Download CH 105 -- TAKE-HOME LAB The Vapor Pressure and Heat of

CH 105 -- TAKE-HOME LAB
The Vapor Pressure and Heat of Vaporization of Water
Purpose:
• To determine the values of vapor pressure and heat of vaporization for water from a
graph of experimental data.
• To use higher order variables and numbers in applying the point/slope formula.
Theory:
1) PV
=
2) Ptotal
3) Y
nRT
=
(Ideal Gas Equation)
Pair + PH2O
=
(m)
4) ln P =
5)
m =
(Dalton’s Law of Partial Press.)
(X)
+b
(Point/slope formula)
-∆H°vap
1
+ b
(Clausius/Clapeyron Equation)
R
T
-∆H°vap
R
6)
-∆H°vap
=
mxR
The Heat of Vaporization ( ∆H vap ) is the amount of energy required to change a substance from a
liquid to a vapor. The ∆H vap value for water is very large at 540 calories per gram. This number explains
why perspiration is such a good coolant for the body. Each single gram of water that evaporates removes
almost three times more heat than ethanol (200 cal/g) would even though alcohols evaporate faster than
water.
Vapor pressure and Heat of Vaporization are physical constants that are characteristic for a pure
substance, such as water. Two scientists, Clausius and Clapeyron, discovered a relationship between vapor
pressure and the heat of vaporization that is expressed in equation #4, above.
Equation #4 uses these changes in the point slope formula in equation #3.
• The variable ( y ) has been replaced by the natural log of the vapor pressure, ( ln P )
• The variable ( x) has been replaced by (1/T ) .
• The slope, ( m ) = the heat of vaporization divided by the gas constant R.
Thus you can calculate the heat of vaporization by multiplying the slope by a value of R. (Eq. #6)
Lab Scenario:
A large 2-liter beaker is filled with water.
A smaller 10-mL graduated cylinder is filled with
about 7 mL of deionized water and quickly inverted
into the 2-liter beaker, trapping a bubble of air, as
shown in the accompanying drawing.
The set up is then placed on a ring stand and
heated with a bunsen burner until the water temperature reaches 80o C. The heat is then removed and the
system is allowed to cool to room temperature. As it
does so, the student records the volume of the bubble
and the temperature of the water at approximately
5 o intervals.
Air
bubble
The data is as follows:
Temp (o C):
79.0
74.5
70.5
65.0
vol (mL)
9.8
8.7
8.0
7.1
At this point, the student adds enough ice to cool the temperature of the water to 4o C. The temperature
and the volume of the bubble are again recorded.
Temp: 3.7o C
vol: 4.7 mL
P atm = 761 mmHg
The student gets the instructor to initial the data sheet, cleans up, and goes home.
Analysis. Before the data can be graphed, some number crunching will be necessary.
1. Notice that the volume of the air bubble had to be read on an inverted scale because the 10mL
graduated cylinder was floating upside down. Correct each of the volume readings by subtracting 0.2 mL in
order to compensate for the inverted meniscus.
2. When the water temperature is close to the freezing point (0o -4o C), the vapor pressure is close to 0.0 mm
Hg. At this point, the bubble contains dry air. Calculate the number of moles of the dry air by using
PV =nRT , using the volume and temperature readings from the chilled air sample at or near 4.0o C.
3. For each temperature/volume data point, calculate the pressure of the dry air in the bubble using the
ideal gas equation, (PV=nRT). Convert temperature to Kelvin, convert volume to liters, and use “n” from #2
above for the number of moles. (n, and R will be the same in each calculation. )
4. Notice that for each data point in #3, the pressure is less than the atmospheric pressure measured
during the experiment. We can assume that the difference in the pressure is due to the water vapor
pressure at that temperature., since according to Dalton’s Law of Partial Pressure,
P atm = Pair + PH2O.
At each temperature, calculate the vapor pressure of water ( PH2O ) by subtracting the partial pressure of
dry air from the atmospheric pressure as recorded in the lab.
5. Take the natural log of each water vapor pressure value.
6. Calculate 1/T for each of the temperature values after converting to Kelvin.
7. Bring the results from (#5) , and (#6) as to the instructor who will show you how to plot a graph using the
computer program in lab. (Note: do NOT graph the point at 4o C)
or
Use your own program to graph lnP on the y-axis, and 1/T on the x-axis.
8. The program will produce a value for (m), the slope of the best fit line through the points.
9.
According to equation (4) from the theory, the slope is equal to:
-∆H°vap = m = [Your calculated value]
R
You must now multiply both sides of this equation by “R” to get a value for the heat of vaporization for
water.
-∆H°vap
=
mxR
Since we want our value to have the units of energy, we have to use the following values for R:
R = 8.314 J/mol-K
to get the answer in Joules
R = 1.9872 cal/mol-k to get the answer in calories
Calculate both values for -∆H°vap. For our purposes report the absolute value of the calculation.
Questions:
1.
Define heat of vaporization. Define vapor pressure.
2. Write out the Clausius-Clapeyron Equation and label the factors that correspond to the factors in the
point-slope formula. State directly what the slope of the graph represents.
3. How is it possible for the Ideal Gas Constant to have different values?
4. The molecular weights of water and methane are quite close. The heat of vaporization of water is nearly
five times that of methane. What property of the water molecule would account for this discrepancy? Explain
briefly.
5. Obtain the value for the heat of vaporization of water from your text. Calculate the % error for your
experimental ∆Hvap value using the following equation.
% error = Theoretical value - Experimental value x 100%
Theoretical value
6. The vapor pressure of water at 75o C is 294.4 torr. Calculate the % error for your value of the water
vapor pressure at 75o C using the value found in the text as the theoretical value.
Summary and Conclusion:
Be sure your results are presented in an organized table.
Use your statement of purpose as an outline for your Conclusion.
Remember to relate the lab to daily life.
Suggested format for your results table:
P atm =
n (air) =
T (oC)
T(K)
1/T
Corrected
Bubble Bubble Vol Bubble Vol
vol (mL) (mL)
(liters)
79.0
9.8
74.5
8.7
70.5
8.0
65.0
7.1
P (Dry air)
P H2O
ln P