ATENEO DE MANILA UNIVERSITY CH 46 PHYSICAL CHEMISTRY LABORATORY I
Liquid-Vapor Equilibrium in an Azeotropic Mixture 1 In a homogeneous mixture of two liquids, the vapor pressures are quit e different from the vapor pressures of the pure components. Three Three different cases may be recognized: those that obey Raoult’s Law, and those that deviate positively or negatively from Raoult’s Law (see Figure 1). For an ideal solution, Raoult’s Law is written P i
0
(1)
X iP i
where P where P i is the partial pressure pressure of the ith component, P˚ i is the vapor pressure of the pure ith component, and X i is the mole fraction of the ith component in the liquid phase.
(a) ideal
(b) positive deviation from Raoult’s Law
(c) negative deviation from R aoult’s aoult’s Law
Figure 1. Boiling point as a function of liquid and gas phase composition (mole fracti on).
In this experiment, we will investigate the boiling point curve of a binary liquid mixture. Aside from that determined experimentally, two other boiling curves will be constructed. One assumes that the mixture behaves ideally, that is, it obeys Raoult’s Law. The other considers non-ideal non -ideal solution behavior and includes activity coefficients obtained from the van Laar equations. The three resulting boiling curves will then be compared. Ideal Solution Behavior Dalton’s Law of Partial Pressures states that the total pressure P is P is just the sum of the partial pressures of the components. For a system consisting of two gaseous components: P P 1
(2)
P 2
If the mixture behaves ideally and does obey Raoult’s Law, Equation 2 may be rewritten as: 0
P X 1 P
0
1
X 2 P 2
(3)
For a two-components system, X system, X 1 = 1-X 2. Equation 3 may then be rewritten in terms of X X 2: X 2
1
P
0
P 2
0
P 1
0
P 1
(4)
Adapted from Sime, Sime, R. J. Physical Chemistry: Chemistry: Methods, Techniques, and and Experiments (Saunders, (Saunders, 1990).
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Thus, the composition of the liquid phase, X 1 or X 2, depends on the total pressure, usually atmospheric, and the vapor pressures of each pure component at the equilibri um temperature. From Daltons’s Law, the composition of the gas phase is: P 2
Y 2 P
(5)
where Y 2 is the mole fraction of component 2 i n the gas phase. From Raoult’s Law, Y 2
0
P 2
X 2 P 2
(6)
P
P
To calculate the boiling point curve assuming ideal solution behavior, vapor pressure equations are available such as the Antoine equation (Boublik et. al., 1973):
log P 0
A
B
(7)
T C
where A, B, and C are the Antoine constants, P is in torr, and T is in C. The boiling point curve can then be determined following these steps: 1. Determine the boiling points of pure components 1 and 2. The boiling point is the temperature wherein the equilibrium between the vapor and liquid phases of a system is reached. This is calculated from the Antoine equation by letting P equal the measured atmospheric pressure. 2. Choose a temperature between the calculated boiling points of the pure components.
0
0
3. At this temperature, calculate P 1 and P 2 using Equation 7. 4. Calculate X 2 and Y 2 using Equations 4 and 6. 5. Plot these points at the chosen temperature. 6. Repeat at several more equally spaced temperatures. Nonideal Solution Behavior
When the solution deviates from the ideal, activity coefficients 1 and 2 are take into account in Equations 1and 5. Thus, P i
0
i X i P i
(8).
From Dalton’s Law: P P 1
0
P 1 X 1 P 2 1
0
2 X 2 P 2
(9)
For the gaseous phase composition, P i
Y i P
0
(10).
i X i P i
At the azeotropic point, the compositions of the liquid and gas phases are equal, i.e., X 1 = Y 1 and X 2 = Y 2. From Equation 9, it follows that the activity coefficients at thee azeotropic point are: P
1,az
0 P 1
(10) and
P
2,az
(11)
0
P 2
To calculate for the activity coefficients at temperatures other than the azeotropic point, the van Laar equations (Hala et. al., 1967) are used namely:
log 1
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A
X 1 1 X 2
A
2
(12)
B
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log 2
B
X 2 1 X 1
A
B
(13)
2
where A and B are the van Laar constants, calculated as follows:
X 2 log 2 A log 1 1 X 1 log 1
2
X 1 log 1 B log 2 1 X 2 log 2
2
In outline form, the calculation for the non-ideal solution boiling point curve i s as follows: 1.
Calculate the activity coefficients 1 and 2 at the azeotropic point using Equations 10 and 11.
2.
From Equations 11 and 12, derive the van Laar constants A and B for the system given the liquid phase composition and activity coefficients at the azeotropic point. 3. Divide the composition, for instance, X 2 into several parts from 0.1 to 0.9 by increments of 0.1. 4. For a certain X 2, determine X 1. With the van Laar constants A and B, compute the corresponding activity coefficients. 5. Insert the calculated mole fractions and activity coefficients in Equation 9. This results to an 0
0
equation with two unknowns ( P 1 and P 2 ). Using the Antoine equation (Equation 7), vary the 0
0
temperature T to determine P 1 and P 2 that will satisfy the equality represented by Equation 9. 6.
Repeat steps 4 and 5 for the other X 2 values.
Apparatus The distilling apparatus shown in Figure 2 is constructed from a 50-mL distilling flask from which the side arm is removed. A small water-cooled condenser is sealed to the neck of the flask near the junction of the neck and the flask.
Figure 2. Apparatus for measuring boiling points as a function of composition. The liquid refluxing into the small glass bulb below the condenser has the composition of the gas phase. The liquid i n the main boiler has the composition of the liquid in equilibrium with that gas phase.
Procedure School of Science and Engineering
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Prepare a series of solutions by weight of known mole fractions approximately equal to 0.25, 0.50, and 0.75 acetone and cylcohexane. The total volume need only be 5 or 10 mL. Weigh to ±0. 5 mg. Keep the solutions tightly stoppered when storing or the composition may change due to evaporation. Measure the refractive indices of these solutions as well as of pure acetone and pure cyclohexane. Prepare a calibration curve of refractive index versus mole fraction. The curve is not generally linear. The measurements of refractive index for the calibration curve and the azeotrope should be done at exactly the same temperature, preferably with the same refractometer. With a graduated cylinder, place about 25 mL acetone in the reflux apparatus and measure the boiling point. With a measuring pipet, add about 2 mL cyclohexane and let the system reflux until the small sample tube below the reflux condenser has been thoroughly rinsed out and contains liquid with the composition of the gas phase (several minutes). Let the apparatus cool somewhat; then remove a sample from the sample tube (gas phase composition) and from the reflux flask (liquid phase composition). Analyze the samples with a refractometer. Repeat this procedure with subsequent additions of 4, 6, 8, and 12 mL cyclohexane. Then discard the mixture, rinse the flask with pure cyclohexane, and fill it with about 25 mL cyclohexane. As above, determine the boiling point of pure cyclohexane, and mixtures of cyclohexane with 2, 4, 6, 8, and 12 mL acetone added.
Results and Calculations Tabulate and plot a calibration curve of refractive index versus mole fraction for your system. Draw a smooth curve through the points. Use this curve to determine the composition of the liquid and gas phases at the recorded boiling temperatures. Tabulate and plot boiling point versus mole fraction for the experimental, ideal, and van Laar case. The Antoine constants A, B, and C for acetone and cylohexane are listed in Table 1. Take note of the tie lines — these are horizontal lines that connect the liquid and vapor composition at equilibrium at a particular boiling temperature. Draw a smooth curve through the points using the tie lines as a guide. Compare the three boiling point curves. Table 1. Antoine Constants for acetone and cyclohexane B Component A acetone 7.11714 1210.595 cyclohexane 6.84941 1206.001
C
229.664 223.148
Source: T Boublik,, V Fried, and E Hala. 11973. The Vapor Pressures of Pure Substances. Amsterdam: Elsevier.
In addition, determine the azeotropic composition and compare it with the literature value, if available.
References: Main: RJ Sime. 1990. Physical Chemistry: Methods, Techniques, and Experiments. Saunders Publishing. 1. TV Boublik, V Fried, and E Hala. 1973. The Vapor Pressures of Pure Substances . Amsterdam: Elsevier. 2. HC Carlson and AP Coburn. 1942. Vapor-Liquid Equilibria of Nonideal Solutions. Ind. Eng. Chem. 34: 581. 3. JM Grow. 1983. Display of Vapor Pressure Data with a Theoretical Fit. J.Chem Educ. 60: 1062. 4. EJ Hala, V Fried, & O Vilim. 1967. Vapor-Liquid Equilibrium, 2/e. NY: Pergamon Press. 5. GN Lewis, & M Randall, revised by K Pitzer & L Brewer. 1961. Thermodynamics. NY: McGraw-Hill. 6. JM Prausnitz, CA Eckert, RV Orye, & JP O’Connell. 1967. Computer Calculations for Multicomponent Vapor-Liquid Equilibria. Englewood Cliffs, NJ: Prentice-Hall. 7. RD Rossini, et. al., 1953. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds. Pittsburgh, Pennsylvania: API Project 44, Carnegie Press. 8. J Timmermans. 1959. Physico-chemical Constants of Binary Systems. NY: Interscience.
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