This Week’s Experiment: Vapor Pressure of a Pure · Vapor Pressure of a Pure Liquid David Robinson [email protected] Office Hours: Wednesday 11 am or by Appointment Beaupre 350

This Week’s Experiment: Vapor Pressure of a Pure

LiquidDavid Robinson

[email protected] Hours: Wednesday 11 am

or by AppointmentBeaupre 350

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Objective

● Measure how vapor pressure changes with temperature

● Use the data to determine the molar heat of vaporization of water

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Theory: Vapor Pressure

● Vapor Pressure: The pressure of a vapor which is in contact with its solid or liquid form

● Equilibrium Vapor Pressure: the pressure of a vapor which is in equilibrium with its’ condensed form. Independent of quantity.

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Consider the equilibrium of a substance between its’ liquid and vapor phases,

X(l) ↔ X(g) (p,T) (1)

which has the relationship between pressure (p) and temperature (T) at equilibrium:

where ΔS and ΔV are the change in entropy and volume for the process, at constant T and p

Clapeyron Equation

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(2)

Clapeyron Equation

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● Since the change in state in (1) is isothermal, ΔG equals zero; therefore, a substitution can be made:

● (3) is known as the Clapeyron Equation, which is an exact expression that may be applied to phase equilibria of all kinds, but is currently presented here to be the one-component liquid-vapor case

● Notice that volume must, intuitively, increase with temperature

(3)

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Heat of Vaporization (ΔH𝑣)For vapor pressures less than 1 atm, we can assume molar volume of the liquid phase is negligible compared to the gaseous (Vl << Vg), so that ΔV = Vg- Vl = ~Vg:

(4)

● Behavior of gasses includes a compressibility factor “Z”. Correction which describes the deviation of behavior from ideal gas

● Conveniently, for an ideal gas Z = 1

PV=nRTZ

● The Compressibility Factor (Z) (for n = 1) is defined as:

Compressibility factor (Z)

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(5)

● Since dp/p = d ln(p), and dT/T2 = -d(1/T), we can simplify this result to (6), the Clausius-Clapeyron equation:

Clausius-Clapeyron Equation

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(6)

(4)

Figure 1. The compressibility factor, Z as a function of reduced Temperature, Tr (Tr = T/Tc)

(pg. 87)

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Boiling Point Method

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Boiling Point Method1. Fill the round bottom flask 1/3 with distilled

water and boiling chips2. Correctly position the thermometer such that

the bulb is even with the top of the round bottom flask

3. Turn on the water for the condenser, make sure it is draining into the sink

4. Close the stopcock on the trap. Using the vacuum, evacuate the system until a steady reading is reached (about 840 mbar)

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5. Check for leaks by turning off the vacuum and checking the pressure for ~5 min. If the pressure changes by ≥ 10 mbar, release the pressure using the stopcock and check connections

6. Once leak free, heat liquid to a steady boil (turn to 60-80 on variastat, then 30)

7. Record the Barometric Pressure (mbar)8. Allow pressure and temperature to

equilibrate, take measurements every 30 seconds until ± 0.1 oC and ± 5 mbar

Boiling Point Method

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Boiling Point Method9. Take 10 readings starting with the increasing cycle first,

then 10 readings with the decreasing cyclePressure Increasing (Manometer Reading):

850, 700, 550, 400, 250, 100 mbarPressure Decreasing (Manometer Reading):

175, 325, 475, 625, 775 mbar10. Repeat process 1 additional time11. For the highest and lowest pressures, record the

pressure and temperature every 30 seconds 10 times, for each other pressure, record the temperature and pressure every 30 seconds until within 0.1 oC and 2 mbar

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Method Notes

● Wear goggles at all times, the evacuated glassware can implode

● Always have the hood glass lowered

● Be careful when adjusting pressure, do not touch the round bottom flask

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Calculations

1. Estimate Z for the saturated vapor at the appropriate temperature using Figure 1

2. Calculate the average pressure and temperature for the highest/lowest pressures recorded

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Calculations3. Convert all Celsius temperatures to Kelvin

Calculate pressure as (Barometric pressure - manometer reading)

Plot ln(P) versus 1/T, excluding data before each plateau in temperature.

Draw linear trendline

4. Calculate the slope from your plot to obtain ΔH𝑣/RZ , and calculate ΔH𝑣 in J/mol

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Error Propagation1. Calculate error in ln(P) and 1/T for the first and last

points of the plot. Draw error boxes for these points.

2. Estimate the error in the slope of the trendline by using the “limiting slope method”

3. Estimate the error in Z by visual inspection

4. Propagate the errors to obtain the error in ΔH𝑣

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Lab Report1. Cover Page: Title of Experiment, Your Name, Your Partner’s Name,

Group Letter

2. Abstract: Single paragraph summarizing the experiment with your experimental heat of vaporization and error result

3. Introduction: Discussion of the purpose of the lab

4. Theory: FULL DERIVATION of Clausius-Clapeyron equation (starts on slide 4), in your own words so there is no disputing your understanding of the material.Describe the compressibility factor Z and where it originates (why is it included in the equation and how is it included?)

5. Procedure: Completed before class and signed

6. Data: Signed before leaving the lab

7. Graphical Analysis: Plot of ln(P) vs 1/T with error bars where necessary18

Lab Report Continued8. Calculations: #1-4 from the presentation

9. Error Analysis: #1-4

10. Discussion & Conclusion: Compare your results with literature values. Use your experimentally determined ΔH𝑣 to calculate ΔSv and compare the results to Trouton’s Rule, explain any differences. (Note: Cite your sources)

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