dimethyl oxalate Diphenyl sulfide Ethyl phenyl ether Furfural I-Heptanol Hydroquinone Methylamine Methvl mercaptan Methyl sulfide Naphthalene
102.1 106.1
139.6 179.0 108.1 204.7 157.0 156.2 144.2 147.5 144.2 156.9 150.2 237.0 165.4 96.2 112.6 132.2 126 6 159.3 126.6 162.3 129.2 139.5 146.1 185.7 45 08 7.4 121 2 193.1 118.1 163.3 186.3 292.5 122 2 172.0 96.08 161.8 116.2 175.8 110.1 286.2 31.06 -6.3 48.10 6.8 62.13 36.0 128.2 217.9
(0.678: (0.068) (0,707) 0,640 0.700 0,704 (0.710) (0.745) 0.641 (0.659) (0.659) (0.711) (0.711) 0.642 0.678 (0.683) (0.687) (0.678) (0.662) (0.740) (0.685) 0.621 (0.601) 0.615 0.655
(42.2) (41 .7) (45.0) 44.6 (25.8) (25.4) (33.0) (48,9) 44.6 (38.6) (38.6) (25.4) (30.4) 52.4 35.8 (39.2) (32.9) (34.8) (48.6) (29.4) (73.4) 73.6 (58.7) 54.6 39.2
a-Nitrohenzaldehyde Nitrobenzene Nitromethane a-Nitrophenol 1-Octanol Phenyl acetonitrile Phthalic anhydride a-Picolene Piperidine Piperonal Pyridine Salicylaldehyde 2,3,4,6-Tetrachlorophenol 1,2,3-Trichlorobenzene 1,3,5-Trichlorobenzene 2,3,5-Trirnethyl acetophenone Trimethylamine 2,4-Xylaldehyde
151.1 123.1 61.04 139.1 130.2 117.1 148.1 93.12 85.15 150.1 79.10 122 1 231.9 181.5 181.5
273.5 210.6 101.2 214.5 195.2 233.2 284.5 128.8 106.0 263 0 115.4 196.5 275.0 218.5 208.4
(0.707) (0.673) 0.637 (0,684) (0,750) (0,692) (0.697) (0.642) (0.648) (0.703) 0.617 (0.679) (0.707) (0,670) (0.670)
(37.3) (43.3) 62.3 (42.7) (26.5) (34.2) (36.1) (43.5) (45.7) (35.3) 55.6 (41 .5) (36,4) (36,6) (36.6)
86.0 135.3 79.5 94.0 95.5 77.1 95.2 93.7 84.5 107.2 84.0 58.3 55.6 54.4
162.2 59.11 134 2
247.5 2.9 215.5
(0.718) 0.637 (0.697)
(26.7) 40.2 (31.9)
77.1 93.5 88.9
82 . ‘7
86.0 89.9 89.3 138.8 134.5 82.9 81.3 93.7 95.7 98.9 97.8 88.5 87.9 92,.9 90.3 96.0 96.0 85.2 81.3 105.1 105.9 88.7 86.7 57.6 57.9 58.7 60.7 57.5 55.9
8
. oint, L,b,
Modzxed Experimental
136.2*O 139,gb 66.2*a 112 3a 57.ba 63 3a 64. 68.1*n 131 , 9*a 77.6a 72.ba 73.1“ 65.7*a 67.6*a 140.ZC 80,8*a
107.5a 104.9a 198.5‘ 122.0e
107.41 75,5a 80.88
89.0
89.0
136.6 80.8 96.4 99.8 96.5 94.6 108.7 86.1 57.6 56.2 80.6 92.1
74.4 94.6 82.7
72.3 93.8 81.1
Deoiation ,from Charm L,b, %
,l./G.
79.1*a 134.9h
Author’s choice
Haggenmacher
145 2
+ 0 9
93.2 94.9 112.3 57.6 63.3 64.5 82.5
90.8*”
89.4*” 107.4a 74,8*Q
92.7c
+ 0.8 + 2 1 - 1.1 + 1.8 + 0.3 + 3.2 - 1.9 + 0.2 + 2.2 4- 4.0 - 3.7 - 1.3
+
-
1.6 2.9
- 3.6 - 2.1
+ 0.4
-
2.2
Giacalone
Kistiokorusi;~
-0.9
-0.1
+0.2 +0.2
-2.9 -1.1 -0.3 +1.4 -0.5 -0.1 -0.2
.s
+1
-0.7 -0.5 $0.3 -1.5
?
77.6 72.6 73.1 69.2 73.7 140.2 83.7 86.7 66.5 79.8 107,s 104.9 135.8 198.5 122.0 103 6 80.8 85 9 88.6 134.9 81.1
97.5a
ModiJied Ofhmer
97.5 98.0 88 3 93.7 95.1 83.7 107.4 86.4 57.9 58.2 56.0 76 1 92.7 81.9
- 4 0 - 22 +l5 6 0.7 - 2 0 1.7 -21
+ + -
0.5
+05 - 1.7 +02 + 1 2 4-30 - 1.7 2.2
-
- 3.7 - 2.9 +03 - 2 0 -26 - 2.6 -12.7 1.6 - 1.5
+ + 1.0 - 0 2 2.8 0.7 - 4.5 -29
-
+
- 2.1 - 0.9
+18.l
+ 0.8 + 3.8 + 2.1 + 2.5 + 0.7
2.6
.s
-1
+1.4 0.0 -4.0 -5.1 +I
4- 1.6
+ 0.5 + 1.3
- 0.4
- 1.1
+ 1.8 + 3.0 - 0.5
+ -
0
-2 6 -3.3 -1.1 +0.2 +3 6 +1.5 4-2.9 +2.2 -3.9 +0.9
+0.2 -3.6 +0.9
4-1 . 8 1.3 0.3
- 1.0
+ 0.4
+ 1.3 + 5.9 + 0.9 + 8.8 +12.5
Average deviation
-2 6 4-0.4 +0.4 +2.7 0.0 -3.7 +1.6
26
-2.1 +2.7 -0.5 +0.9
+2 7 -2.2
+o
2
+1 .0
17
-0.9 +1 .0
+2.2 +0.3 -5 7 -0.4 -U.6 -3.7 f0.8 -1 . 8 -7 0 -0.7 -1.5 -0.4 -0.2
-1,2 -0.1 -0 +O
1 8
-0 3
+o
2
-1.8 -0.2 -0.4 -0 9 +0.9
-2.9 -1.4 $0.3 0.0 +4 3 -0 2 -5.0 2 -1 0 1,3
+I
NOTE:Experimental Lvb values shown with an asterisk are determined by the condensation method. Values in parentheses are estimated.
SOURCES OF EXPERIMENTAL LATENT HEAT DATA (a) Perry, J. H. (ed.), “Chemical Engineers’ Handbook,” 3rd Ed., p. 216,McGraw-Hill, New York, 1950. (b) Coleman, C. F., De Vries, T., .I. Am. Chcm. Sac. 71, 2839 (1944). (c) “The Methylamines,” Rohm and Haas Co. (dj Perry, J. H. (ed.), “Chemical Lngineers’ Handbook,” 3rd Ed., p. 265,McGraw-Hill, New York, 1950. (e) Osborne, D. W., e t al., J. Am. Chem. Sac. 6 4 , 165 (1942). (f) Ibid., 169 (1942). ( 9 ) Calculated at t b by Watson equation from experimental value of 86.3 cal./g. at 167.7O C., data of Barrow, G. M., McClellan, A. L., J. Am. Chem Soc. 73, 573 (1951). (h) Pitzer, K.S . and Givinn, W. D., J. Am. Chem. Soc. 63, 3313 (1941).
VOL. 5 5
NO. 6 J U N E 1 9 6 3
55
Chloral hydrate represents a very interesting case : The Handbook value of Lob for this compound is given as 131.9 cal./g. Compare this with the much lower calculated values. The experimental value seems, in reality, to be the sum of the heats of condensation of chloral and water, plus the heat of reaction of the two compounds. Chloral hydrate evidently decomposes to chloral and water vapor at the atmospheric boiling point, and recombines on condensation. Even latent heats measured by the usually reliable heat input method (see Part I) are subject to error. For instance, you will note that the selected value of L o b for methyl sulfide is not taken to be the experimental value. The most probable value in this case was determined by averaging the calculated and experimental values. Lob for methyl sulfide was also determined from the very accurate vapor pressure data of Rossini (26). A value of 103.7 cal./g. was obtained. The measured value is approximately 47-too high. Two experimental values are given for naphthalene. Both were determined by electrical input methods, yet the values differ by 7y0.
I t is well to note that for substances of this type the Watson equation (Part I) may yield very inaccurate results. In Conclusion
It has been our aim in this series of articles to present in some detail methods which allow rapid, accurate calculations of latent heats of vaporization. Several existing equations have received a critical review and new methods have been presented. However, it has not been our objective to describe all existing calculation procedures. Excellent comprehensive reviews of this nature by Reid and Sherwood (23) and by Gambill (Chemzcal Engzneerzng, page 261, December 1357 and page 159, January 13, 1958) are already available to the interested reader. No one calculation method should be relied upon exclusivel>- to yield an accurate value for L,. The methods are only as good as the input data used. The calculation methods described are neither time consuming nor difficult to apply. So when calculating L,, fox a given compound, it is a good idea to use at least two independent methods to check the results. Latent heats at other than the normal boiling point may then be calculated by the L\-atson equation (Equation 1.17) or by Equation 2.10.
Substances Which Undergo Partial Vapor Phase Association
Where the input data are reliable, the Haggenmacher, modified Othmer, Riedel, Giacalone, and modified Klein equations all yield accurate calculated molal heats of vaporization. However, for design purposes latent heats must be known on a weight basis. The conversion is simply made by dividing by the molecular weight of the vapor. For most substances this is identical to the simple formula weight. Many substances, though, consist of mixtures of monomers and dimers in the liquid and in the vapor phase. Some examples are the carboxylic acids, HCN, and the nitriles, NO2, Na, and K. T o calculate heats of vaporization per unit weight for these substances, the average molecular weight of the vapor must be known. The ratio of monomers to dimers in the vapor phase often changes markedly with temperature. In some instances this variation has the odd effect of producing a maximum value of latent heat above the freezing point of the compound. For acetic acid this maximum occurs approximately at the normal boiling point and the heat of vaporization decreases as the saturation temperature is lowered below this point. ERRATA
NOMENCLATURE
B, C d
constants of Antoine vapor pressure equation distance between centers of density of positive and negative charges in polar molecule K K ~= correction factor for Kistiakowsky equation Lob = latent heat of vaporization at the normal boiling point M = molecular weight n = number of carbon atoms in molecule Ph = saturation pressure, atm. P, = critical pressure, atm. tb = normal boiling point, 7 b = normal boiling point, O K. T , = critical temperature, O K. Vb = molal volume of the saturated vapor at the normal boiling point, ml./g. mole = magnitude of electrical charge in polar molecules LIZ = difference between compressibility factor of saturated vapor and saturated liquid Zgh = summation of horizontal dipole components 2~~ = summation of vertical dipole components
c.
z
L I T E R A T U R E CITED See Part 1 of this series for the complete bibliography.
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REPRINTS
Two errors occurred in preparation of the first article of this series, INDUSTRIAL AND ENGINEERING CHEMISTRY, Vol. 5 5 , No. 4, pages 20 to 28 (April 1963). These changes should be noted: Page 26, Examples 1.1, Part (b): T h e assumed value of P, should be 27.5 atm. This value should then be used throughout the calculations. Page 27, Table 1.4, Lines 8 and 9 : These striictures should, of course, be,
One to nine eopies-$1.25 10 to 49 copies-l5% discount 5 0 to 99 copies-ZO% discount Prices for larger quantifies on request Address orders to REPRINT DEPARTMENT
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In the second article of the series (May 1963), we Equation 2.20 failed to define the terms BR and C,. should read as follows: BR and CR are the Antoine constants for the reference substance. I
INDUSTRIAL A N D ENGINEERING CHEMISTRY
... , . . .
The three articles in lhis series on calculaling latent heats of vaporization are available as a combined reprint Prices for Ihe 2 5 - p a g e package are:
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56
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