Determination of the Latent Heat of Vaporization of Ethanol through the Ramsay-Young Method Alvarillo, Camille Margaret1, Buensuceso, Maria Crispina 1, Gonzales, Ysabel Marie1, Uy, Jaron Nicolas 1 1
Department of Chemical Engineering, University of the Philippines – Diliman Diliman Quezon City, Philippines
Abstract The determination of the experimental latent heat of — The vaporization of ethanol was accomplished using the RamsayYoung Method. Saturation temperature values were obtained by varying vacuum pressures. Experimental values of the latent heat of vaporization of ethanol were then obtained by using the Clausius-Clapeyron equation, and the following Equations of State (EOS): (EOS): van der Waals, Redlich-Kwong, and SoaveRedlich-Kwong, which resulted to 6.088%, 4.583%, 4.198%, and 3.601% relative deviation, respectively. The Soave-RedlichKwong relation provided the most accurate value, as the acentric factor, as well as the liquid volume, were taken into consideration. Keywords: latent heat of vaporization; Ramsay-Young; Ramsay-Young; ClausiusClapeyron; Equations of State; saturation temperature
I.
I NTRODUCTION
The Ramsay-Young Experiment, proposed in the namesakes’ study, study, On a New Method of Determining the Vapour-pressures of Solids and Liquids, and on the Vapour pressure of Acetic Acetic Acid , investigates a method of as certaining the vapor pressure of liquids. liquid s. This study involved the use of thermometer, Sprengel’s Sprengel’s pump, and several laboratory apparatuses that contained the acetic acid, which were sealed and kept air-tight to ensure that the measured temperatures and pressures were kept constant throughout throughout the experiment. The saturation temperatures at varying pressures were also determined determined (Ramsay & Young, 1862). In obtaining the theoretical boiling temperatures of the substance at different pressures, the Antoine Equation was used:
=
+
Equation 1
For pure ethanol, the Antoine’s constants (Smith, Van Ness, & Abbott, 2005) are found in Table in Table 1. Table 1. Antoine’s Coefficients for Pure Ethanol (kPa, °C)
A B C
16.8958 3795.78 230.918
In a confined space where vapor to liquid phase change is expected to happen, molecules will move from the vapor
interface to liquid phase because of pressure build up. As the rate of transfer from one phase to another becomes equal, the system goes into dynamic equilibrium and consequently, boils. At this stage, the liquid vapor pressur e will equal the pressure inside the closed vessel, and its relationship with saturation temperature is shown by the Clausius-Clapeyron Equation. It can be derived from the fact that two phases coexist in equilibrium during phase change, such that their molar Gibbs energy remains equal:
=
Equation 2
where and represent two different phases. Furthermore, since the two components are at equilibrium with one another, the rates at which the Gibbs energies change will als o be equal.
=
Equation 3
By applying the fundamental property
=
Equation 4
with Equation 2 and Equation 3, 3, the following can be obtained:
=
Equation 5
The equation can further be r earranged to obtain Equation obtain Equation 6.
= = ∆ ∆
Equation 6
By applying the Second Law of Thermodynamics to Equation 6, Equation 7 can be obtained.
= ∆ ∆
Equation 7
For the Clausius-Clapeyron Equation, the volume of the vapor is assumed to be significantly larger than that of the liquid, which can be expressed as
Other parameters for the different equations of state used are shown in Table 2. Table 2. Parameters for the Equations of St ate
∆ = ∆ =
Equation 8
EoS
Lastly, substituting Equation 8 into Equation 7 will result to
VdW RK SRK
= ∆ 2
Equation 9
Integrating this, the working Clausius-Clapeyron Equation can be obtained.
= ∆ where
Equation 10
P is the saturation pressure T is the saturation temperature R is the gas constant H is the latent heat of vaporization of pure liquid
The Clausius-Clapeyron Equation relates the pressure and saturation temperature to the latent heat of vaporization. The latent heat is essentially the heat effect that accompanies phase change that occurs at a constant temperature. It can be determined by plotting lnP vs. regression.
and
performing linear
In lieu of the Clapeyron Equation, equations of state (EOS), namely the van der Waals, Redlich-Kwong and Soave-Redlich-Kwong may also be used to obtain the change in volume, V, associated with the phase change. This will allow the direct use of Equation 7 to calculate for the latent heat of vaporization without the simplifying assumption that the volume of the vapor is s ignificantly larger than that of the liquid. The latent heat of vaporization may then be calculated using the changes in volume predicted by each equation of state.The equations of state to be used are all in the form in Equation 11 obtained from Smith et al. (2005).
= ++ where
R is the gas constant Tc is the critical temperature Tr is the reduced temperature Pc is the critical pressure
1
−.
SRK
0 1 1
0 0 0
1/8 0.08664 0.08664
= 2 2 0.480 1 + + 1.574 0.176 ( ) ∙1. where
27/64 0.42748 0.42748
3/8 1/3 1/3
Equation 12
is the acentric factor
Through the Ramsay-Young method, the study aims to experimentally determine the latent heat of vaporization of ethanol through the method’s application, as well as the use of the Clausius-Clapeyron Equation, van der Waals, RedlichKwong and Soave-Redlich-Kwong equations of state. Furthermore, this study also aims to compare the experimental data from the various equations used and the literature values of the latent heat of vaporization of ethanol. II.
MATERIALS AND METHODOLOGY
Figure 1. Setup o f Ramsay-Young Experiment (“Chemical Engineering Thermodynamics Laboratory Manual,” 2013)
The setup for the Ramsay-Young Method was prepared as shown in Figure 1. Equation 11
P is the pressure of the system T is the temperature of the system V is the volume occupied by the system
2 2 = = Ω
Zc
In the setup, a vertical flask is closed at the top by an accurately fitting cork perforated with a hole for a thermocouple probe to pass. Rubber tubing connects this flask to another flask, which is immersed in an ice bath. This second flask is connected to a vacuum pump and to a manometer, which is controlled by a manometer valve. Once the vacuum pump and manometer valve were turned on, a constant pressure reading on the manometer was obtained. The theoretical saturation pressure of ethanol was then obtained using this pressure through the Antoine Equation. The temperature of the hot plate was then adjusted a few degrees above the theoretical saturation temperature. Then, once the temperature reading of ethanol was constant, it was recorded.
Figure 2. Saturation Pressure vs. Temperature
The system pressure is decreased by increments of 3 inglycerol, and the procedure was repeated until the pressure could no longer be decreased. III.
the actual boiling temperature. One of the challenges of this experiment was keeping the temperature and pressure reading stable since fluctuations are often caused by the presence of air leaks in the experimental set-up.
R ESULTS AND DISCUSSION
The Ramsay-Young Method was utilized to determine the experimental boiling temperature of ethanol for the varying pressures, as shown in Table 3. These pressures were also used to determine the theoretical boiling temperature through the Antoine’s Equation. Table 3. Comparison of Experimental and Theoretical Boiling Temperatures of Ethanol Pressure (kPa)
Experimental Temperature (K)
Theoretical Temperature (K)
Relative Error (%)
93.256 95.203 97.275 99.064 101.326
343.55 344.15 344.45 344.95 345.55
349.27 349.79 350.33 350.78 351.31
1.639 1.612 1.678 1.662 1.650
Based on the data provided in Table 3, it can be observed that as the pressure of the system is increased, the temperature, both for experimental and theoretical values, also increase. The experiment began at a low pressure setting of 93.256 kPa given that this was the pressure and temperature of the set up that was held stable for a period of time. Starting at a low pressure allows a trend in the temperature and pressure differences to be observed. Since the boiling points are lower at lower pressures, once a higher pressure is set, the solution would stop boiling and more heat would need to be added to increas e the temperature to the new boiling point. If the experiment were performed starting from high pressures, the solution would already be above the boiling point once a new pressure is set, and will simply boil more vigorously. This may increase the temperature readings obtained as the thermocouple and heating flask ma y be above
Through Figure 2, it can be seen that both experimental and theoretical boiling temperatures follow the same trend – increasing pressure with increasing temperature. From the pressure vs. temperature plot, the experimental data have an R 2 of 0.991 when fitted to a linear trendline, suggesting that the boiling point increases linearly with temperature, as predicted by the Antoine equation. The slope of the trendline for the experimental data,
, is 4127.39 Pa/K and deviates
from the theoretical slope of 3887.52 Pa/K by 6.2%, which still suggests adequate agreement between the theoretical and experimental results.
The experimental boiling points are consistently lower than the theoretical boiling points, with an average deviation of around 1.60% or 5.77 K throughout all the trials. This suggests that deviations from the predicted boiling points based on Antoine’s equation are due to some systematic error. The error may be due to the cooling of the ethanol vapor before coming in contact with the thermocouple used to record temperatures. Since the thermocouple was not submerged in the solution, there were also likely convective heat losses in the region above the ethanol solution, which lowered the recorded temperature by the thermocouple. There may have also been leaks in the set-up as the manometer reading fluctuate when the heating flask is moved. Leaks from the heating flask would result to a lower actual pressure within the flask and would decrease the boiling point of the ethanol. This may not have been reflected in the manometer reading as it was directly connected to the condensing flask, and not the heating flask where the ethanol was boiled. To obtain the latent heat of vaporization, a plot of lnP versus
was made, as shown in Figure 3.
Figure 3. Plot of ln(P) vs. 1/T
Based on Equation 10, the slope of this graph is
∆, so the
latent heat of vaporization may be obtained by multiplying the slope by the gas constant, R. The experimental latent heat of vaporization obtained is 41.893 kJ/mol, which deviates from the theoretical value of 39.488 kJ/mol (Dong, Lin, & Yen, 1988) by 6.088%. The R 2 of the plot is 0.9899, which suggests a good linear fit of th e data to the theoretical model.
Alternatively, the latent heat of vaporization was also calculated using the van der Waal (vdW), Redlich-Kwong (RK), and Soave-Redlich-Kwong (SRK) equations of state. These were used to obtain the volume of the liquid and vapor, from which the change in volume may b e obtained. This was then used with the Clapeyron equation, shown in Equation 7, to calculate for the latent heat of vaporization. The rearranged version of the equation is:
Equation 13
∆ = ∆ where
is the slope of
Figure 2, previously obtained
to be 4127.39 Pa/K The change in volume and latent heat of vaporization obtained for each equation of state is shown in Table 4. Table 4. Volume and Enthalpy Values for EOS
∆ (m /mol) 3
Trial 1 2 3 4 5
vdW
RK
0.0302 0.0301 0.0296 0.0295 0.0290 0.0289 0.0285 0.0284 0.0279 0.0278 Average
∆ (kJ/mol)
SRK
vdW
RK
SRK
0.0299 0.0293 0.0287 0.0282 0.0276
42.802 42.063 41.226 40.589 39.810 41.298
42.650 41.911 41.074 40.438 39.659 41.146
42.412 41.674 40.838 40.203 39.425 40.911
It may be seen that the different equations of state give different results for the change in volume associated with the phase change, and give different latent heats. These are due to the different assumptions with each equation of state. The van der Waals equation of state is the simplest and takes into account the volume of the particles, and the effect of inter-particle attractions on the pressure. The RedlichKwong equation of state improved on the van der Waals equation and accounted for the temperature dependence of the attraction parameter suggested by van der Waals (Craig, 2000). Finally, the Soave-Redlich-Kwong equation takes into account the shape of the molecule through the acentric factor. Table 5. Comparison of Enthalpy Values Obtained through ClausiusClapeyron, Van der Waals, Redlich-K wong, and Soave-Redlich-Kwong Equations
Equation
Experimental Enthalpy (kJ/mol)
Clapeyron vdW RK SRK
41.893 41.298 41.146 40.911
Theoretical Enthalpy (kJ/mol)
Relative Error (%)
39.488
6.088 4.583 4.198 3.601
Based on the results, the Clausius-Clapeyron Equation yields the least accurate results, as the volume of the liquid is assumed to be negligible. In this case, only the volume of the vapor is accounted for. The various Equations of State, on th e other hand, are more accurate and have a smaller relative deviation because they account for liquid volume. Furthermore, the Soave-Redlich-Kwong EOS has the smallest relative error of 3.601% because it takes into account the acentric factor, which is significant for ethanol as it is a polar molecule (ω = 0.645). Possible sources of error for this experiment include the lack of a well-sealed/airtight/vacuum set-up. Having air leaks
in the system caused the pressure readings to heavily fluctuate, thus making it difficult to measure the experimental saturation temperatures of the system. In addition, because the thermocouple was not in contact with the ethanol upon measurement, it is possible that there are dis crepancies in the measured temperature which is another source of error in this experiment. IV.
CONCLUSIONS AND R ECOMMENDATIONS
The objective of this experiment is to determine the latent heat of vaporization of ethanol using the Ramsay-Young method, and through the applications of the ClausiusClapeyron equation and the van der Waals, Redlich-Kwong and Soave-Redlich-Kwong equations of state. Among the 4 equations used, the Soave- Redlich-Kwong provided the most accurate latent heat of vaporization with a 3.601% relative deviation from the theoretical value. This was because it accounted for the polarity of ethanol which decreased deviation from literature value. In this experiment, it was also observed that as the system pressure is increased, the saturation temperature of ethanol also increased. This was a consistent observation for both the experimental and theoretical data provided in this s tudy. The objectives of this experiment can be explored further by performing an alt ernative method such as calorimetry to determine the latent heat of vaporization of substances of interest. This experiment can be improved by performing an alternative method such as calorimetry to determine the latent heat of vaporization of compounds of interest. Moreover, more accurate data can still be obtained if the sources of error were mitigating. This can be done by assuring that the Ramsay-Young set-up is well sealed. Perhaps, instead of using masking tape to seal the set-up, more rubber stoppers that completely seal the cover of the flasks may be used to avoid air leaks. Lastly, a longer thermocouple that can come in contact with the ethanol solution may be used to avoid discrepancies in temperature measurement. ACKNOWLEDGEMENTS We would like to thank Engr. Myron Alcanzare of the Department of Chemical Engineering for his invaluable input and never-ending support that led towards the success of this study. R EFERENCES [1] Chemical Engineering Thermodynamics Laboratory Manual. (2013), 1, 45. [2] Craig, N. C. (2000). Molecular Thermodynamics (McQuarrie, Donald A.; Simon, John D.). Journal of Chemical Education, 77 (1), 31. https://doi.org/10.1021/ed077p31.2 [3] Dong, J.-Q., Lin, R.-S., & Yen, W.-H. (1988). Heats of vaporization and gaseous molar heat capacities of ethanol and the binary mixture of ethanol and benzene. Canadian Journal of Chemistry, 66 (4), 783 – 790. https://doi.org/10.1139/v88-136 [4] Ramsay, W., & Young, S. (1862). On a New Method of Determining the Vapour-pressures of Solid s and Liquids, and on the Vapour-pressure of Acetic Acid. Journal of the Chemical Society, (42), 42 – 45. [5] Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2005). Introduction to Chemical Engineering Thermodynamics. Chemical Engineering (Vol. 27). https://doi.org/10.1021/ed027p584.3
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