Purpose:
The purpose of this lab is to determine the vapor pressure of water
using the Clausius-Clapeyron equation.
Background:
A sample of air is trapped in an inverted 10mL 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 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. When the beaker is cooled with ice to a
temperature close to 0◦C, 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 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 Clausius-Clapeyron equation is a mathematical expression
relating the variation of vapor pressure to the temperature of a liquid:
ln(P) = -(∆Hvap/RT) + C
where ln(P) is the natural logarithm of the water vapor pressure, ∆Hvap
is the enthalpy of vaporization of water, R is the gas constant (8.314 J/mol·K),
T is the temperature in Kelvins, 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
-∆Hvap/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.
Materials
 Tall beaker
 10mL graduated cylinder
 Ring stand
 Wire gauze
 Hot plate
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Thermometer (0.1◦C)
Beaker tongs
Tub filled with ice
Ice cream salt
Safety Precautions:
There are no particular hazards in this lab except for the care need in
handling the beaker of hot water. Wear chemical splash goggles, and a
chemical-resistant apron.
Procedure:
1) Record the outside barometric pressure in mmHg at the start of the lab.
2) Fill a 10mL graduated cylinder about 2/3 full of water, close the top with a
finger, and quickly invert and lower the graduated cylinder into a tall beaker
half filled with water.
3) Add water to the beaker until the water level extends above the cylinder.
4) Use a ruler to measure the difference in height (in mm) between the top of the
water in the beaker and the top of the water in the cylinder, h.
5) Heat the beaker to about 80◦C, being sure to continuously stir the water in
the beaker to ensure an even distribution of heat. The air trapped inside
the graduated cylinder should not expand beyond the scale on the
cylinder. If it does, remove the graduated cylinder (using tongs), and
start again with a smaller initial volume of air. Record the temperature
and the volume of air in the cylinder.
6) Cool the beaker (continue stirring) until the temperature reaches 50◦C,
recording the temperature and volume of air in the cylinder every 5◦C.
7) After the temperature of the beaker reaches 50◦C, rapidly cool it to near
0◦C by transporting the beaker to the tub of ice and surrounding the
beaker with a mound of ice. Measure and record the volume of air and
temperature at this low temperature.
Lab Questions:
1) What is vapor pressure and why does it change with temperature?
Vapor pressure is the pressure exerted by a liquid’s vapor. As
the temperature rises, the kinetic energy of molecules increases, which
means that molecules are moving more and more rapidly. Thus, the
pressure of the vapor phase increases.
2) What is enthalpy of vaporization?
Enthalpy of vaporization is the heat required to cause one mole
of a substance to change from the liquid phase to the gas phase.
3) The assumption was made that the vapor pressure of water is negligible
at a temperature lose to zero. Find the actual vapor pressure of water at
your low temperature and comment of the validity of the assumption.
The vapor pressure of water at 7.8C was 7.7 mmHg. This is a
small percentage of most of the values recorded, so the assumption is
valid.
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.
It requires a depth of 13.6 mm of water to change the pressure
of the gas by 1 mmHg. Since the atmospheric pressure was 763 mmHg,
the relative effect on the atmospheric pressure is extremely small.
5) Were your data values close to a straight line graph?
The values were close to a straight line, linear regression.
6) Write out the long “two-point” form of the Clausis-Clapeyron equation.
Why does the graphical method of analysis give a better value for the
enthalpy of vaporization than does this form of the equation using two
temperature-vapor pressure values?
lnP = (-Hvap / (RT)) + C
The graphical analysis averages a larger number of values, thus
resulting in a more accurate answer.
Conclusion:
The vapor pressure of water at temperatures between 50C and 80C
ranges from 74.626 mmHg to 412.89 mmHg, respectively. By using the ClausiusClapeyron equation and a graphical analysis of the data, the natural log of the
water pressure and the reciprocal of the temperature of the water are found, and
can then be used to calculate the enthalpy of vaporization of the water. A graph
of the logarithm of vapor pressures versus the reciprocal of absolute
temperature allows the calculation of the enthalpy of vaporization, or Hvap of
H2O.
Sources of Error
As was mentioned above, some error was due to the assumptions made, which
amounted to less than a percent for 0mmHg as the partial pressure at 0_C (which
could compound and be more or less of an error later on, though) and an unknown
amount for letting h be constant. Another source of error was that we did not use
distilled water for the experiment. The dissolved ions would have lowered the
measured partial pressure of the water. For the calculations, a (hopefully) small error
could have arisen due to rounding
after every step to 3 or 4 significant figures (depending on the numbers in the
equations). Finally, Steven could have been a source of error because he kept taking a
little water out of the beaker to boil on the hot plate. This would change the pressure
the water exerts on the air and could skew the volume measurements.
Observations:
The higher the temperature of the water got, the higher the amount of air
in the graduated cylinder got. Conversely, the lower the temperature of water,
the lower the amount of air in the graduated cylinder. At one point, when the
temperature was rather high, the graduated cylinder floated around in the
beaker, still maintaining the amount of air in the cylinder.