Heats of Mixing a n d Excess Thermodynamic Properties a t 25OC.
of Binary Systems of Methanol, Ethyl Alcohol, 1-Propanol, a n d 2-F'ropanol with Ethyl Acetate
.
P. S. MURTI' nn.4 UATTUFW v.AN WINKLE University of Texas, Austin, Tex.
A
s a t i s f a c t o r y d e s i g n method for e x t r a c t i v e a n d a z e o t r o p i c distillation columns should i n d u d e enthalpy b a l a n c e s o n e a c h p l a t e to allow c a l c u l a t i o n of t h e quantity of both liquid and vapor l e a v i n g and entering t h e plate. Colburn (3) brought out c l e a r l y i n t h e case of n-butane-isobutene separation u s i n g furfural a s the extracting agent, t h e importance of taking into account t h e h e a t e f f e c t s produced on mixing t h e components a n d showed that approximately 30% error o c c u r s in t h e n e t h e a t evolved. Neglect of t h i s l a r g e quantity in d e s i g n obviously r e s u l t s i n c o n s i d e r a b l e uncertainty i n operation of t h e tower. However, a s e a r c h i n t o t h e literature r e v e a l s that t h e r e are few d a t a o n h e a t of mixing and that t h i s s u b j e c t h a s not been i n v e s t i g a t e d t o a d e g r e e comparable t o that of vapor-liquid equilibria. In many cases t h e reported d a t a form a small fraction of what is a c t u a l l y required for d e s i g n purposes. E x c e s s thermodynamic properties, which a r e express r e l a t i v e t o i d e a l behavior of a s y s t e m , c a n b e e a s i l y 6 a c c u r a t e l y determined from vapor-liquid equilibrium measu ments. T h e s e properties reveal t h e extent of departure 0. s y s t e m from i d e a l behavior and, more important, t h e d e g r e e of a s s o c i a t i o n or d i s s o c i a t i o n of a component i n a particular mixture. T h e p r e s e n t investigation w a s conducted t o determine experimentally t h e h e a t of mixing of t h e binary s y s t e m s of methanol, ethyl alcohol, 1-propanol, and 2-propanol with ethyl a c e t a t e i n a new type of calorimeter which w a s ini t i a l l y t e s t e d with methanol-benzene mixtures and found to g i v e good results. Also, i t w a s proposed to c a l c u l a t e t h e e x c e s s thermodynamic properties of t h e four binary systems of a l c o h o l s with e t h y l a c e t a t e from t h e smoothed vaporliquid equilibrium data.
e f f e c t i v e stirring medium. T h i s t y p e of calorimeter h a s t h e d i s a d v a n t a g e of a constant e x c h a n g e of h e a t between t h e calorimeter and the ambient air in t h e l a r g e Dewar f l a s k for which i t is n e c e s s a r y t o apply a correction. T h i s correction varied as much as 8 t o 20% of t h e total h e a t of mixing i n t h e experiments of Scatchard and others. In 1953, T s a o and Smith (10) d e s c r i b e d another calorimeter, some f e a t u r e s of which were modified and u s e d in t h i s work. A s e m i s e c t i o n a l view of t h e calorimeter in full size and a l i n e diagram of the various connections a r e shown in F i g u r e s 1 and 2. A is a s p e c i a l Dewar f l a s k made of b o r o s i l i c a t e g l a s s a n d w a s ground a t t h e top to fit a graundg l a s s s t o p p e r , B . T h e c a p a c i t y of t h e calorimeter is about 1 4 0 ml. I t w a s heavily silvered both i n s i d e and o u t s i d e and is almost flat, i n s t e a d o f hemispherical, a t t h e inner when l i q u i d s ~
G
MATERIALS
B e n z e n e of t h e following properties w a s u s e d without further purification: Boiling p int, OC. Density" ', grams per Refractive/Ind. = n"
9
D
80.1 CC.
0.87374 1.49806
puriricauon a n a m e p n y s i c a i p r o p e r t i e s of methanol, e t h y l a l c o h o l , 1-propanol, 2-propan01, a n d e t h y l a c e t a t e h a v e been d e s c r i b e d (6). i n e memoas
01
APPARATUS
A good review o f v a r i o u s calorimeters w a s given by Weissberger (11). In 1952 Scatchard, Ticknor, G o a t e s , and McCartney (8) d e s c r i b e d a very s i m p l e calorimeter which c o n s i s t s e s s e n t i a l l y of a circular tube provided with t w o wells: one f o r the thermistor, and the other for the heater. T h e two liquids, for which t h e h e a t of mixing is t o b e determined, a r e s e p a r a t e d by a quantity of mercury in t h e tube. T h e whole a s s e m b l y is then p l a c e d in a l a r g e Dewar f l a s k and rotated through a n a n g l e of 270' either manually or mechanically. Mercury fin t h e calorimeter s e r v e s a s a n 'Pvesent addtera, Department of Chemical Technology, Andhrs University, Waltair, India. 1958
..
TO MAINS
F
C
c
-
v I
T
I
II
O
M A I N HEATER
L
Ic
. 4
1'0 POTENTIOMETER
J Figure
2 , L i n e diagram of various connections t o calorimeter
of different d e n s i t i e s a r e mixed. T h e ground-glass stopper, but for t h e taper a t t h e ground portion, is almost cylindrical. I t is open at t h e top, t h u s leaving a n empty s p a c e which is filled with a s b e s t o s powder to minimize heat transfer t o t h e surroundings from t h e top of t h e calorimeter. T h i s stopper h o l d s a Beckman thermometer, C, h a s a ground-glass joint, D for t h e buret, H, and two l e a d s , E , for t h e heater. T h e Beckman thermometer w a s attached to t h e calorimeter through a tight-fitting rubber s l e e v e which w a s changed for e a c h run. T h e heater, F, is 5 f e e t of 30-gage Nichrome wire wound i n t o a coil and surrounded by a glass tube. Proper c a r e w a s taken to see that t h e electrical copper l e a d s were attached t o t h e heater at the points where they were completely immersed in t h e liquid, t h u s avoiding two l e a d s from the s a m e end, o n e for t h e current and t h e other for t h e measurement of the potential drop. To prevent sliding of t h e Nichrome wire i n s i d e t h e glass tube, constrictions were introduced a t t h o s e p l a c e s where t h e copper l e a d s were soldered t o the heater wire. T h e g l a s s coil w a s filled with General E l e c t r i c s i l i c o n e oil of light visc o s i t y t o allow rapid h e a t transfer from t h e heater t o t h e liquid without appreciable time lag. G is a g l a s s stirrer with t h r e e paddles of t h e same size, s p a c e d a t approximately 0.5-inch intervals, and another a t t h e entrance of t h e stirrer s h a f t i n t o t h e calorimeter. T h e bottom paddle w a s a d j u s t e d t o about 0.25 inch from t h e bottom of t h e Dewar flask, To prevent vapor loss through the stirrer s h a f t , t h e standard t y p e of mercury seal w a s provided. T h e stirrer w a s rotated by a s m a l l motor, and the s p e e d w a s controlled by means of a powerstat.
66
INDUSTRIAL AND ENGINEERING CHEMISTRY
H is a jacketed 50.0-ml. borosilicate glass buret certified by t h e National Bureau of Standards. Water from a constant temperature water bath maintained a t 25 f 0.01 'C. w a s circulated by a midget rotary pump. T h e calorimeter w a s mounted on a rectangular framework of 5/-inch s t e e l rods and the Dewar f l a s k rested i n a b r a s s cup contoured to the s h a p e of the bottom of t h e Dewar. T h e calorimeter w a s clamped a t the top to t h e framework to prevent any vibrations during stirring. T h e current to the heating coil w a s supplied by two 6-volt batteries] J , arranged i n s e r i e s , including a rheostat i n t h e circuit. T h e potential drop a c r o s s t h e heating coil w a s measured with a standard potentiometric circuit using a Leeds & Northrup T y p e K-1 potentiometer. T h e current p a s s i n g through the heater w a s measured by noting t h e potential drop a c r o s s a standard manganin resistor of 0.01 ohm. T h e s e two voltage drops were measured with t h e s a m e potentiometer by making connections through a doublethrow switch. T h i s allowed readings to be taken quickly. T h e working current t o t h e potentiometer w a s supplied through a rheostat i n the circuit by two >volt dry battery cells. T h e time w a s measured by an electric stopwatch, M , which w a s synchronized with t h e heater circuit.
N, a dummy resistor, w a s used to discharge t h e batteries for an hour or s o before a run, s o that they would come t o a constant voltage. V O L . 3, NO. 1
TECHNIQUE O F MEASUREMENT
CALCULATIONS
T h e calorimeter w a s checked by measuring t h e h e a t s of mixing of methanol-benzene mixtures. Data on t h i s s y s t e m were reported by Wolf, P a h l k e , and Wehage (14)a t 2OoC.; Williams, Rosenberg, and Rothenberg (12) a t 2 0 ° C . ; Scatchard, Ticknor, G o a t e s , and McCartney (8) a t 2 0 ° C . ; and T s a o and Smith (10) a t 25'C. About 70.0 ml. of one of t h e components were introduced from a calibrated buret into the s p e c i a l Dewar f l a s k and t h e s e c o n d component w a s placed i n t h e j a c k e t e d buret. T h e whole assembly w a s placed i n a c o n s t a n t temperature bath and water from t h i s bath w a s circulated through t h e j a c k e t of the buret. T h e liquid in t h e buret w a s allowed t o a t t a i n the temperature of t h e bath for 1 to 1.5 hours. During t h i s period, the c o n t e n t s of the buret were frequently stirred by means of a long copper rod, the end of which w a s bent into a loop of s u c h diameter as to p a s s freely into t h e buret. At the end of t h i s period, the temperature w a s recorded by a thermometer a c c u r a t e within 0 . l o C . T h e c o n t e n t s of the Dewar flask were next brought t o t h i s temperature by t h e supply of current t o t h e heater. When both t h e components were a t t h e same temperature, a known amount of the component in t h e buret w a s admitted i n t o t h e Dewar f l a s k and the drop or rise i n temperature w a s carefully noted by means of t h e Beckman thermometer, which could b e read with a magnifying l e n s t o 0.005°C. It w a s , however, not n e c e s s a r y to know t h e final temperature using t h e technique employed in t h i s investigation. Next t h e heater c i r c u i t w a s turned on and the s t o p watch w a s s t a r t e d a t t h e same time. T h e r a t e of h e a t i n g w a s so s e t in t h e bezinning t h a t there w a s 0.10 C. r i s e for every minute. The power input t o the h e a t e r w a s calculated after noting t h e current p a s s i n g through t h e heater by measuring the voltage drop across t h e standard r e s i s t o r , t h e voltage drop a c r o s s the h e a t e r i t s e l f , and the total time required t o bring t h e c o n t e n t s to the i n i t i a l temperature. During t h e c o u r s e of a run, about four t o f i v e readings were t a k e n after e a c h s u c c e s s i v e addition of t h e component from the buret. T h e s p e e d of t h e s t i r r e r w a s observed t o b e fairly c o n s t a n t a t 250 t o 300 r.p.m., a s p e e d a t which thorough mixing w a s produced without a n appreciable e f f e c t on temperature. T h e heating current w a s fairly c o n s t a n t as evidenced by the c o n s t a n c y i n t h e voltage drop a c r o s s t h e standard resistor. T h e variation in the r e s i s t a n c e s of the heater wire w a s negligible over a temperature range of 2' t o 3OC.
H e a t of Mixing. T h e h e a t of mixing w a s c a l c u l a t e d using t h e following equation:
The maximum error resulting from vaporization and condensation effects and in the measurement of experimental heat of mixing data was estimated a s follows: Vaporization-Condensation Effects Vapor space volume in calorimeter = 60 ml. Assumptions 1. Activity coefficients from 4OoC. data can be used at 2 5 " ~ for . computation of vcporization l o s s 2. Equilibrium between vapor and liquid Calculation 1. Calculate moles of component 1 i n air space above liquid at start 2. Calculate moles of component 2 in vapor s p a c e above liquid after component 2 was added and equilibrium reached 3. Calculate heat effect caused by vaporization of the quantity of component 2 4. Calculate heat effect caused by condensation of the displaced quantity of component 1 5. Compute the net heat effect and the per cent error. For methanol-ethyl acetate it w a s found to b e 0.8% (Run 111) Evaluation of Measurement Errors Voltage measurement 0.2% Resistance measurement 0.2% Time measurement Negligible Temperature measurement liquid from buret 0.25% Energy input, stirer 0.20% Mass measurement 0.50% Heat transfer to surroundings Negligible 1.35% Total YOmeasurement Total of vaporization and measurement errors about 2.35% maximum 1958
where
AH:
= integral h e a t of mixing,
calories per mole
V = potential drop a c r o s s heater, v o l t s V, = potential drop a c r o s s standard resistor, v o l t s
R,
=
r e s i s t a n c e of standard resistor, ohms
n = t o t a l number of moles of mixture t = time, s e c o n d s Excess Thermodynamic Properties. T h e following method w a s adopted after a number of other u n s u c c e s s f u l attempts t o c a l c u l a t e t h e e x c e s s thermodynamic properties from vapor-liquid equilibrium data. T h e experimental and calcul a t e d v a l u e s for h e a t of mixing agree with e a c h other within limits of experimental accuracy of t h e h e a t of mixing measurements. A preliminary smoothing of t h e activity coefficient v a l u e s w a s made using one of t h e solutions of Gibbs-Duhem equation. T h e variation of the activity coefficient with composition was s u c h that the van L a a r e q u a t i o n s could be emp1oye.d to represent the experimental d a t a , d e s p i t e t h e fact that van L a a r made restrictive assumptions i n deriving t h e equations. 4 s pointed out by Wohl (13) and Carlson and Colburn (2), t h e c o n s t a n t s a s rearranged by t h e l a t t e r workers a r e regarded a s mere empirical c o n s t a n t s without a t t a c h i n g any p h y s i c a l s i g n i f i c a n c e t o them. V a l u e s of A and B reported earlier (6) were u s e d t o c a l c u l a t e t h e activity c o e f f i c i e n t s a t even v a l u e s of composition. T h i s w a s repeated for e a c h isothermal run. Since e x c e s s free energy c a n be expressed by E q u a t i o n s 2 and5,
hG;
= 2.303 R T ( X , log y ,
+ X, log y,)
(2)
(3)
(4)
AG; = AHE X - TAS;
A H ; = AH: when t h e same reference state is chosen for both cases. T h e reference state chosen is that of the pure component a t t h e same temperature. I t w a s a s s u m e d in t h e s e c a l c u l a t i o n s that a linear variation of e x c e s s free energy with temperature is valid over t h e range 25" t o 6OoC. In other words, i t w a s assumed t h a t t h e e x c e s s entropy of mixing is independent of temperature. Correlation of Heat of Mixing Data. Scatchard and others ( 8 ) proposed a n empirical equation b a s e d on a n analogy of e x c e s s free energy i n which t h e heat of mixing w a s exp r e s s e d a s a power s e r i e s in (xi- %) as follows:
AH," = X,X, [ A , + A , (x, - XJ
+ A,
(x,
- x,)'
+
-
*
.I
(8)
where xi, x1 are the mole fractions of components 1 and 2, r e s p e c t i v e l y , and A's a r e c o n s t a n t s which are functions of temperature and the s y s t e m properties. C H E M I C A L AND E N G I N E E R I N G D A T A S E R I E S
67
Table I.
Experimental Heat o f Mixing at 25OC.
i
Methanol, (kj/Mole)
Benzene, Xla
AH:
0.9664 0.9098 0.8360 0.7528 0.5760 0.4678 0.3446 0.2 145 0.1015 0.0334
0.8
0.0574 0.1530 0.2641 0.3768 0.5811 0.6734 0.7345 0.7 139 0.5899 0.3446
W
. a
20.6
aMole fraction of methanol.
8 Table I I . Experimental Data an Heat of Mixing a t 25OC. Methanol-Ethyl Acetate
Xte
AH:
0.9796 0.9438 0.8990 0.8371 0.7805 0.7401 0.6530 0.5698 0.4941 0.4075 0.3211 0.2246 0.1680 0.1025 0.0678
(kj/mole) 0.0659 0.1599 0.2869 0.4443 0.5771 0.6604 0.8894 0.9771 1.0424 1.0539 0.9952 0.8538 0.7420 0.5005 0.3702
1-Propanol-Ethyl Acetate
X; 0.9592 0.9062 0.8387 0.7576 0.6714 0.59 14 0.5857 0.5732 0.5070 0.5059 0.4241 0.4026 0.3265 0.2898 0.2364 0.1825 0.16 15 0.0842 0.0730
A
