When a sample of liquid is introduced into a container, molecules tend to escape from the confinement of the liquid state into the gaseous state in the process called evaporation. Eventually, the rate of vaporization and the rate of condensation will become equal, and the pressure in the container will level off at some constant value. The system is said to be in equilibrium, and the pressure of gas that exists over the liquid is called the vapor pressure. The higher the vapor pressure, the more volatile is the liquid. Moreover, vaporization is an endothermic process, since energy is required to overcome the attraction that a liquid molecule feels for its neighbors. The energy required to evaporate one mole of a substance at constant temperature and pressure is called the molar enthalpy of vaporization, ∆Hvap. Its magnitude is a measure of the strengths of intermolecular forces in a pure substance.

The mathematical relationship between vapor pressure and enthalpy of vaporization of a pure liquid is summarized by the Clausius-Clapeyron equation. The relationship can be written simply as:

ln P = - ΔH_vap/(RT)+C
where ΔH_vap is the enthalpy of vaporization of the liquid, P is the vapor pressure, T is the temperature, R is the universal gas constant and C is a constant that needs to be evaluated experimentally. Several assumptions are involved in the derivation of this equation, the main ones being that the molar volume of liquid water is assumed to be much smaller than the molar volume of water vapor and that the water vapor is an ideal gas.

Based on the first equation, it can be seen that this equation fits a straight line y = mx + b where y = lnP, x=1/T, and slope, m = -∆H_vap/R. If a graph is made of ln P versus 1/t, the heat of vaporization can be calculated from the slope of the line.

Henceforth, the main purpose of this experiment is to calculate the enthalpy of vaporization of water by obtaining the vapor pressure of water over a range of temperatures with the application of Clausius-Clapeyron equation.

Experimental

In an inverted 10mL graduated cylinder, a sample of air is trapped. The cylinder is submerged in a beaker of water. The beaker is heated to 80^oC and the volume of the air is measured. While stirring the water in the beaker to be sure of even heat distribution, water is cooled and the volume of the gas is recorded every 5^oC. After the temperature of the beaker reaches 50^oC, the beaker is further cooled to near 0^oC by adding ice. The volume of air and the near-zero temperature is measured.

Data

Graduated cylinders are designed to measure volume standing in upright position. Since volume is measured in an inverted position, there will be a slight error, since the meniscus of the water is also inverted. To account for this error, 0.20 mL is subtracted from each measurement to give the corrected volume.

Table 1. Measured Volume and Corrected Volume of air-vapor mixture at different temperatures.

Temperature(oC)	Volume(mL)
85	7.10
80	6.40
75	5.30
70	4.90
65	4.40
60	2.80
55	2.30
50	2.20

Assuming that a negligible amount of water vapor is present below at near 273 K and the air behaves as ideally, the <5oC volume reading can be used to determine the number of moles of dry air nair in the cylinder by the virtue of ideal gas equation

n_air=PV/RT

where P is the barometric pressure, R is the universal gas constant, V is the volume of gas mixture, and T is absolute temperature at 5^oC.

Since the pressure in the cylinder was equalized with the atmosphere before measuring, By Dalton’s Law, the pressure from the water vapor can be determined by subtracting the calculated pressure of the dry air from the atmospheric pressure.

P_water = P_atm – P_air
At 85 C, Vapor Pressure = 761.00 – 151.823 = 609.177 mmHg

Table 2. Partial Pressure of Air and Vapor Pressure of Water at different absolute temperatures

Absolute Temperature(K)	Partial Pressure of Air(mmHg)	Vapor Pressure(mmHg)
358.15	209.3871	551.6129
353.15	229.046	531.954
348.15	283.3607	477.6393
343.15	290.6908	470.3092
338.15	319.0069	441.9931
333.15	493.8843	267.1157
328.15	592.2267	168.7733
323.15	609.7122	151.2878
275.15	761.4154	0

Based on the first equation, it can be seen that this equation fits a straight line y = mx + b where y = lnP, x=1/T, and slope, m = -∆Hvap/R. In order to linearize the Clausius-Clapeyron Equation, there is a need to obtain values of lnP and 1/T.

Table 3. Summary of Tabulated Values

Volume	Absolute Temperature	Vapor Pressure	1/T	ln P
7.10	358.15	551.6129	0.002792	6.312846
6.40	353.15	531.954	0.002832	6.276557
5.30	348.15	477.6393	0.002872	6.168856
4.90	343.15	470.3092	0.002914	6.15339
4.40	338.15	441.9931	0.002957	6.091294
2.80	333.15	267.1157	0.003002	5.587682
2.30	328.15	168.7733	0.003047	5.128556
2.20	323.15	151.2878	0.003095	5.019184
1.50	275.15	0	0.003634	infinity

Applying linear regression, the equation of best-fit line is y=-4636.7x + 19.467 with slope equal to -4636.7 and y-intercept of 19.467. Having calculated the slope, it is now possible to calculate the experimental enthalpy of vaporization of water using the Clasius-Clapeyron Equation.

ΔHvap= -R (slope) = -8.3145J/molK(-4636.7) = 38.5516 KJ/mol
The standard value for enthalpy of vaporization of water is ΔHvap= 40.65 kJ/mol.
Hence %error can be calculated as %error = |40.65-38.5516|/40.65 x 100% = 5.162%

Results and Discussion

Based on Table 2, it is evident that vapor pressure increases with increasing temperature. Hence, vapor pressure is directly proportional to temperature. This is because at higher temperatures, the liquid has more energy, and likewise there is a greater probability of the gas escaping, and the escaped gas has more energy so it exerts a greater force on the container resulting to greater pressure.

The relatively high magnitude of vaporization enthalpy of water compared to other liquids indicates a strong intermolecular force of attraction between water molecules due to its hydrogen bonding. Since its value is positive, It was also verified in the experiment that vaporization is endothermic or heat-absorbing.

The calculated linear relation corresponded to the collected data with R-squared value of 0.8677 which indicates a good linearity of the regression line. This means that there was a little error with the precision of data collection since it followed the linear function quite well.

Although the procedure was properly observed, a slight error of 5.162% was obtained. This is due to the following reasons: The actual vapor pressure of water near zero centigrade is not exactly 0mmHg as opposed to what is assumed since water vapor still exists at this temperature. Thus, the recorded value for the amount of air in the cylinder is somewhat greater than the actual. Though, this number is somewhat insignificant compared to the 2 to 3 figure pressures from 50 to 80 C.

Another thing is that the water in the cylinder is not constantly equal to the water level in the water bath. Water pressure changes considerably depending on the depth, and the gas measurement could change visibly just by moving the cylinder up or down a few centimeters. Hence, the pressure in the cylinder is not actually equal to the prevailing barometric pressure. Pressure corrections should have been made to compensate the difference in water levels to minimize this effect.

On the other hand, water vapor does not behave exactly as ideal gas since there is a strong attraction between water molecules and it was not carried out in very high temperature and very low pressure. Van der Waals equation or Virial equation of state could have been used to minimize this problem, however, this is a bit tedious. In addition, only one trial has been performed and statistically, this is prone to errors. More accurate results would have been obtained if more trials were made.

References
Atkins Physical Chemistry
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