~NDUSTRIALAND ENGINEERING CHEMISTRY
SEPTEMBER, 1937 TABLE
MaIM.4 111. APPROXIMATE
Name
OF PILOTS Relative Eliminatio; Max , C.Q
Formula
127
Dimethyldiaminoanthraquinone 141 Diethyldiaminoanthraquinone
Burch, C. R., and Bancroft, F. E . , Brit. Patents 303,078 and 303,079 (Sept. 21, 1927); U. S.Patent 1,955,321 (April 17, 1934). Embree, N. D., IND.ENQ. CHEM.,29, 975 (1937). Hickman, K. C. D., Ibid., 29, to be published (1937). Hickman, K. C. D., S. FranklinInst., 213, 119 (1932). Ibad., 221, 215 (1936). Hickman, K. C. D., Nature, 138, 881 (1936). Hickman, K. C. D., U. S. Patent 1,925,559 (Sept. 5, 1933). Hickman, K. C. D., Hecker, J. C., and Embree, N. D., IND. EKQ.CHEM.,Anal. Ed., 9, 264 (1937). Hickman, K. C. D., and Weyerts, W. J., J. Am. Chem. SOC.,52, 4714 (1930). Washburn, E. W., Bur. Standards S. Research, 2,476 (1929). Waterman, H. I.. and Elsbach. E. B., Chem. Weekblad, 26. 469 (1929). Young, Sydney, “Distillation Principles and Processes,” p. 18, London, Maomillan Co.. 1922. RECEIVEDJune 1, 1937.
153
97s
Communication 029 from the Kodak Researoh
Laboratories.
158
CO
Dipro yldiaminoa n t Braquinone
NCHi
NHC~HI 162
THEORY OF ELIMINATION CURVE N. D. EMBREE Eastman Kodak C o m p a n y , Rochester, N. Y.
KHChHs I71
Dibutyldiaminoanthraquinone
183
N H C H i a C H s
/v
NHCsHii
Dixylyldiaminoanthraquinone 210-2 15
217
Quinizarin Green
Hickman (2) has shown that certain substances which distill under molecular conditions may be studied and identified by means of elimination curves. Such curves are derived here by theoretical methods. The effect of the properties of the substances distilled and the effect of the nature of the distillation procedure upon the shape and location of these curves are indicated by several examples.
NH? Anthraquinone Blue
Sky
183
/v “2
a Determined approximately with 10’ C. temperature intervals; more accurate d a t a with 5’ intervals are being compiled.
multiple purification, generally called “fractionation,” has been attempted, since the author’s purpose has been to extend a little the degree of precision attainable with simple evaporation under molecular conditions. In this he has been aided by collaborators, each well versed in some part of the work. It is a pleasure to acknowledge indebtedness to J. C. Hecker for suggesting the double reservoir for the cyclic still; to J. G. Baxter and A. 0. Tischer for preparing large quantities of constant-yield oil; to J. G. Baxter for making the pure pilot dyes; to E. LeB. Gray for performing the more accurate distillations; and to N. D. Embree for making many suggestions concerning the theory of the work.
Literature Cited (1) Baxter, J. G., Tischer, A. O., and Gray, E. LeB.,“Preparation and Characteristics of Synthetic Constant-Yield Mixtures,” to be published. (2) Brgnsted, J. N., and Hevesy, G., Phil. Mag., 43, 31 (1922). (3) Burch, C. R.. Proc. Roy. Soc., 123A,271 (1929).
T
H E degree of separation which can be obtained by molecular distillation is not much better than that given by distillation in a simple pot still at higher pressures. The concentration of a substance in the material condensing is proportional to the partial pressure in the distilland in pot distillation; in molecular distillation it is roughly proportional to the partial pressure divided by the square root of the molecular weight of the substance. This property of molecular distillation .makes it impossible to separate, by a single distillation, substances having values of the P to ratio which do not differ considerably. I n those cases where information concerning the constituents of a mixture is required rather than their separation, Hickman ( 2 ) has shown that much may be learned from a single, carefully controlled molecular distillation. The mixture is exposed for evaporation for a certain time a t each of a series of temperatures, and the amount present of a substance being considered is measured in each fraction. These yields, plotted against the temperatures at which the fractions had been distilled, provide a distillation curve which Hickman (6)has called the elimination curve. The amounts of the substance in each fraction increase with the temperature a t first, since the vapor pressure is increasing. The yields, however, findly reach a maximum and then decrease rapidly to zero because the supply of the substance in the distilland becomes exhausted. The elimination curve has an easily recognized
da
INDUSTRIAL AND ENGINEERING C H E M I S T R ~
976
shape, and the maximum can usually be located within a few degrees. A study of the elimination curve from a simple distillation not only provides a valuable means of chemical analysis but is a necessary forerunner of later studies concerning multiple distillation or molecular fractionation. The purpose of the present paper is to derive the elimination curve mathematically from certain physico-chemical concepts of distillation.
Langmuir’s Equation The rate of molecular distillation of organic substances may be calculated theoretically by the formula that Langmuir (3) used for the rate of evaporation of metals in a vacuum. When the vacuum is so high that the distance from the evaporating surface to the condenser is small compared with the mean free path of the molecules of vapor, the rate, n, in moles per second, is given by n =
where P A M R T
PA
4-2-
(1)
27rMRT = vapor pressure, dynes/sq. cm. = area of distilling surface, sq. cm. = molecular weight = ideal gas cons2ant = temperature, K.
Washburn (4) and Burch (1) have already applied this equation to the distillation of organic substances under “molecular” vacuum. When solutions are studied, the partial pressure, p , must be used instead of the vapor pressure, P . The equation gives the theoretical explanation for the fact that whentwo or more constituents in a solution have the ratio P / d M with nearly the same value, the separation due to a single distillation will not be very great.
Definition of Distillability
,
I
For distillation under any conditions, the rate of distillation of a substance is roughly proportional to its concentration and to its vapor pressure. I n molecular distillation, heat is given to the oil under almost equilibrium conditions, and practically all molecules leaving the distilland are collected by the condenser immediately. Therefore, the rate of heat input (at constant temperature) and the shape of the still are not significant variables, as they are in ebullient distillations, Limiting the discussion to molecular distillation, the rate might be said to be proportional to the product of the number of molecules and the probability that any molecule will distill. This probability or tendency to distill may be called the “distillability.” This concept is quite valuable in molecular distillation. More exact, but less illuminating, definitions are: “The distillability of a substance is proportional to its rate of distillation divided by its concentration,” or “the rate of distillation of a substance is proportional to the product of its concentration and its distillability.” Algebraically expressed, V =,kND where V = rate of distillation k = proportionality constant N = concentration expressed as a mole fraction D = distillability
Combining the terms which are constant for any one apparatus and substance, the rate of distillation, V ,in units not necessarily moles per second, is: V
=
kNP/fl
Distillation from a Nonvolatile Solvent at a Series of Increasing Temperatures The “analytical” distillation curves described by Hickman (W) may be closely approximated mathematically. To do this most simply, a distillation of a substance in dilute solution in a completely nonvolatile solvent a t a series of temperatures increasing in an arbitrary way is first postulated. Indicating the mole fraction of the substance at the beginning of the distillation by N o , the mole fraction a t any later time, since the substance is held in dilute solution, is given by : N = (1 - & ) N o (4) where Q = fraction of ori inal amount of substance present which has distille$ up to this time The proportionality constant, k , in Equation 2 is now defined so that the distillability equals the rate of distillation at the beginning of the distillation. Therefore, k = 1/N”
(5)
Because the vapor pressure of a substance and, for practical purposes, its distillability increase by a constant factor at each of a series of increasing temperatures, if the series is so chosen that the inverse of the absolute temperature decreases by a constant amount at each temperature in the series, such a series will be assumed for this hypothetical distillation. (The effect of using a series with constant temperature increments will be shown later.) The distillability a t the start of the distillation will be indicated by b, and it will increase by the factor r a t each of the series of temperatures. Thus, at the temperatures To, T I , . . . T,,the distillabilities will be, respectively, b, br, . . . br’. The rate of distillation will be expressed as the percentage of the original amount of substance distilling per unit time. At the beginning of the distillation, the rate equals the distillability, which is b, so that if the change in concentration did not decrease the rate, b per cent of the substance would be distilled a t the end of the first time unit. The distillation will be allowed to proceed for m units of time at each temperature. At the first temperature, To, the rate at any time, t , i s given by
vo
= (1
-
&o)b
using Equations 2, 4, and 5. Since
If the distilland may be assumed to be an ideal solution, the partial pressure of the substance considered, p , may be taken to be N times P-that is, the mole fraction times the vapor pressure of the pure substance, The rate of distillation in moles per second is, then, by Langmuir’s equation: n =
NPA
4 2 27rMRT
(3)
I n this case the distillability is proportional to P/dz As a useful approximation, the distillability varies directly with the vapor pressure of a substance, since the changes in l / d T are very much smaller than the changes in P.
(2)
.
VOL. 29, NO. 9
then The solution of this equation gives Vo = he-bt,”OO and
Q,,
1
- e-btllw
SEPTEMBER, 1937
INDUSTRIAL AXD ENGINEERING CHEMISTRY
After distillation has proceeded for m units of time, the temperature is raised to TI and the distillability becomes br instead of b. The fraction of the substance distilled at the start of the distillation a t temperature Tlis the same as the fraction distilled a t the end of the distillation a t To, or Ql(0) = @(m) = 1 -
e-bm/loo
The fraction distilled at time t during the distillation at TI is
From Equations 2, 4, and 5 , VI = (1 - Ql)br
977
Let the distillation be carried out for one unit of time a t each temperature, or m = l The per cent fraction of the total amount of substance distilled out a t each temperature is calculated by Equation 9. A chart showing the per cent yield and distillation temperature of each fraction is given in Figure 1. It is much more convenient, especially when comparing one distillation with another, to construct a curve instead of a chart. This “elimination” curve is made by plotting the per cent yields as ordinates against an arithmetic series of abscissas representing the distillation temperatures. The resulting skew curve is also shown in Figure 1.
Therefore
YIKLD -TEM-
Z
which, when solved, gives
VI and
= [l
Q1 = 1
- Q1(0)]bre-~W~~
f
- [l - Q1(0)]e-Wloo
z
9
T h e fraction distilled a t the end of the distillation a t T1 is Ql(m) = 1 - [I
=
L I M I N A T I O N CURVE
0 10 t,a
5,
IZ
- Ql(0)]e-brt/lOO
Q2(0)
The fraction of the substance distilled out while the ternperature was T1is QZ(0) - QI(0) = (I
TEMPERATURE
O F OISTICLATION
FIGURE 1. YIELDus. TEMPERATURE CHARTAND ELIMINA-
- e--bnr/100) e-bm/100
TION
CURVE
=lm$dt
B y following the same procedure, the rates and yields of the distillation at any temperature may be calculated. Genequations which describe the distillation at temperature Ti where the distillability equals bri have been worked out; for the fraction distilled:
where
Qi(0) = 1 - e-
bm(l+r+
....+
vi-‘)
100
(7)
for the fraction distilled while the temperature was Ti: (9) =
[l - Q,(O)][1 - e-%]
Numerical values will be assigned to the parameters b, r , .and m, so that the actual course of a distillation can be examined. Let the initial temperature TObe so chosen that the distillability and the rate of distillation at the start of the distillation is one per cent of the total quantity per unit time, .or b = l
Let the temperature series be so chosen that the distillability increases by a constant factor, 2/%,at each temperature. Then r
=
d5
The temperature a t which the maximum in the elimination curve occurs is a definite property of the substance, if the distillations are always carried out so that the material is distilled for the standard length of time a t a temperature series so chosen that the distillability increases by the same factor a t each higher temperature. The temperature a t which the distillation starts has no effect on the temperature of the maximum. This is shown in Figure 2 by curves calculated for distillations started at the temperatures To, T4. and Ts. These last two curves are calculated from Equation 9, starting with Q4 (0) = 0 in one case and Qs(0) = 0 in the other. The initial temperature should be lower than that of the maximum; otherwise a less determinate elimination curve, like that starting at T11, will be obtained. The actual series of temperatures chosen does not affect the temperature of the maximum, so long as the factor of increase in the distillability is the same in the curves compared. The curve starting at TOin Figure 2 represents a distillation a t T I , 2 at T2, etc. where the distillability is 1 at To,4% About halfway between To and T1 a temperature exists which may be called T(112)1 where the distillability is 2(l/4);between ~) the distillability is T1 and TZis a temperature T ( I ~ ,where 213/4),etc. If the percentage yields of a distillation of the substance at the series of temperatures T(l,z), T ( I ~ /etc., ~ ) , are calculated and then plotted against abscissas halfway between TOand TI, TI and Tz,etc., the points indicated by small crosses in Figure 2 are obtained. They show clearly that the shape and the location of the maximum of the curve were not affected by using the two different series of temperatures. The position of the elimination curve is markedly affected by the length of time during which the substance distills a t each temperature in the series. Figure 3 shows elimination
INDUSTRIAL AND ENGINEERING CHEMISTRY
978
VOL. 29, NO. 9
the pure state; in fact, for the types of molecular stills that are used here, it is desirable that a small amount of solvent distill over with each fraction t o help remove the distilIate from the condenser. The term "solvent" includes all the components present in the solution being distilled, with the exIS
'
/
"
'
'
I
"
'
"
'
FIGURE3. EFFECTOF TIMEOF DISTILLATION ON ELIMINATION CURVES ception of the particular substance studied. If 2 per cent of the solvent distills into each fraction, the percentage of the vo!atile distilled a t temperature Ti will be given by
FIGURE 2. EFFECTOF INITIAL TEMPERATURE ON ELIMINATION CURVES curves calculated for the same substance and temperature series as in Figure 1. I n addition to the curve des'cribing the distillation which takes place for one minute a t each temperature ( m = l), curves showing distillations taking place for 2 units (m = 2) and 4 units ( m = 4) of time a t each temperature are shown. They show that increasing the time of distillation shifts the niaximum of the elimination curve to a lower temperature. The elimination curves for substances which have a markedly different vapor pressure- temperature relation have somewhat different shapes. Figure 4 shows a curve calculated for a substance whose distillability increases 2(l times a t each temperature increment (T = 2('13)) contrasted with the original hypothetical substance whose distillability increases 2(1/2)times. The substance with the lower rate of change of distillability with temperature has a lower and flatter elimination curve. It has been mentioned that the distillability is almost proportional to the vapor pressure. The variation of vapor pressure with temperature is given closely by the equation, InP = -
+$+ constant
Hence, for substances with a high heat of vaporization, the distillability will increase rapidly with temperature, and the elimination curve will be narrow and steep; substances with a low heat of vaporization will have a broader and flatter curve. The elimination curves given so far are calculated for conditions which are difficult to duplicate in a real distillation. Seldom does the volatile substance studied distill over in
instead of by Equation 9. A curve calculated for these conditions (Figure 56) is somewhat narrower and steeper.
Z
0
C
YIGU
YEAT
FIGURE4. EFFECTO F HEATO F VAPORIZ.4TION TION CURVES
ON
3
ELIMINA-
If the distillation is carried out at an arithmetic series of temperatures instead of a series chosen so that the distillability increases by a constant factor at each temperature, the curve will have a somewhat different shape. For comparative purposes, a substance with a distillability of 1 at 100' C., 2(lj2) a t 105O, 2 a t 110.7", etc., will be assumed; then log D" =
-.4244'3 -+ 11.3789 T
The temperature series, To, TI,Tz,TS . . . , will be assumed to be loo", 105", 110",115" . . . . If the distillation takes place for one unit of time at each temperature, the per cent of the total substance distilled in each fraction will be
SEPTEMBER, 1937
['
INDUSTRIAL AND ENGINEERING CHEMISTRY
V"i dt = 100 [l
-
The per cent of the total amount of substance distilled between the temperatures T$-I and Ti is,
D "i
(O)] [l
Q"i
- e-=]
(11)
. O
The elimination curve calculated from this equation (Figure 5 c ) is lower and flatter than that for the first hypothetical distillation calculated by Equation 9.
Distillation from a Nonvolatile Solvent at a Continuously Increasing Temperature
.
For some distillations, it is convenient to have the distillability increase continuously instead of by discrete jumps This situation might arise when a still is being supplied more power than necessary to maintain constant temperature, or when the distilland trickles down a column heated a t the bottom. The ways in which the distillability can vary with time are infinite, but for the simplest equations, let it be assumed that the distillability increases by the factor r every rn units of time. Then, D = br ( t / m ) if we let b represent the distillability and the rate of distillation at t = 0. The distillation starts at the temperature To. After m units of time, the temperature is T I , after 2m units of time it is T z , and after irn units of time it is Ti. Since a dilute solution in a nonvolatile solvent is again assumed, the mole fraction AT at any time t during the distillation is given h y
N
=
(1
979
100 [Qi.- Qi-l] = 100 [exp. -
bm(ri-1 l ) - exp. 100 lnr bm(r' 100 lnr -
"I
(I2)
Figure 6a shows the eliminatiQn curve for this type of distillation if b = 1, r = 2("*), and m = 1. The shape of this curve is almost the same as that for the distillation with discontinuous temperature changes shown in Figure 1. The effect of raising the temperature more slowly by letting m = 2 and also 4 is shown in Figure 6b and G . This shifting of the temperature of the maximum yield to a lower value when more time is taken is similar to that of the first type of distillation shown in Figure 2 . S
I
,
,
,
,
I
"
'
I
I
