I N D U S T R I A L A N D ENGINEERING CHEMISTRY
380
Discussion
-
The rate of sorption of water by the different samples of lactose in the desiccator was not constant. This is not surprising, since the surface of the crystals exposed per unit weight of sugar undoubtedly differed even though each container held about the same weight of material that had been sifted through an 80-mesh screen. There is also the possibility in experiments of this kind that some water will condense on the containers. The data show conditions under which beta anhydrous lactose will adsorb moisture and revert to the stable alpha hydrate modification. I n other experiments it was found that pure crystalline beta lactose did not adsorb water when left for 30 days at 20" and 30" C. in an atmosphere of 90 per cent humidity, and that a t 20" C. in a desiccator over water there
Vol. 22, No. 4
was only a small increase in weight after 2 weeks. These data, therefore, indicate that pure crystalline beta anhydrous lactose is sufficiently stable under ordinary humidity and temperature conditions not to affect seriously its commercial possibilities. Conclusions
The continued presence of approximately 0.5 to 1.0 per cent of free water on crystals of pure beta anhydrous lactose is sufficient to cause them to change to alpha hydrate lactose. Literature Cited (1) Hudson and Brown, J . Am. Chem. Soc., SO, 960 (1908). (2) Schmoeger, Bcr., 13, 1915 (1580). (3) Wright, J . Dairy Soc., 11, 240 (1928).
Vapor Pressure and Heat of Vaporization of Toluene' D. S. Davis DEPARTMEKT OF TECHNICAL SERVICE, M E A DPULP AND PAPERCOMPANY, CHILLICOTHE, OHIO
Equations are presented correlating recent toluene SING a statistical vapor-pressure data and the Cox method of plotting m e t h o d , Krase and is shown to be superior to the usual log p vs. 1/T plot. Goodman (11) have New constants, to insure the constancy of the value recently determined the vapor c, are introduced in the van der Waals' equation pressure of toluene from the expressing vapor pressure in terms of the critical data. boiling point to the critical Latent heats calculated from these data by various t e m p e r a t u r e , and the new empirical formulas are compared with values reported data amear to warrant the in the literature. determination of the pressuretemperature relationship and the calculation of the latent heat of vaporization.
U
A -
I shows the calculated vapor pressure exceeding the actual p r e s s u r e over t h e entire range. Figure 1 represents a plot of log p vs. 1/T for both the new data of Krase and Goodman and the older data of Barker ( I ) . The equations of the lines are:
(KraseandGoodman) l o g p =
Pressure-Temperature Relationship
Integration of the Clausius-Clapeyron equation,
(Barker)
10gp =
-
1661'7 T + 4.4055 -
-
1927.7
+ 5.0395
(1) (2)
The upper and lower range data plot separately in straight lines, but a single line to include both would be curved. It where p is the pressure, T is the Centigrade-absolute tem- has been shown (5,6, perature, L is the molal heat of vaporization in gram-calories, 7') that the Cox method of plotting vapor-presand R is the gas constant 1.985,, leads to the expression, sure data leads to more n e a r l y straight lines. than does t h e usual from which it is seen that the pressure-temperature relationprocedure, and that the ship is of the form, Cox method amounts A log@ = T B to plotting log p vs. l/(t 230), where t is where A and B are constants. Chipman (6) has been able to predict the values of A and the Centigrade t e m p e r a t u r e . Figure 2 B for many substances by means of the equation, shows such a plot for g Tb log(82.07 Tb) log @ = g log(82.07 Tb) - . the data in question. T where p is the vapor pressure in atmospheres; g is-a constant Here the Barker and for a given class of substances, approximating 1.08 for ben- the Krase and Goodzene, toluene, naphthalene, and anthracene; Tb is the boiling man data plot as parts point under atmospheric pressure in Centigrade-absolute of the same s t r a i g h t units; and T is the temperature of the vapor in the same line, but are separated units. Substitution of the boiling point, Tb = 383.8, in to a v o i d a n u n d u l y large figure. T h e the above equation yields equation of the line is: 1864 4.858 log = - T 1425.5 The predicted constants are evidently too high, since-Table log P = - mo
+
+
+
1 Received
February 13, 1930.
+ 4.1972
Figure 1
.
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
April, 1930
The temperature scale may be drawn either by constructing abscissas proportional to l/(t 230) or by first drawing a water line a t any convenient angle and marking off temperatures corresponding to pressures as obtained from steam tables.
+
381
Calculations of the latent heat using both the new and old data follow: (Krase and Goodman) L = 2.303 (1.985) 1661.7 = 7600 gramcalories
(Barker)
.
L
= 2.303 (1.985) 1927.7 = 8810 gram-
calories
Various empirical formulas have been advanced for calculation of latent heat. Evaluation of several of the more prominent follow. The boiling point, Tb, of toluene is taken as 383.8. NAME Trouton Nernst (14) Nernst (14) Forcrand (8) Bingham ( 2 ) Lagerlof (IO) Herz (9)
Cederberg (4)
--
L L L
LATENT HEAT,
EQUATION
L
= (8.5 log Tb) T b
- 0.007 Tb) Tb - 1.5 - 0.009 Tb
(9.5 log Tb (10.1 log Tb
+
4-0.0000026 T b * ) T b
7780 8430 8380 9580
8150 = (17 0.011 Tb) T b L = 1000 (0.0207 I b 5.6), where ibis Centigrade
L
+ boiling point
7890
= 0.239 M
dcTc Substituting d c = -2 Mp RTc L = 0.239 RTb log 1 L = 2‘303 1 - -
T b
(
- ,’c)
7530
Tb
7850
TC
The value reported by Mathews ( I d ) and quoted in the International Critical Tables is 7970. I n the above formulas t b is the Centigrade boiling point, M is the molecular weight; p,, T,, and d, are the respective critical pressure, critical temperature, and critical density; and R is the gas constant, 82.07 cc. atmospheres. Confirming the usefulness of the Cox method, Kagornov ( I S ) ,working with mixtures of benzene and cyclohexane, found the logarithm of the vapor pressure to be a linear function of l/(t 4- a ) , where CY was approximately 230, varying from 223 to 235 according to the analysis of the mixture. Table I-Comparison
TEMPERATURE
c.
110.7 214.4 264,O 320.6
of Calculated and Actual Pressures
Calcd. Afm. 1.0 10.7 24.4 52.2
PRESSURE Actual Alm. 1.00 9.89 21.39 41.60
DEVIATION Per cent 0 9 14 25
Van der Waals (15) gives an approximate equation for vapor pressure in terms of the critical data as follows: log& = c
P
(+ - 1)
where p , and T , represent the critical pressure and critical temperature, respectively, stating that the value of the constant, c, is about 3. By substituting the toluene data of Barker and of Krase and Goodman in this equation, c is found to vary considerably, as shown in Figure 3, where c is plotted against T,/ ( T - I). Altering van der Waals’ equation to read: log
.>
($ -
c becomes a true constant.
then reads: log
(y-
0.28)
= c
($ - 1) + 6
The revised equation for toluene = 3.106
(y-
Figure 3
Literature Cited (1) (2) (3) (4) (5) (6) (7) (8)
0.08158)
Latent Heat
Consideration of the integrated form of the ClausiusClapeyron equation indicates that the molal latent heat is given by the expression: L = 2.303 RA where the symbols are defined as before.
(9) (10) (11) (12) (13) (14) (15)
Barker, Z . physik. Chem., 71, 235 (1910). Bingham, Mortimer, J . A m . Chem. Soc., 44, 1429 (1922). Calingaert and Davis, I N D .ENG.CHEX., 17, 1287 (1925). Cederberg, “Thermodyn. Berechnung. chem. Affinitaten,” Friedlander, Berlin, 1916. Chipman, J. P h y s . Chem., 32, 1528 (1928); 33, 131 (1929). Cox, IND. END. CHEM.,16, 592 (1923). Davis, I b i d . , 17, 735 (1925). Forcrand, Millard, “Physical Chemistry for Colleges,” hfcGrdw-Hill, 1921, p. 82. Herz, 2. Elektrochem., 26, 323 (1919). Lagerlof, J . p r a k t . Chem., 98, 136 (1918). Krase and Goodman, IND. END. CKEM.,22, 13 (1930). Mathews, J. A m . Chem. Soc., 48, 562 (1926). Nagornov, A n n . inrl. anal. p h y s . Chem. (Leningrad), 3, 562; Chem. Zenlr., 98 (II), 2668 (1927). Nernst, Millard, “Physical Chemistry for Colleges,” McGraw-Hill, 1921, p. 82; Nachr. Ges. Wiss. Gtillzngen, 1906. Van der Waals, “Die Continuitat des gasformigen und Bussigen Zustandes,” 1’01. I. p. 147, Barth, Leipzig, 1899.
