O n Latent Heat of Vaporization, Surface Tension, and Temperature D. S. VISWANATH and N. R. KULOOR Department of Chemical Engineering, Indian Institute of Science, Bangalore, India
A semitheoretical equation for latent heat of vaporization has been derived and tested. The average error in predicting the value at the normal boiling point in the case of about 90 compounds, which includes polar and nonpolar liquids, i s about 1.8%. A relation between latent heat of vaporization and surface tension is also derived and i s shown to lead to Watson's empirical relation which gives the change of latent heat of vaporization with temperature. This gives a physico-chemical justification for Watson's empirical relation and provides a rapid method of determining latent heats b y measuring surface tension.
THE CHAKGE of latent heat of vaporization with tempera'
ture has been a subject of many investigations. The exact method of evaluation using the rigorous Clausius-Clapeyron equation suffers from the disadvantage that the necessary data often are lacking. Several relations (16, 24, 25, 28, 31) for calculating the latent heat a t a given temperature are available, but they need data such as conipressibilities of vapor and liquid, the value of latent heat a t a particular temperature, or the use of a reference substance. Guggenheim (15) has shown that, in the region of temperature T < 0.65 T,, the vapor pressure-temperature variation follows the reaction In P / P , = A
- BT,/T
(1)
with A s B and equal 5.30. The relation was further tested and found valid, although A and B depend upon the class of substances investigated. Guggenheim also noted that -4 s B (16). The values, for example, were 4.30 for alcohols, 2.92 for ethers, benzene, acetones, and 5.30 for spherical, nonpolar substances. However, the value of neither A nor B is needed for the present work.
The latent heat of vaporization a t constant volume according to the Clausius-Clapeyron equation is given by T ( d P / d T ) ( V ,- VI)
h =
(6)
Substituting for ( V , - VI) from Equations 3 and 4, and using Equation 5 yields
Equation 7 is similar to the one derived by ,Veissner (21). Figure 1 shows [h (1 - l / T e ) ] / T eplotted as a function of P, and also experimental values for various substances. The experimental values are believed to fall within 5%. -4calculation of h values using Equation 7 a t the normal boiling point indicated that the experimental and calculated values were in better agreement if the constant was changed from 4.35
c -1
PRESENT WORK
Differentiating Equation 1 gives d In P
dT
-2
- BT, T2
-3
Applying the relation PV = Z RT for 1 mole of both the gas and the liquid phases, and rearranging, gives
-I= L.
-4
Y
412
(V, -
VI) =
(2,
-
RT 21)P
(3)
-5
m
CARBON
TETRACHLORIDE
0
METHYL
ALCOHOL
A
ACETONE
A
OXYGEN
X
AMMONIA
B
WATER
ETHYL
The quant'ity (2,- 2,) is a function of reduced pressure only, independent of the nature of the substances. The data(16) plotted as a function of (1 - P?) gave the relation
-6
-7
(Z,
for 0.01
- 21) =
0.95(1
-
Pr)O.sB
P 1 T 2 Po (1 - T , / T )
d In P To -=-In--.
dT
VOL. 11, No. 1, JANUARY 1966
V
ETHANE
B
CARBON OlOllOE NITROGEN
(4)
< P, < 0.4. Equations 2 and 1 give
ETHER
-8
I
I
0.1
I
I
I
I
I
0.2
0.3
0.4
0.5
0.6
0
Pr
(5)
Figure 1. Relation between latent heat of vaporization and pressure
69
to 4.70. Table I shows X values calculated using Equation 7 and a value of 4.7 for the constant. The average deviation of some 90 compounds tested is about 1.8o/c. The values are also compared with those calculated using Riedel's equation (28) and Giacalone's equation (28). The present relation is slightly superior to either Giacalone's relation or Riedel's relation and also correlates well substances such as ethylene. Experimental calorimetric values from primary souwes are also listed in Table I along with the literature values from secondary sources. As the difference between these two values is negligible, the so-called literature values were used in calculating the per cent errors.
LATENT HEAT TENSION
OF VAPORlZATlON AND SURFACE
and surface tension are both Latent heat of surface phenomena and are defined by the relations XPlP,
(dP/dT) =
VPl
(8)
- Pg)
and = [Pl(Pl
- Po)
(9)
M
Table I. Latent Heat of Vaporization at the
Substance
Literature Value
% Error0
Experimental Value
1
2
3
Inorganic Ammonia Argon Bromine Carbon disulfide Carbon monoxide Chlorine Hydrazine Hydrogen bromide Hydrogen chloride Hydrogen iodide Hydrogen sulfide "eon Nitric oxide Nitrogen Nitrous oxide Oxygen Phosgene Phosphine Sulfur dioxide Water
5,580(17) 1,590(85) 7,420 (17) 6,400 (17) 1,444(17) 4,880 (17) 9,637 (28) 4,210(17) 3,860(17) 4,720 (17) 4,460(17) 440 (25) 3,290(17) 1,330(17) 3,960 (17) 1,630 (17) 5,830 (17) 3,490(17) 5,950(17) 9 720 (17)
1,557.5(6) 1,443.6(4) 4,878.0(9) 4,210.0 (12) 3,860.0 (11) 4,724.0 (13) 4,463 .O (7) 3,292 (19) 1,630.7(6,8) 3,489.0(30) 5,960.0(10)
-1.2 -1.9 $2.3 -3.4 -3.9 -1.4 0.0 $2.6 +1 .o +1.9 +3.6 -2.5 $1.5 -5.2 -0.5 -4.3 -3.3 -4.9
-2.3
$1.6 -1.9
-4.9
-3.6
$1 . 2 $2.7
-1.6 -2.8
-2.9
-1.5 ... ...
-1.9
-1.2
-1.0
-1.3 -3.7
$1.3 $2.9
-1.5 +17.3
-4.6 $11.7
-0.3
~
...
...
... , I .
...
...
...
...
... ...
Hydrocarbons Methane Ethylene Ethane Propene Isobutane n-Butane 1-Butene n-Pentane Methyl cyclohexane Benzene Toluene Hexane n-Octane o-Xylene cis-2-Butene n-Heptane Cyclopentane Cyclohexane 3-Methyl hexane 2,4-Dimethylpentane 2,2,3-Trimethylbutane Methyl cyclopentane trans-2-Butene 1,3-Butadiene Ethyl benzene rn-Xylene Naphthalene Propane
1,960 (17) 3,240 (17) 3,520(17) 4,400 (17 ) 5,090 (17) 5,350 (17) 5,240 ( I 7) 6,160(17) 7,580 (17 ) 7,350 (17) 8,000 (17) 6,921 (17) 8,343 (26) 8,750 (24 ) 5,580 (17) 7,580 (17) 6,525 (17) 7,190 (17) 7,358 (28) 7,050 (28) 6,918 (28) 7,002 (28) 5,438(28) 5,367 (28) 8,599 (28) 8,800 (85) 10,240 (28) 4,490 (17)
-6.1 -4.0 -4.5 -3.2 -3.3 -3.6 -4.0 -2.6 -0.9 -0.8 -2.0 -2.6 -1.3 -1.1 -4.8 -3.4 -1.5 -1.4 -3.9 -2.3 -3.3 -0.6 -1.8 -3.6 -1.7
1,955.0(17)b 3,237 .O ( 5 ) 3,514.0 (33) 4,402.0(67) 5,089 .O (8) 5,351.O (3) 5,239 .O (1 6,262 .O (23) 7,353 8,000
(17)b (17)b
8,215 8,800
(17)a (84)b
7,660
(86)
8,700
(84)b
0.0
-0.8 -2.9
4,487 .O (20)
...
... ...
... -0.8 ...
... $0.7
... , . .
... -0.6
... -0.9 +0.4 +1 .o -1.2 -1 .o -0.8 $1 .8 -0.5 -2.9 -1.4 +0.2 -1.2 -0.4
... .
I
.
... .
.
I
-2.5 ...
... $0.7
... ... ... -0.8
... -2.9 -0.2 -0.3
-3.2 -3.3 -3.2 -0.7 -1.4 -3.6 -1.5 0 .o -1.3 -2.0
-
70
JOURNAL
OF CHEMICAL AND ENGINEERING DATA
From Equations 8 and 9, noting that the logarithm of vapor pressure varies linearly with reciprocal absolute temperature, one derives the relation (10) where B denotes the values a t the boiling point. Assuming ideality of vapor and p1/pIB E 1.O, one derives the relation ?/YE
(11)
=
face tension were taken from the International Critical Tables (18).The values of y B were either read from a graph of surface tension us. temperature or obtained from the relation y = yo (1 - T,)y after fitting the equation using the available experimental data. The exact relation from Figure 2 is T/"fB =
i.02(Y/YB)3'16
(12)
(x/hB)3"6
From the surface tension-temperature relation noted above, one can derive from Equation I 1 that
Figure 2 shows the validity of the relation y / y B = f(y/yB) for compounds of different chemical nature. The values of surBoiling Point in Calories per Gram Mole
Substance
Literature Value
% Errora
Experimental Value
1
2
3
-3.8 -0.2 +1.6 $3.0 0.0
-7.4
-1.5
-2.8 +0.6 ...
$3.4 +5.7
-1.1 -1.6
$0.8
$0.6
$1.0 $1.3
+2.6 +4.6
+2.5 +5.0
Alcohols Methyl alcohol Ethyl alcohol Isopropyl alcohol n-Propyl alcohol Isobutyl alcohol
8,430 (17) 9,220 (17) 9,650 ( 1 7 ) 9,890 (17) 10,220(25)
...
... ...
Hydrogenated Compounds Carbon tetrachloride Methyl chloride
7,170 (17) 5,165(25)
Chlorobenzene Chloroform Difluorodichloromethane Methyl fluoride Trichloromethane Fluorobenzene Bromo benzene Iodobenzene Ethyl bromide
8,736(25) 7,400 (24) 4,850 (17) 4,230 (17) 7,020 (17 ) 7,534 (28) 8,966 (28) 9,548 ( 2 8 ) 6,349(28)
5,147.0 (29)d 5,138.0 (22)
-1
.o
+1.9 -2.6 -1.1
-2.0 -2.6 -6.3
... ... ...
-0.6 -0.6 -1.6 -6.3
...
... ... -0.5 -0.7 -1.4 -5.0
Esters Ethyl formate Ethyl propionate Methyl acetate Methyl formate Methyl isobutyrate n-Propyl acetate n-Propyl formate Ethyl acetate
7,191 (25) 8,168(25) 7,454 (25) 6,738(25) 7,969 (25) 8,189 (25) 7,756(25) 7,750 ( 2 4 )
+0.1 +4.5 +0.7 -0.1 $0.2 +0.4 $0.5 +0.7
... ...
... $0.1
I . .
... ... -1.9
...
, . .
...
...
...
+1 .o
... +1.4
... -1.0 +1.7
0.0
Other Organic Compounds Acetaldehyde Acetone Acetic acid Ethyl ether Ethylene oxide Methyl amine Ethyl amine Methyl ether Phenol p-Cresol Isobutvric acid Diethyl amine Triethyl amine Aniline Acetonitrile Ethyl mercaptan Diethyl sulfide
6,500 (17) 7,100(17) 9,526 ( 6 8 ) 6,220 (17) 6,100(17) 6,109 (24 1 6,583 (25) 5,141(28) 10,760(28) 11,250 ( 2 8 ) 10,620(28) 6,975 (28) 7,675 (28) 10,360 ( 2 8 ) 7,500 (28) 6 400 (28) 7,591 ( 2 8 ) ~
+3.1 -2.8 +2.1 -3.2 -2.0 -1.5 +1.7 -1.6 -1.3 -2.4 -0.3 -0.4 +0.2 -1.7 -3.4 -0.3 -1.4
... ...
... f3.4 ... ...
,..
...
$1.9 -1.0 -4.5
+3.5 -0.6 -1.1 -3.0
-8.0
-3.0 -0.1 +0.7 -3.3 -4.7 0.0
-1.4
+0.9
-0.4 -0.5 4-0.6 -3.3 +0.3 -1.6
1 refers to present correlation, 2 refer- to Riedel'c;, and 3 to Giacalone's. The values according t o Riedel's and Giacalone's method arc taken from Tables IV-VI of Reid and Sherwood (28). "c Error = 100 X (literature value - calculated value)/ lite:ature value. Agrees with A.P.I. values. Corrected value from 5256.1 at 266.72' K. to boiling point. Calculated from vapor pressure values.
VOL. 11, N o . 1, J A N U A R Y 1 9 6 6
71
”
ACKNOWLEDGMENT
“I
The authors express their thanks to the Director-General, Council of Scientific and Industrial Research, New Delhi, for financial assistance given during this investigation.
I
N 0 M ENCLATU RE
A , B = constants in Equation 1 m , n = constants in Equation 13 P = vapor pressurr P, = reduced \rapor pressure, P / P c R = universal gas constants, cal./gram mole K. T = temperature, OK. T, = reduced temperature, T / T c v = volume z = compressibility factor Y = surface tension, dynes/cm. A = molal latent heat of vaporization, cal./gram mole P = density [PI = Sugden parachor O
OXVQEN CHLOROFORM CHLORINE M E T H Y L CHLORIDE M E T H Y L ALCOHOL ACETONE
C A R I I O N DISULFIDE BENZENE
Subscripts
CARBON TETRACHLORIDE ACETIC ACID
B C g I
ETHVL ETHER WATER
0.1
1
1
1
1
0.2
1
1
1
I
1
I
1
5.0
A0
Figure 2. Surface tension-latent heat of vaporization
Ethyl ether Benzene Acetic acid Chlorine Oxygen \F7ater Xethyl alcohol
L/
Exptl.
Ba
B Calcd.
Dev.
15.2 21.2 18.0 26.2 13.2 58.9 18.5
14.8 20.8 17.5 26.5 19.5 54.0 22.5
2.6 1.9 2.8 1.1 47.6 8.3 21.6
LITERATURE CITED
Aston, J.G., Fink, H.L., Bestul, A.B., Pace, E.L., Szasz, G.J., J . Am. Chem. SOC.68, 52 (1946). Aston, J.G., Kennedy, R.M., Schumann, S.C., Zbid., 62, 2059 (1940).
Table I I . Calculated and Experimental Values of Surface T’ension at Boiling Point
Compound
boiling point critical point = gas = liquid
= =
/c
Extrapolated or interpolated values using experimrntal data at other temperatures obtained from the International Critical Tahlcs ( f 8).
Aston, J.G., Messerley, G.H., Zbid., 62, 1917 (1940). Clayton, J.O., Giaque, W.F., Zhid., 54, 2610 (1932). Egan, C.J., Kemp, J.D., Zbid., 59, 1264 (1937). Frank, A,, Clusius, K., 2.Physik. Chem. B42, 395 (1939). Giaque, W.F., Blue, R.W., J . Am. Chem. SOC.58,831 (1936). Giaque, W.F., Johnston, H.L., Zbid., 51, 2300 (1929). Giaque, W.F.>Powell, J.M., Zbid., 61, 1970 (1959). Giaque, W.F., Stephenson, C.C., Zhid., 60, 1389 (1938). Giaque, W.F., Wiebe, R., Zbid., 50, 101 (1928). Giaque, W.F., R’iebe, R., Zbid., 50, 2193 (1928). Giaque, W.F., Wiebe, R., Zhid., 51, 1441 (1929). Glasstone, S.,“A Textbook of Physical Chemistry”, 2nd. ed., p. 526, Van Sostrand, Princeton, Y.J., 1958. Guggenheim, E.A., “Thermodynamics,” pp. 169-71, North Holland Publishing Co., Amsterdam, 1957. Hougen, O.A., Watson, K.M., Ragatz, R.A., “Chemical Process Principles,” Part I, pp. 272-6, Wiley, New York, 1958.
thus leadinq to the \Vatson’s correlation ( 3 2 ) .By using ii = 3.16 from Equation 12, and jn = 1.2 according to Guggenheim ( I S ) , one finds
Howerton, M.J., “Engineering Thermodynamics,” pp. 307-8, Van Sostrand, Princeton, S.J.,1962. International Critical Tables, Vol. V, pp, 441-7, 1928. Johnston, H.L., Giaque, W.F., J . Am. Clzem. SOC.51, 3194 (1929).
Kemp, J.D., Egan, C.J., Zbid., 60, 1521 (1938). Meissner, H.P., Znd. Eng. Chem. 33, 1440 (1941). Messerlay, G.H., Aston, J.G., J . Am. Chem. SOC.62, 886 which is the empirical relation according to Katson (52). Equation 12 s h o w that, if y A and X B are known, X can be estimated from surface tension measurements. -4s noted earlier, A B can be evaluated using Equation 7 . A reasonably good corielation (14) can be obtained for y B from Equation 0 by neglecting the vapoi density, thus leading to (15)
Table 11 s h o w the validity of Equation 15. The parachor and molal volume values were calculated using the values given in the Chemical Engineers’ Hnndbook (25). The values of y,,3hould be found by two measurements on wrface tension. Surface tension measurements appear to provide a rapid way of finding latent heats of vnporization. The method is simple, raliid, and allows resonable accuracy.
12
(1940).
Messerle?; G.H., Kennedy, R.M., Zhid., 62, 2988 (1940). Partington, J.R., “An Advanced Treatise on Physical Chemistry,” Vol. 11, pp. 310-66, Longmans, Green, Kew York, 1951. Perry, J.H., Ed., “Chemical Engineers’ Handbook,” 4th ed., pp. 3-112, 223, McGraw-Hill, New York, 1963. Pitzer. K.S., J . Am. Chem. SOC.62, 1224 (1940). Poxvell, J.H., Giaque, W.F., Zbid., 61, 2366 (1939). Reid. R.C., Sherwood, T.K., “Properties of Gases and Liquids,” pp. 87-99, McGraw-Hill, Yew York, 1956. Shorthose, D.N., Food Investigation Board, Department of Scientific and Industrial Research, (Great Britain), Special Report 19, 1924. Stewhenson. C.C.. Giaaue, W.F.. J. Chem. Phus. ” 5.. 149 .
I
(1937). ’ Su, G.J., 2nd. Eng. Chem. 38, 923 (1946). Watson, K.M., Zbid., 23, 362 (1931);35, 398 (1943). X t t , R.K., Kernp, J.D., J . Am. Chem. SOC.59, 273 (1937). RECEIVED for review hfarch 11, 1965. Accepted October 15, 1965.
JOURNAL OF CHEMICAL AND ENGINEERING DATA
