Vapor Pressure and Enthalpy of Vaporization of Water

Introduction

The purpose of this lab was to determine the enthalpy of vaporization of water. The vapor pressor was determined at increments of five degree ranging from 80º C - 50º C. The vapor pressure of a pure substance is dependent on the enthalpy of vaporization, the gas constant, the temperature, and a constant according to the Clausius-Clapeyron equation (eq 1).

P=(-∆H_vap/RT) + C (1)

In Equation 1, ∆H_{vap  is the} enthalpy of vaporization, R is the gas constant, T is the temperature and C is a constant.

The Clausius-Clapeyron equation was put into linear form (eq 2).

lnP=lnA -∆H_vap/RT (2)

The Ideal Gas Law (eq 3) was used to calculate the partial pressures of air for each temperature.

P_air = N_air RT/V (3)

Dalton’s Law of Partial Pressures (eq 4) was used to calculate the vapor pressor of water at different temperatures.

P_water = P_atm - P_air (4)

Procedure

A 10 mL graduated cylinder was filled with 9.4 mL water and inverted into a beaker full of water. The beaker was heated to 80º C and as it was cooled the volume of the air trapped in the graduated cylinder was measured every 5º C. It was then rapidly cooled to 5 ºC and the air volume was measured. For each temperature reading the partial pressure of air was calculated using the Ideal Gas Law. The vapor pressure was calculated using Daltons Law of Partial Pressures. Plots were created and the enthalpy of vaporization and the pressure of water at 65º C were calculated using the line of best fit from the partial pressure of water versus 1/temperature plot (fig. 2) and the Clausius-Clapeyron equation (eq 1).

Detailed procedures can be found in reference 1.

Results 

Table 1 gives the raw data collected with 0.2 mL subtracted from the volumes to take into account the space taken up by the graduated cylinder.

Table 1. Volume and corresponding temperature data

Volume (L)	Temperature (K)
0.0076	353.15
0.0068	348.15
0.0062	343.15
0.0057	338.15
0.0051	333.15
0.0052	328.15
0.0048	323.15
0.0036	278.15

The Ideal Gas Law was used to calculate the partial pressure of air at each temperature and volume shown in Table 1. 

Figure 1 shows the vapor pressure of water and the temperature of water.

Figure 1. The vapor pressure versus the temperature of the water.

The natural log of the vapor pressure versus the inverse temperature of water was used to linearize and plot the data according to the Clausius-Clapeyron Equation (eq 2), this can be found in Figure 2.

Figure 2. Plot of linearized data according to Equation 2

The best-fit line and Equation 2 were used to calculate the heat of vaporization to be 37.45 kJ/mol, and the pressure of water at 65ºC to be 183.2 torr. 

Discussion

The heat of vaporization of water was calculated to be 37.45 kJ/mol. When compared to the value of 44.02 kJ/mol (ref 1) it has 15 % relative error. The pressure of water at 65ºC was calculated to be 183.2 torr, which has a 2% relative error when compared to the value of 187.5 torr (ref 2). The error of the heat of vaporization is likely caused by inaccurate volume reading due to foggy glass and rotation of the graduated cylinder.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206, Department of Chemistry, Southern Oregon University: Ashland, OR, 2010

2. Brown, LeMay, Burnsten, Murphy. Chemistry: The Central Science. 11^th Edition. Pearson Prentice Hall. Upper Saddle River, NJ. 2009.