Vapor Pressure and Enthalpy of Vaporization of Water

VAPOR PRESSURE AND ENTHALPY OF VAPORIZATION OF WATER

INTRODUCTION:

This experiment is designed to find the vapor pressure of water at temperatures between 50oC and 80oC. A graph of the natural logarithm of vapor pressure versus the reciprocal of absolute temperature (in Kelvin) allows the calculation of the enthalpy of vaporization.

A sample of air is trapped in an inverted 10-ml graduated cylinder which is immersed in a tall beaker of water. As the water in the beaker is heated to about 80oC, the air in the graduated cylinder expands and becomes saturated with water vapor. The temperature and volume are recorded. The total air and water vapor pressure inside the cylinder is equal to the barometric pressure plus a small correction for the pressure exerted by the depth of the water above the trapped air. The water in the beaker is allowed to cool. The volume of air contracts, and less water vapor is present at the lower temperature. The temperature and volume are recorded every 5oC between 80oC and 50oC. Next, the beaker is cooled with ice to a temperature close to 0oC. At this temperature the vapor pressure of water is so low that it can be assumed that all of the gas in the graduated cylinder is air.

The moles of air molecules in the cylinder can be found by using the volume of dry air present at the temperature near 0oC and the ideal gas equation. Knowing the moles of air in the container, the partial pressure of air can be calculated at each temperature, and the vapor pressure of water can be obtained by subtracting the pressure of air from the total pressure inside the cylinder.

The Clausius-Clapeyron equation is a mathematical expression relating the variation of vapor pressure to the temperature of a liquid. It can be written:

ln P = -  Hvap + C RT where lnP is the natural logarithm of the water vapor pressure, Hvap is the enthalpy of vaporization of water, R is the gas constant (8.314J/moleK), T is the temperature (Kelvin, and C is a constant which does not need to be evaluated. It can be seen that this equation fits the straight line equation y = mx + B where y is equal to lnP, x is equal to 1/T and the slope m, equals –Hvap/R.

If a graph is made of lnP versus 1/T, the heat of vaporization can be calculated from the slope of the line.

Equipment: Thermometer, preferably +/- 0.1oC Graduated cylinder, 10 ml Beaker, 1 Liter Ring stand, ring, wire gauze, Bunsen burner

55 VAPOR PRESSURE AND ENTHALPY OF VAPORIZATION OF WATER

Thermometer

Tall Beaker

“h” Air Water Water

Figure 1. Diagram of Apparatus PROCEDURE:

Refer to Figure 1. Fill a 10 ml graduated cylinder about 2/3 full of water. Close the top with your finger and quickly invert and lower the cylinder in a 1 liter beaker half filled with water. Add water to the beaker until the water level extends above the cylinder.

Use a ruler to measure (in mm) the difference in height between the top of the water in the beaker and the top of the water in the cylinder, h.

Heat the assembly with a Bunsen burner until the temperature is about 80oC. The air inside the cylinder should not expand beyond the scale on the cylinder. If it does, remove the cylinder (use tongs) and start again with a smaller initial volume of air. Record the temperature and the volume of air (+/- 0.01 ml) in the cylinder. Be sure to continuously stir the water in the beaker to ensure an even distribution of heat.

Cool the beaker (continue stirring) until the temperature reaches 50oC. Record the temperature and volume of gas in the cylinder every 5oC. You may add some ice or ice water to the beaker to speed up the cooling slightly, but try to keep the volume of water in the beaker about the same.

After the temperature has reached 50oC, cool the baker rapidly to about 0oC by adding ice. Record the gas volume and temperature at this low temperature.

Record the barometric pressure in mmHg.

CALCULATIONS:

1. There is a small error in the measurement of the volume of air caused by using the upside- down graduated cylinder because the meniscus is reversed. Correct all volume measurements by subtracting 0.20 ml from each volume reading.

2. Calculate the total pressure of the gas in the cylinder from the barometric pressure and the difference in water levels between the top of the water in the beaker and the top of the water inside the flask, h. The pressure inside the cylinder is slightly greater than the atmospheric pressure. This increased pressure can be calculated by using the measured difference in water depth, h, and multiplying by the conversion factor that the pressure exerted by

56 VAPOR PRESSURE AND ENTHALPY OF VAPORIZATION OF WATER

1.00 mmHg is the same as that exerted by 13.6 mmH2O. This factor results from the fact that the density of mercury is 13.6 times that of water. We will assume that this correction is constant through the experiment. If the water depth is changed significantly, this calculation will need to be repeated.

Pcylinder = Patmosphere + h(mmH2O) x 1.00 mmHg 13.6 mmH2O

o 3. Calculate the moles of trapped air, nair, by using the volume of air present near 0 C and the ideal gas equation. At this low temperature we are assuming that the vapor pressure of water is negligible, so almost no water vapor is present in the cylinder.

nair = PV RT

4. For each temperature between 50oC and 80oC, calculate the partial pressure of air in the cylinder:

Pair = nairRT V

5. Calculate the vapor pressure of water at each temperature:

Pwater = Pcylinder - Pair

6. Plot ln Pwater on the vertical axis versus 1/T on the horizontal axis. Draw the best fitting straight line through the points. Determine the slope of the line, and calculate the value of

Hvap of water. Compare to the reported value for the enthalpy of vaporization of water.

CONCLUSION:

1. What is vapor pressure and why does it change with temperature?

2. What is enthalpy of vaporization?

3. The assumption was made that the vapor pressure of water is negligible at a temperature close to zero. Find the actual vapor pressure of water at your low temperature and comment on the validity of the assumption.

4. The assumption was also made that the slight changes in “h”, the depth under the surface of the water, will not significantly change the total pressure in the graduated cylinder. Comment on the validity of this assumption.

5. Were your data values close to a straight line graph?

6. Write out the long “two-point” form of the Clausius-Clapeyron equation. Why does the graphical method of analysis give a better value for the enthalpy of vaporization than does the form of the Clausius-Clapeyron equation using two temperature-vapor pressure values?