Experiment

8Vapor Pressure and Enthalpy of Vaporization of Water

Introduction:

This experiment is designed to find the vapor pressure of water at temperatures between 50°C and 80°C. A graph of the logarithm of vapor pressure versus the reciprocal of absolute temperature 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 80°C, 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 lower temperature. The temperature and volume are recorded every 5°C between 80°C and 50°C.

The moles of air in the cylinder can be found by using the volume of dry air present at the temperature near 0°C 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 Clausius­Clapeyron equation is a mathematical expression relating the variation of vapor pressure to the temperature of a liquid. It can be written

Ln P = ­ΔHvap + C

R T

where ln P is the natural logarithm of the water vapor pressure, ΔHvap is the enthalpy of vaporization of water, R is the gas constant (8.314 J/mol-K), T in the Kelvin temperature 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 ln P, x is equal to 1/T, and the slope, m, equals ­ΔHvap.

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

Materials:

Thermometer

Beaker, 1-L, tall form

Graduated cylinder, 10-mL

hot-plate (orBunsen burner with ring stand, ring, wire gauze)

tap water

Procedure:

  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 tall-form beaker half filled with water. Add water to the beaker until the water level extends above the cylinder.
  2. 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.
  3. Heat the assembly until the temperature is about 80°C. The air inside the cylinder should not expand beyond the scale on the cylinder. If it does, remove the cylinder, using 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 with the thermometer to ensure an even distribution of heat. While you are waiting for the water to heat, complete the pre-lab activity below.
  4. Cool the beaker (continue stirring) until the temperature reaches 50°C. Record the temperature and volume of gas in the cylinder every 5°C. You may add some ice or ice water to the beaker to speed up the cooling, but try to keep the volume of water in the beaker about the same.
  5. After the temperature has reached 50°C, cool the beaker rapidly to about 0°C by adding ice. Record the gas volume and temperature at this low temperature.
  6. Record the barometric pressure in mmHg

Preliminary Lab Assignment (to be completed while waiting for the water to boil):

1. A graduated cylinder containing some air is immersed in water as shown. The height between the water surface and the top of the water inside the graduated cylinder is 106 mm. Calculate the correction that must be added to the barometric pressure to find the total pressure of gases in the cylinder.

2. The following experimental values are for ethanol.

Temperature (°C) / Vapor Pressure (mmHg) / Temperature (K) / 1/K / Ln Pvap
10.0 / 23.8
15.0 / 32.0
20.0 / 44.1
25.0 / 59.0
30.0 / 78.6

Graph the data as shown in the experimental directions.

Label the axes; draw the best straight line plot.

Calculate the value for ΔHvap.

Data and 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.
  1. 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 is the pressure exerted by 1.00 mmHg, which 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 throughout 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

  1. 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.
  1. Calculate the vapor pressure of water at each temperature.

Pwater = Pcylinder ­ Pair

T (°C) / T (K) / V (mL) / Corrected
V (mL) / Pair
(mmHg) / Pwater
(mmHg) / Ln Pwater / 1/K
(K­1)
  1. Plot ln P on the vertical axis. Draw the best-fit line and determine the slope of the line; calculate the value of ΔHvap of water. Compare to the reported value for the enthalpy of vaporization of water by calculating % error.

Questions:

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

1