Transcript Colligative Properties of an Cyclohexane/1

Colligative Properties of a Binary Liquid: Cyclohexane & 2Propanol
A. Sinclair, C. Jordan (Grunst), & U. Dennis
Washington State University, Chemistry 335
Surface
Tension
Viscosity
Phase Diagram
Introduction
Liquid- Vapor phase diagrams are an important tool used to represent the
distillation of a binary liquid pair. A binary phase diagram is used to show
the relationship between the boiling temperature and the composition of
the liquid and the vapor in
equilibrium at a constant pressure.
This phase diagram shows no
boiling point azeotrope.
Introduction
Introduction
Introduction
Viscosity, (also called the coefficient of viscosity), is the proportionality constant between
the force that causes a laminar flow and velocity gradient of that flow, over an area that is
parallel to the direction of the flow. The relationship described can be illustrated with
Newton’s law:
Surface tension occurs because of the intermolecular forces in a liquid. It
produces a resistance between the surface expanding or contracting. Under
constant temperature and pressure we can measure different surface tensions
due to the various concentrations that we used. We calculated surface tension
using the simple relationship of dW  dGs  dAwhere γ is surface tension in
units of ergs/cm2.
With ideal conditions partial molar volumes of a binary mixture are
independent of concentration. Therefore, we can calculate a total volume by
adding the two individual partial volumes. The following equation defines
total volume:
 dv 
f  A 
 dr 

 bt

A Newtonian liquid near the walls of the capillary tube can be considered stationary,
while the liquid in the center flows with the greatest velocity in the center of the tube.
Procedure
With the capillary viscometer, diameter of 200 µm, we can calculate an unknown
viscosity using a known viscous liquid to calibrate the apparatus and find the constant b
for the following equation:
Before performing the distillation process, the refractive indices of the
prepared solutions were measured so that a standardization curve could be
created. The refractive indices were plotted vs. the mole fractions.
t = efflux time
The mixtures were made by placing small amounts of cyclohexane into
pure 2-propanol. These were for our high concentration points for 2propanol, the liquid curve. Then the same method was repeated and the
vapor curve was produced by the high concentrations for cyclohexane.
Then the constant, b, we can solve for all the viscosities of our ten
solutions. Placing about 10 mL into the viscometer we drew the
liquid up using a vacuum and then timed the liquid as it dropped
from mark a to mark b. This is our efflux time and with this you
then plot viscosity versus mole fraction of cylcohexane.
Results
Results
Index of Refraction
1.43
1.42
1.41
1.4
1.39
1.38
1.37
0
0.2
0.4
0.6
0.8
1
 dV 
 dV

 n1 
 n2 
 dn1  n2 ,T , P
 dn2

Wg  W p
V
Results
Density
Surface Tension
0.81
26
25.5
25
24.5
24
0.8
ideal
measured
0.79
0.78
23.5
0
0.2
0.4
0.6
0.8
1
Cyclohexane Mol Fract
0.77
23
1.2
Mole Fraction of Cyclohexane
0
22.5
0
0.2
0.4
0.6
0.8
1
0.2
propanol/cyclohexane ideal vs. experimental
From the data shown above we can see that the viscosity is gradually decreasing with the
increase of the mole fraction of cyclohexane. Our experimental cyclohexane has a
viscosity of 1.02cP and 2-propanol has a viscosity of 2.04cP. These compare nicely with
the reference values for cyclohexane and 2-propanol of 1.07cP and 1.97cP respectively.
This gives us an error of 4.9 percent for cyclohexane and 3.4 percent for 2-propanol.
80
bp temp (deg C)
78
76
ideal liquid
ideal vapor
measured vapor
measured liquid
74
72
70
68
0
0.1
0.2
0.3
0.4
0.5
cyclo mole fract
0.6
0.7
0.8
Conclusions
By distilling a cyclohexane/2-propanol mixture, it was found that the
system does not form a boiling point azeotrope. Deviations in the phase
diagram can be accounted for since the data obtained was taken at 700 mm
Hg, compared to the ideal value of 760 mm Hg. In addition, the binary
mixture was very volatile, and some of the vapor product may have been
lost to the surroundings when the liquidus samples were taken.
Furthermore, flash vaporization may have occurred when cyclohexane was
added to the reaction flask.
The conclusions for this experiment are that the surface tension does not have
a linear relationship with the concentrations/compositions. Our percent errors
for the measured values were for 2-propanol, 0.421 and for cyclohexane 0.203.
mg
Rl
2
2
2

 RC  2
 RC  2
 RC  2 
2
 RC  
  m
   
  Rl
  
 Rl 
 m 

2
2
2


g

m
g

m
g






2
2
2
2
 RC  
 Rl 
  m 2    
2 
  Rl 
 Rl 
 Rl 

Perry, R.H, and D.W. Green. Perry’s Chemical Engineers’ Handbook. 7th Edition. McGraw-Hill, New York: 1997.
   2    2    2 
2
      b     t      
 t 
 b 

  
2
2
2
2  t  2b  b  2t  bt 2 
2
2
2

Shoemaker, David P., Carl W. Garland, and Joseph W. Nibler. Experiments in Physical Chemistry. 6th Edition.
McGraw-Hill, New York: 1996.
“Surface Tension.” Wikipedia Encyclopedia. November 15th, 2006. WSU Libraries.
University, Pullman, WA.<http://en.wikipedia.org/wiki/Surface_tension>.
1
1.2
As shown in our graph we had very similar result to the reference data. The
mixing caused only a slight inconsistency from the ideal behavior.
Conclusions
Error Propagation
Bettelheim, Frederick A. Experimental Physical Chemistry. W.B. Saunders Company, Philadelphia: 1971.
  b t  
0.8
The reference values that we found for cyclohexane and 2-propanol are
0.779 g/mL and 0.803g/mL respectively. Our values were 0.77836±0.001
for cyclohexane and 0.80222±0.002 for 2-propanol. These compare well to
the reference values. However, due to the inconsistency of our solutions
with the ideal behavior we cannot assume that the partial molar volumes are
additive.
References
Propagation of Error

Conclusions
RC 
Using equation seven we can see that the laminar layer separation versus the molecular
equilibrium separation will decrease as viscosity decreases, or for our example as the
mole fraction of cyclohexane increases. This shows that the solution is becoming less
viscous, meaning a larger laminar layer and also that the molecular spacing will increase
more and thus the ratio laminar layer separation versus molecular equilibrium separation
will decrease.
0.6
Mole Fraction of Cyclohexane
Error Propagation
Conclusions
0.4
1.2
M ole fraction of Cyclohe xane
As mentioned above, the standardization curve was plotted by plotting the
index of refraction vs. mole fraction for each of the prepared solutions.
The data was fitted using the most accurate method, or the method with
the best R2 fit, which in our case is a polynomial fit.


 n2 ,T , P
Pycnometer that are 25 mL were cleaned, dried and then weighed. These
same pycnometers were then filled with the ten different solutions, weighed
and recorded. Then by the use of the following equation various densities
were found.
Density (g/mL)
+ 0.0367x + 1.3754
R² = 0.9995
Our results shown for cyclohexane and 2-propanol are relatively similar for the
literature values that were found. For cyclohexane our surface tension was
equivalent for the literature values of 25.5 dynes per cm2. For 2-propanol the
literature value was 23.78 and our experimental value was 23.1±0.029 dynes
per cm2, a bit further off but still very close.
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
Procedure
Results
Surface Tension (dynes/cm)
y=
0.0231x2
Viscosity (cP)
Calibration Curve
First, in order to make sure the apparatus,
Du Noűy Tensiometer, was calibrated we placed a 100 mg piece of paper on
the meter and recorded a measurement. We found that our correction factor
was 1.42. This was found by using the equation mg/R; m=mass of paper,
R=measurement reading, and g=acceleration of gravity. Then we placed our
various concentrations into the dish and recorded the different measurements.
We then made or graph of mole fraction of cyclohexane versus surface tension.

 bt

From the phase diagram below, there is no boiling point azeotrope for the
cyclohexane/ 2-propanol mixture.
Vtot
Procedure
ρ=density
Vtot  n V  n1V2
0
1 1
In reality you will not be able to add these volumes due to intermolecular
forces, so the following equation allows us to determine liquid mixture
volumes.
Procedure
Mix Cyclohexane and 2-propanol at various concentrations and heat until
equilibrium is reached, Tboil. Record the temperatures and collect samples
of the distillate and residue. Cool samples in a 20oC water bath. Refractive
indices were taken for all the samples.
Density
Washington State
 V
V 
 W
g

2
2
2
 2


  Wg   V  2Wp

 W 
p 


2
2
1 2
1 2
 V     Wg     W p


2