Expt HV
1
Heat of Vaporization (HV)
Objective
The purpose of this experiment is to determine the heat of vaporization of methanol.
Background
In this experiment, you will investigate the relationship between the vapor pressure of a
liquid and its temperature. When a liquid is added to an Erlenmeyer flask, it will evaporate into
the air above it in the flask. Eventually, equilibrium is reached between the rate of evaporation
and the rate of condensation. At this point, the vapor pressure of the liquid is equal to the partial
pressure of its vapor in the flask. Pressure and temperature data will be collected using a Pressure
Sensor and a Temperature Probe. Liquid will be placed in a flask and heated to boiling in a water
bath (water will not be boiling) to allow the vapor to fill the flask and displace any air. The flask
will be sealed and the temperature varied. As the water bath temperature is varied, the
temperature of the liquid is varied and the effect of temperature on vapor pressure is observed.
Pairs of temperature and pressure data are collected.
Caution
Methanol is flammable and poisonous.
Theory
As shown in your Physical Chemistry textbook, it is possible by setting the change in
chemical potential of two phases equal to each other dµA = dµB to derive the equation
dp/dT = ∆S/∆V
(1)
where dp is the change in pressure and dT is the change in temperature along a phase diagram
line separating two phases (A and B). ∆S is the entropy difference and ∆V is the volume
difference between one mole of two phases. Eq. (1) can be modified since ∆S = ∆H/T to give
dp/dT = ∆H / ( T ∆V)
(2)
Expt HV
2
where ∆H is the molar enthalpy change associated with a phase change between the two phases.
Either Eq. (1) or (2) above may be referred to as the Clapeyron Equation.
In the special case of liquid and vapor equilibrium, ∆H is ∆Hvap the heat of vaporization and
T is the boiling point which depends on the external pressure. ∆Vm, the change in volume per
one mole of gas, is given by Vm – Vm,liq where Vm is the volume of one mole of the gas (molar
volume) and Vm,liq is the volume of one mole of the liquid. To a very good approximation ∆Vm
may be given by Vm since the gas volume is so much greater than the volume of an equivalent
amount of liquid. Therefore, since for a mole a gas n = 1 then
pV=nRT
(3)
becomes
p Vm = RT
(4)
and Eq. (2) becomes
dp/dT = ∆Hvap / ( T Vm ).
(5)
Eq. (4) may be rewritten as
Vm = RT / p
(6)
and substituting Eq. (6) into Eq. (5) gives
dp/dT = ∆Hvap / ( R T2 / p ).
Rearranging Eq. (7) gives
dp/dT = p (∆Hvap / R T2 )
or
(7)
Expt HV
dp/p = ( ∆Hvap / R T2) T –2 dT
3
(8)
Integrating both sides of the equation above where the heat of vaporization is assumed to be
constant
∫ p–1 dp = ∫ (∆Hvap/R) T–2 dT
(9)
ln p = (∆Hvap/R) ( – T –1 ) + B
(10)
gives
where B represents some positive constant. Eq. (10) can be written as
ln p = – (∆Hvap/R) ( 1/T ) + B
(11)
Notice that a plot of ln p (y axis) versus 1/T (x axis) the above equation gives a slope equal to
Slope = – (∆Hvap/R)
(12)
And thus we can determine the heat of vaporization.
To determine the units of a slope you need to look at the units of the rise over the run (∆y/∆x)
which is based on ln p versus 1/T where the temperature must be in units of kelvin. Logarithms
are always unitless so this becomes
∆y/∆x = 1/ (1/ K) = K
A comparison to the value from (∆Hvap/R) gives
(∆Hvap/R) = (J/mol)/ (J/mol K) = K
so therefore the units are correct. YOU MUST ALWAYS CHECK UNITS IN ANY
CALCULATION! DO NOT ASSUME THE UNITS WORKOUT CORRECTLY. For example,
Expt HV
4
in the above calculation if you used the R value 0.08206 (L atm/ mol K), the units would not
work and this would tell you that you had made a mistake in your choice of R.
We are ignoring some more detailed aspects of the theory and analysis by assuming that we
are dealing with an ideal gas and that ∆Hvap is constant over a range of temperature. For a real
gas
pVm = z R T
(13)
where z is the compressibility. For extremely low pressures, z is close to 1 and you have ideal
gas behavior. For moderate pressures, z is slightly less than 1. As temperature is increased. both
z and ∆Hvap tend to decrease so the ratio of these tends to remain constant. To simplify your
calculations, we are assuming z =1 (methanol vapor is acting like an ideal gas) and ∆Hvap is
invariant with temperature. These assumptions are one source of error in your experiment.
Procedure
1. Prepare the Temperature Probe and Pressure Sensor for data collection.
a. The Pressure Sensor should to Channel 1 of the interface device.
b. The Temperature Probe should be connected to Channel 2.
c. Locate the rubber-stopper assembly and the piece of heavy-wall plastic tubing connected
to one of its two valves. Attach the connector at the free end of the
plastic tubing to the open stem of the Pressure Sensor with a
clockwise turn. Leave its two-way valve on the rubber stopper
2
2
open (lined up with the valve stem as shown in Figure 1) until
later.
Figure 1
3. Prepare for data collection for data collection on electronic device. The vertical axis may
have pressure scaled from 90 to 135 kPa. The horizontal axis will need to have temperature
scaled to fit the data range you collect.
4. The temperature and pressure readings should be displayed in the Meter Window. Record
the value for atmospheric pressure in your lab notebook (round to the nearest 0.1 kPa).
Record the barometric pressure using the mercury manometer or pressure gauge on the wall
Expt HV
5
(ask your instructor for directions to use) and convert to kPa. Is your electronic reading
close? Record the room temperature on the wall thermometer and compare to your electronic
reading. Are the two temperatures close? Make sure the pressure and temperature are
reasonable values for the room before continuing.
5. Set up the apparatus shown in Figure 2. Place about 10mL of methanol into the 125mL
Erlenmeyer flask. Add about 10 to 15 boiling chips to flask. Place the large liter beaker on
the heater/stirrer. Place stir bar in beaker and partially fill with water. Clamp flask as low as
it can go into beaker and place and clamp temperature probe into water next to flask. Fill
with water to top of beaker. The mouth of the flask will be above the water. Set stir on
maximum or close to maximum.
Figure 2
Temperature Sensor
Pressure Sensor
Methanol with boiling chips
Water
Stir bar
Heater/Stirrer
Expt HV
6.
6
Turn on heater and heat water (always with stir bar stirring) until you observe the methanol
begin to boil. When methanol boiling starts (the water itself will be hot but not boiling) turn
off the heat and let the methanol continue to boil for about 90 seconds to completely fill flask
with vapor and displace all the air initially present. Let the water temperature rise to between
70 to 75oC but not above 75oC. Securely insert rubber-stopper assembly (with heavy-wall
plastic tubing leading to pressure sensor) into the 125mL flask. Twist the stopper into the
neck of the flask to ensure a tight fit.
After about 30 seconds, close the 2-way valve above the rubber stopper
closed
open
as shown in Figure 3—do this by turning the white valve handle so it
is perpendicular with the valve stem itself.
2
2
2
Figure 3
7. At this point the flask and stopper are a closed system so it is important to not go too
high or too low in pressure so flask will not break. Range of temperature should be 55
to 75oC and pressure between about 50 to 140 kPa.
8. Monitor and collect pressure and temperature data: When the pressure and temperature
readings displayed in the Meter window stabilize, equilibrium between methanol liquid and
vapor has been established. Record this first pressure-temperature data pair is now stored.
9. To collect another data pair at lower temperature use large syringe to remove about 30 mL
(more or less as needed) of hot water from bath and replace with cooler water. The objective
is to lower the temperature by about 2 or 3 degrees for each new reading so you end up with
about 7 or more readings to span a 20 degree temperature range. As you remove the hot
water, place into a beaker so you can use if needed to raise the temperature. You need a
range of temperatures but they don't have to be exactly the same increment each time. Wait
long enough so that the temperature and pressure are holding steady before you collect the
second data pair.
10. Repeat the above steps collecting at least 7 data point pairs (T and P) in the temperature
range no higher than 75oC and no lower than 55oC. It is important to watch the pressure
2
Expt HV
7
range. When the flask is sealed with stopper, you do not want to let the pressure go above
about 140kPa or below 55kPa. Since the flask is sealed, we do not want to go to a pressure
too high or too low that might cause the flask to break.
11. Sometimes data may be lost. To err on the side of caution, as data is collected, you should
also record values by hand in your lab notebook.
12. Open the side valve of the Pressure Sensor so the Erlenmeyer flask is open to the atmosphere.
Remove the stopper assembly from the flask and dispose of the methanol into PCHEM
hazardous waste bottle in the hood. Boiling chips should be discarded in paper towel in trash.
13. When you are finished, use "Shut Down" to turn off the computer, and clean up your work
area.
Calculations
In your EXCEL spreadsheet create columns with p(kPa), T(oC), T(K), ln p, 1/T values and a plot
with linear regression.
1. Celsius temperatures must be converted to Kelvin (K) prior to analysis.
2. The Clausius-Clapeyron equation describes the relationship between vapor pressure and
temperature:
ln P = – ΔHvap / RT + B
where ln P is the natural logarithm of the vapor pressure, ΔHvap is the heat of vaporization,
T is the absolute temperature, and B is a positive constant. If this equation is rearranged in
slope-intercept form (y = mx + b):
1
ln P = (– ΔHvap / R ) • T + B
the slope, m, should be equal to -ΔHvap / R. If a plot of ln P vs. 1/T is made, the heat of
vaporization can be determined from the slope of the curve.
3. Create new columns to generate ln P and 1/T values.
Expt HV
8
4. Plot ln P versus 1/T using EXCEL and perform a linear regression least squares fit. Leave
out highest temperature value (first data point collected) so that the temperature range is not
too broad. The heat of vaporization is a function of temperature so it is best to not consider
too broad a temperature range.
5. Report slope, intercept, and r2 values and determine units for the slope, m, of the regression
line.
6. Use the slope value to calculate the heat of vaporization for methanol
m = -ΔHvap / R.
7. You report will include a data table and plot of ln(P) versus 1/T from which you will
calculate the heat of vaporization. Show calculation of heat of vaporization from slope. Note
that in your analysis you are assuming the solvent vapor follows ideal gas law behavior so
that z=1. Compare your ∆Hvap to that of the literature value of ∆Hvap of methanol at its
normal (1 atm) boiling point.