THE COPPERBELT UNIVERSITY

SCHOOL OF MINES AND MINERAL SCIENCES

DEPARTMENT OF CHEMICAL ENGINEERING

NAME : SHADRICK SOLE
SIN : 21166173
PROGRAM : CHEMICAL ENGINEERING
COURSE : CE 430
TASK : EXPERIMENT 2
SUPERVISOR: MR MUGALA

GROUP MEMBERS;
AARON KISHIKI 21161993
MOSES BANDA 21168801
MUSENGE MUSENGE 21163656
KATEBE DOROTHY 21166849
TITLE: A PHASE DIAGRAM FOR THE PROPANONE-ETHANOLSYSTEM
ABSTRACT
The aim of this experiment was to assess the thermodynamic consistency of vapor-liquid
equilibrium (VLE) data and calculate the theoretical stages needed to achieve a 90 mol%
propanone separation. Thermodynamic consistency was verified using the Gibbs-Duhem
equation, where data satisfying the condition of summing to zero were deemed consistent.
Minor deviations were likely due to experimental errors, such as measurement inaccuracies,
sampling inconsistencies, data analysis limitations, or instrument precision issues (e.g.,
thermometer or barometer readings).
Using the x-y equilibrium plot, the required number of theoretical stages was determined for
a 50 mol% propanone feed under total reflux conditions. The analysis showed that four
theoretical plates were sufficient to achieve the desired separation.

INTRODUCTION
Vapor-liquid equilibrium (VLE) is a key principle in thermodynamics and separation
processes, referring to the balanced state where a liquid and its vapor coexist without net
mass transfer. In this equilibrium, evaporation and condensation rates are identical, making
VLE crucial for designing phase-change systems like distillation.
This experiment investigates VLE in binary mixtures, analysing how liquid and vapor
compositions stabilize under equilibrium conditions. Such studies provide essential
thermodynamic insights for chemical engineering applications, particularly in separation
processes.
To interpret the experimental data, thermodynamic models, namely the Van Laar and
Margules (Redlich-Kister) equations are applied. These models compute the activity
coefficients, quantifying deviations from ideal mixture behaviour. By comparing model
predictions with experimental results, the most accurate representation of the system is
identified.

The primary aims of this lab are to investigate the thermodynamic consistency of VLE data,
derive activity coefficients using thermodynamic models, and construct a McCabe-Thiele
diagram based on equilibrium data. From this diagram, the number of theoretical stages
required to achieve a desired separation under total reflux conditions can be determined.

AIMS
1. To check the thermodynamic consistency of the data.
2. To present the thermodynamics characteristics and constant of Margules equation for
the given system.
THEORY
Vapour-liquid equilibrium (VLE) is a key concept in thermodynamics and chemical
engineering that explains how a chemical species is distributed between the vapor and liquid
phases. At equilibrium, the concentration of a vapor in contact with its liquid counterpart is
typically expressed using vapor pressure, especially when other gases are present. This
pressure represents the balance between the two phases, ensuring no net change in phase
occurs.

Equilibrium Composition in VLE

In a binary system, the equilibrium composition is defined by the mole fractions of each
component in both the liquid and vapor phases. The mole fractions of a component (i) in the
vapor phase (denoted as y₁) and the liquid phase (x₁) are related by the equilibrium constant
(K₁), which depends on temperature and pressure. This relationship can be expressed as:
𝑃
𝑦𝑎 = 𝜋𝑎 𝛾𝑎 𝑥𝑎 = 𝐾𝑎 𝑥𝑎 … (1)
𝑎

The mole fraction of a component in the vapor phase usually differs from that in the liquid
phase. This relationship can be explained using Raoult’s Law for ideal mixtures or modified
with activity coefficients for non-ideal mixtures.
Raoult’s Law states that the partial vapor pressure of a component in a mixture is
proportional to its mole fraction in the liquid phase:

𝑃𝑖 = 𝑋𝑖 𝑃𝑖∗ … (2)

Where:

• Pᵢ is the partial pressure of ith component in the vapor phase

• xᵢ is the mole fraction of ith component in the liquid phase
• Pᵢ⁎ is the vapor pressure of the pure ith component

Relative volatility is used to describe how easily two components (A and B) can be separated
by distillation. It is calculated as:
𝑦𝐴
1−𝑦𝐴
𝛼𝐴𝐵 = 𝑥𝐴 … (3)
1−𝑥𝐴

Non-Ideal Behaviour and Thermodynamic Analysis

To account for non-ideal behaviour in mixtures, the Van Laar equations are employed.
These equations relate the activity coefficients of the components to their mole fractions in
the liquid phase:

𝑎
𝑙𝑜𝑔𝑦𝐴 = 𝑎𝑥 2
… (4)
(1+ 𝐴 )
𝑏𝑥𝐵
 𝑏
𝑙𝑜𝑔𝑦𝐵 = 𝑏𝑥𝐵
2 … (5)
(1+ )
𝑎𝑥𝐴

Here, a and b are Van Laar coefficients derived from experimental VLE data. If 𝑦𝐴 = 𝑦𝐵 , the
system is said to form an azeotrope, where the liquid and vapor compositions are identical,
making separation by distillation challenging.

Finally, the Gibbs-Duhem equation is used to check the thermodynamic consistency of VLE
data. The equation is evaluated using the following integral:
1 𝑦
∫0 ln 𝑦1 𝑑𝑥 … (6)
2
If the integral result is zero, the data is considered thermodynamically consistent.

MATERIALS AND METHOD

Materials
❖ Mixtures A, B, C and I (of unknown substance)
❖ Flat bottomed flasks
❖ Thermometers
❖ Test tubes
❖ Clamp holder
❖ Heating element
❖ Power source
Method

❖ A moderate amount of Mixture A was transferred from a flat-bottomed flask into a

test tube.
❖ The initial temperature of the mixture was recorded.
❖ The test tube was then placed on a heating element, held securely by its mouth.
❖ A thermometer was inserted into the test tube, ensuring it remained above the liquid
level to avoid full immersion and reduce the risk of sudden pressure buildup.
❖ The test tube and thermometer were held in position until the mixture began to boil.
❖ The boiling point of the mixture was then recorded.

This procedure was repeated for each of the different mixtures

RESULTS AND DISCUSSION

Results

Table 1.0: Properties of components

Component Density (30°C) Molecular weight Boiling point R.I
(kg/m3) (kg/kmol) (°C) (30°C)
A 779.1 58.08 56 1.359
 B 780.97 46.068 78.37 1.359

Table 2: Table of compositions obtained from the T-xy diagram below

Group Mixture T (°C) Propanone Ethanol Propanone Ethanol
No. mol % in mol % in mole % in mole %
liquid liquid vapor in vapor
1 A 64 38 62 59 41
2 B 74 8 92 21 79
3 A 64 38 62 59 41
4 C 62 50 50 67 33
5 C 63 43 57 63 37
6 I 64 38 62 59 41

T-xy diagram
85

80
Temperature (°C)

75

70
T-x
T-y
65

60

55
0 0.2 0.4 0.6 0.8 1
Mole fraction of propanone (xA,yA)

Figure 1.0: Dew point curve (T-y) and bubble point curve (T-x) of the measured
temperatures.
Table 3: Activity coefficients at corresponding temperatures
𝛄
T (°C) XA YA 𝛄𝐀 𝛄𝐁 ln𝛄𝐀 ln𝛄𝐛 ln𝛄𝐀
𝐁
78.3 0 0 0 0.999 - -0.001 -
73 0.1 0.262 1.5205 1.0198 0.411 0.0196 0.3994
69 0.2 0.417 1.371 1.065 0.315 0.0629 0.2525
65.9 0.3 0.524 1.268 1.1338 0.237 0.1255 0.1118
63.6 0.4 0.605 1.1718 1.212 0.158 0.1922 -0.0337
61.8 0.5 0.674 1.119 1.2011 0.112 0.2624 -0.1499
60.4 0.6 0.733 1.071 1.381 0.068 0.3228 -0.2542
59.1 0.7 0.802 1.041 1.485 0.0401 0.3954 -0.3553
 58 0.8 0.865 1.019 1.596 0.0188 0.4675 -0.4486
57 0.9 0.929 1.007 1.757 0.00697 0.5636 -0.5566
56.1 1 1 1.006 0 0.005982 - -
Detailed calculations in appendix

ln(YA/YB) vs XA
0.5

0.4

0.3

0.2

0.1

0
ln(YA/YB)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7
XA

Figure 2: Relationship of areas under the curves

The percent error is found to be 56.7%, showing that the data is not thermodynamically
consistent (detailed calculation in appendix).
 Equilibrium curve diagram
1
0.9
0.8
0.7
0.6
0.5
Y

0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
X

Figure 3: Equilibrium curve data and theoretical number of plates

Figure 3 above indicates that from a mixture of 50mol% and 90mol% propanone distillate,
the theoretical plates from the 90% mole fraction is approximately 4.2 or 5.

lnYA & lnYB vs XA

0.45 0.6
0.4
0.5
0.35
0.3 0.4
0.25
lnYA

lnYB

0.3
0.2
0.15 0.2
0.1
0.1
0.05
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
XA

Series2 Series1

Figure 4: Relationship of ln𝛾𝐴 , ln𝛾𝐵 and xA

Discussion

The experimental investigation of the propanone-ethanol binary system revealed important

thermodynamic and separation characteristics. The T-xy phase diagram clearly demonstrated
the existence of a minimum-boiling azeotrope, where the mixture exhibited lower boiling
points than either pure component. This azeotropic behaviour, evident from the converging
bubble point and dew point curves, significantly influenced the vapor-liquid equilibrium
(VLE) compositions. The equilibrium data showed that propanone, having a lower pure-
component boiling point (56°C), consistently enriched in the vapor phase compared to
ethanol (boiling point 78.37°C). However, the azeotropic composition limited the maximum
achievable purity through simple distillation, a crucial consideration for separation process
design.

Thermodynamic consistency analysis using the Gibbs-Duhem equation revealed significant

deviations, with a calculated error of 56.7%. This substantial inconsistency suggested
potential experimental limitations that warrant discussion. Temperature fluctuations during
sampling and composition measurements likely contributed to these deviations, as even
minor variations could significantly impact the refractive index readings used for
composition analysis. Furthermore, the time required to achieve true equilibrium between
phases might have been insufficient in some experimental runs. These findings emphasize the
challenges in obtaining precise VLE data and highlight the importance of rigorous
experimental controls in thermodynamic studies. The observed inconsistencies do not
invalidate the results but rather underscore the complex nature of this binary system and the
need for careful data interpretation.

The calculated activity coefficients provided valuable insights into the system's non-ideal
behaviour. Both components exhibited activity coefficients greater than unity across most
compositions, indicating positive deviations from Raoult's Law. This non-idealist was
particularly pronounced in ethanol-rich mixtures, where stronger molecular interactions
became apparent. The asymmetric nature of the ln ((γA /γB) versus composition plot further
confirmed the composition-dependent molecular interactions in the system. These findings
have practical implications for process modelling, as they demonstrate that simple ideal
solution assumptions would be inadequate for accurate predictions in this system. The Van
Laar and Margules models provided reasonable approximations of the activity coefficients,
though the observed deviations suggest opportunities for improved thermodynamic modelling
approaches.
The McCabe-Thiele analysis yielded practically significant results for separation process
design. From an initial 50 mol% propanone feed, approximately 4.2 theoretical stages were
required to achieve a 90 mol% propanone distillate under total reflux conditions. This result,
while theoretically sound, must be interpreted in light of the azeotropic limitation discussed
earlier. The analysis assumed constant molar overflow and equilibrium at each stage, which
while useful for preliminary design, would require refinement for actual industrial
applications. The relatively low number of theoretical stages suggests favourable separation
characteristics for this mixture below the azeotropic composition, though the energy
requirements would still need careful evaluation in a complete process design. These findings
provide a valuable foundation for further studies on more complex separation strategies, such
as azeotropic or extractive distillation, that would be necessary to achieve higher purities
beyond the azeotropic point.

RECOMMENDATIONS

❖ Use hands-free apparatus to secure test tubes.

❖ Switch to digital thermometers for better precision.
❖ Avoid overfilling to allow space for vapour expansion.
❖ Consistently use appropriate PPE and ensure good ventilation.
❖ Position thermometers properly in the vapour phase for accurate readings.

CONCLUSION

This study confirmed the non-ideal VLE behaviour of the propanone-ethanol system,
identifying a minimum-boiling azeotrope that limits simple distillation efficiency. Despite
56.7% thermodynamic inconsistency, the data revealed positive deviations from Raoult’s
law, with stronger non-idealist in ethanol-rich mixtures. Thiele analysis showed 4–5
theoretical stages are needed to achieve 90 mol% propanone from a 50 mol% feed under total
reflux. However, azeotropic constraints necessitate advanced separation methods for higher
purity. These findings support the design of more efficient distillation processes for this
binary system.
REFERENCES

1) Mugala, A, N, Chipili, P, & Musonda, J. (2023). Chemical Engineering Lab and Project
Manual for DCE 240 and CE 430. Kitwe: The Copperbelt University, School of Mines,
Department of Chemical Engineering.
2)
3) Atkins, Peter and Julio de Paula, Physical Chemistry, 7th ed. New Yoke. H. Freeman and
Co. 2002.
4) Stanley M. Walas, Phase Equilibria in Chemical Engineering, p180 Butterworth Publ.
ASBN 0409-95162-5, 1996
5) Van Ness, H.C., & Isermann, H.P. (1995). Thermodynamics in the treatment of
vapor/liquid equilibrium (VLE) data. Pure & Applied Chemistry, 67(6), 859-872.
 APPENDIX

Calculation of saturation partial pressures

Using the Antoine equation and the A, B, C constants of propanone and ethanol:
B
log10Pi* = Ai - T(℃)i+ C
i

Table 4: Constants of properties

Constant of propanone Constant of ethanol
A 7.31414 8.1122
B 1315.67 1592.864
C 240.479 226.184

At 78.3°C
1315.67
log10Ppropanone* = 7.31414 - = 3.1868
78.3 + 240.476
Ppropanone* = 1537.6 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.88
78.3 + 226.184
Pethanol* = 760.05 mmHg

At 73°C
1315.67
log10Ppropanone* = 7.31414 - = 3.117
73 + 240.476
Ppropanone* = 1319.15 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.788
73 + 226.184
Pethanol* = 614 mmHg

At 69°C
1315.67
log10Ppropanone* = 7.31414 - = 3.06
69 + 240.476
*
Ppropanone = 1153.73 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.716
69 + 226.184
*
Pethanol = 520.02 mmHg

At 65.9°C
1315.67
log10Ppropanone* = 7.31414 - = 3.019
65.9 + 240.476
Ppropanone* = 1046.84 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.6587
65.9 + 226.184
Pethanol* = 455.779 mmHg

At 63.6°C
1315.67
log10Ppropanone* = 7.31414 - = 2.991
63.6 + 240.476
 Ppropanone* = 980.905 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.6154
63.6 + 226.184
Pethanol* = 412.545 mmHg

At 61.8°C
1315.67
log10Ppropanone* = 7.31414 - = 2.961
61.8 + 240.476
Ppropanone* = 915.372 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.2511
61.8 + 226.184
Pethanol* = 381.166 mmHg

At 60.4°C
1315.67
log10Ppropanone* = 7.31414 - = 2.941
60.4 + 240.476
Ppropanone* = 873.7 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.554
60.4 + 226.184
Pethanol* = 358.175 mmHg

At 59.1°C
1315.67
log10Ppropanone* = 7.31414 - = 2.9224
59.1 + 240.476
Ppropanone* = 836.393 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.5288
59.1 + 226.184
Pethanol* = 337.884 mmHg

At 58°C
1315.67
log10Ppropanone* = 7.31414 - = 2.9062
58 + 240.476
*
Ppropanone = 805.796 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.5072
58 + 226.184
*
Pethanol = 321.481 mmHg

At 57°C
1315.67
log10Ppropanone* = 7.31414 - = 2.8914
57 + 240.476
Ppropanone* = 778.767 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.4874
57 + 226.184
Pethanol* = 307.158 mmHg

At 56.1°C
1315.67
log10Ppropanone* = 7.31414 - = 2.8779
56.1 + 240.476
Ppropanone* = 755.068 mmHg
1592.864
log10Pethanol* = 8.1122 - = 2.4694
56.1 + 226.184
Pethanol* = 294.733 mmHg
Activity coefficient
P T yi
Activity coefficient is given by γi = where PT = 760 mmHg
P∗i xi
At 78.3°C
760 × 0
γpropanone = =0
1537.6 × 0
760 × 1
γethanol = = 0.999
760.05 × 1

At 73°C
760 × 0.262
γpropanone = = 1.50945
1319.15 × 0.1
760 × 0.738
γethanol = = 1.0198
614 × 0.9

At 69°C
760 × 0.417
γpropanone = = 1.371
1155.73 × 0.2
760 × 0.583
γethanol = = 1.065
520.02 × 0.8

At 65.9°C
760 × 0.524
γpropanone = = 1.268
1046.84 × 0.3
760 × 0.476
γethanol = = 1.1338
455.779 × 0.7

At 63.6°C
760 × 0.605
γpropanone = = 1.17187
980.905 × 0.4
760 × 0.395
γethanol = = 1.212
412.545 × 0.6

At 61.8°C
760 × 0.674
γpropanone = = 1.119
915.372 × 0.5
760 × 0.326
γethanol = = 1.3
381.166 × 0.5

At 60.4°C
760 × 0.739
γpropanone = = 1.071
873.7 × 0.6
760 × 0.261
γethanol = = 1.385
358.175 × 0.4
At 59.1°C
760 × 0.802
γpropanone = = 1.041
836.393 × 0.7
760 × 0.198
γethanol = = 1.485
337.884 × 0.3

At 58°C
760 × 0.865
γpropanone = = 1.019
805.796 × 0.8
760 × 0.135
γethanol = = 1.596
321.481 × 0.2

At 57°C
760 × 0.929
γpropanone = = 1.007
778.767 × 0.9
760 × 0.071
γethanol = = 1.757
307.158 × 0.1

At 56.1°C
760 × 1
γpropanone = = 1.006
755.068 × 1
760 × 0
γethanol = =0
294.733 × 0

Calculation of the Van Laar constants;

xB logγB 2
a = logγA (1 + )
xA logγA

xA logγA 2
b = logγB (1 + )
xB logγB

Therefore, at 73°C,
0.9log1.0198 2
a = log1.2505(1 + ) = 0.367527
0.1log1.5205

0.1log1.5205 2
b = log1.0198(1 + ) = 0.09697
0.9log1.0198

Calculation of area
Area above X-axis
Area = Trapezoid 1 + trapezoid 2 + triangle
1 1
Trapezoid 1 = 2(a + b) h = 2(0.25 + 0.4) (0.1) = 0.0325 units
1 1
Trapezoid 2 = 2(a + b) h = 2(0.25 + 0.1) (0.1) = 0.0175 units
 1 1
Triangle = 2(b) (h) = 2(0.375) (0.1) = 0.01875 units

Area = 0.0325 + 0.0175 + 0.01875 = 0.06875 units2

Area below the X-axis
Area = Trapezoid + triangle
1 1
Trapezoid 2 = 2(a + b) h = 2(0.15 + 0.56) (0.4) = 0.142 units
1 1
Triangle = 2(b) (h) = 2(0.15) (0.13) = 0.00975 units

Area = 0.142 + 0.00975 = 0.15175 units2

Difference in terms of percentage:
(Area below x−axis)−(Area above x−axis) 0.15175−0.06875
= × 100%
(Area below x−axis) 0.15175

Percentage difference = 54.7 %