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.

Acid Analysis by Titration Determination of Molecular Weight

Table 1. Data from standardization of NaOH titrant with KHP.

Trial	Mass KHP (g)	Initial Burette Volume (mL)	Finial Burette Volume (mL)	NaOH Concentration (M)
1	0.1133	0.23	20.15	0.02785
2	0.1148	20.15	40.21	0.02802
3	0.1118	20.97	40.38	0.02820
4	0.1104	1.48	20.97	0.02774

The average NaOH concentration was calculated to be 0.02795 M with a standard deviation of 0.00020.

Table 2. Data from molar mass determination of unknown number 519A.

Trial	Mass KHP (g)	Initial Burette Volume (mL)	Finial Burette Volume (mL)	Molar Mass (g/L)
1	0.2175	0.48	18.70	426.7
2	0.2037	18.70	35.31	438.7
3	0.1982	0.28	16.63	433.7

The average molar mass the unknown was determined to be 433.0 g/L with a standard deviation of 6.1.

The Ideal Gas Law

Introduction

The purpose of this lab was to investigate relationships between the properties of gas, including pressure, volume, moles, and temperature, and then use the Ideal Gas Law (eq 1) to explain observations made. The lab consisted of a pressure-volume experiment and a pressure-temperature experiment.

Equation 1 is the The Ideal Gas Law, where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature. 

PV=nRT (1)

In equation 2, Boyle’s Law, pressure multiplied by volume equal a constant.

PV=Constant (2)

In equation 3, Charles Law, pressure divided by temperature equal a constant.

P/T=Constant (3)

Procedure

Detailed procedures may be found in reference 1.

Results 

Figure 1 shows the pressure compared with the volume from part one. 

Figure 1. The pressure of air measured by controlling the volume.

The average volume was 0.014 L ± 0.004 and the average pressure was 1.4 atm ± 0.4. The curve of Figure 1 means the pressure was inversely related to volume. 

Figure 2 shows the pressure compared with 1/volume of the air from the same data. 

Figure 2. The pressure of air versus the inverse volume.

The data in Figure 1 was used to solve Equation 1 for the number of moles of air in the syringe, which was calculated to be 7.71 x 10^-4 moles. The pressure was multiplied by the volume for each data point according to Boyle’s Law (eq 2). The results from each data pair were constant, confirming Boyle’s Law.  The value of R, calculated using equation 1 and the slope of the trendline in Figure 2, was 0.0757 L atm/mol K.

Figures 3 and 4 show the relationship of temperature versus pressure of the data obtained from the pressure-temperature experiment. Figure 3 is atmospheres versus degrees Celsius, Figure 4 is atmospheres versus degrees Kevin.

Figure 3. The relationship of pressure (Atmospheres) versus temperature (Celsius) of air.

Figure 4. The relationship of pressure (Atmospheres) versus temperature (Kelvin) of air.

It is known that pressure and temperature are normally directly related ¹ (eq 3), which was tested using the data from Figure 4. Pressure was divided by temperature for each data point to determine if they equal one constant value. The calculated values remained relatively constant, they got smaller as the temperature and pressure increased, which agrees with equation 3.

By setting the pressure (y value) equal to zero and solving for the volume (x value) in the trendline of figure 4, the pressure was calculated to be 12.1 atm. Then trendline was solved for the pressure when the temperature equaled 200 and 400 degrees K. It was found that when the temperature was doubled that the pressure also doubled. 

Discussion

The Ideal Gas Law was tested by observing a pressure-volume relationship and a temperature-pressure relationship. The R value was calculated with the data in Figure 1 to be 0.0757 L atm/mol K. This value is smaller than the accepted R value of 0.08206 L atm/mol K.¹ Error in this value may be due to composition of the air in the room that the lab was done deviated from where the accepted value was determined. 

Temperature would double if pressure was doubled. When temperature increases the amount of kinetic energy in molecules, in the form of heat, increases with with pressure. With the increase of kinetic energy the molecules increase in velocity and collide more frequently.

References

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