Purpose

To examine the properties of a sample of a non-ideal gas.

Expected Learning Outcomes

Through this experiment, students will be expected to be able to

• Use the ideal gas law and van der Waals equation to characterize properties of a gas
• Evaluate the assumptions behind different derived values.
• Evaluate the appropriateness of different scientific models for problem-solving.

Textbook Reference

Tro, Chemistry: Structure and Properties, 2nd Ed., Ch. 6.8 and 6.10.

Introduction

It can be shown that many gases under common conditions can be described by the ideal gas law

[latex]pV=nRT[/latex]

where p is the pressure (in atm), V is the volume of the gas (in L), n is the number of moles of gas, and T is the temperature (in Kelvins).^[1] In this case, we find that R, the ideal gas constant, has the value 0.08206 L.atm/mol.K.

In this experiment, you will vaporize an organic liquid in an Erlenmeyer flask, and measure the temperature and pressure of the gas. In addition, you will determine the mass of the organic liquid present.

However, as you may recall from Tro, Chemistry: Structure and Properties, 2nd Ed., Ch. 11.2, a liquid would have similar amounts of kinetic energy as their intermolecular forces. Therefore, the liquids you vaporize have significant intermolecular forces that are neglected in kinetic molecular theory (as described in Tro, Chemistry: Structure and Properties, Ch. 11.7, which are not accounted for in the ideal gas law.  In addition, in kinetic molecular theory the gas molecules are assumed to have negligible volume, which is not always a valid assumption.

To correct for these problems, we sometimes use the van der Waals equation:

[latex]\left(p + \frac{n^2a}{V^2}\right)(V-nb) = nRT[/latex]

where you will see two correction terms:

• The a term modifies the pressure and accounts for the presence of intermolecular forces.
• The b term modifies the volume, adjusting for the fact that one molecule cannot access the volume occupied by another molecule (the excluded volume).

In this experiment, you will estimate the b value using the published density of the liquid state of the organic compound by assuming that the molecules are perfectly packed together (with no empty space between molecules) in the liquid phase.  You can then solve the van der Waals equation to find the value of $a$, and then compare your results to those reported in the literature.

Procedures

Hints and Safety Rules

• You may be asked to do Part B before Part A in order to ensure that everyone has access to the fume hood.  This will not affect your experimental results.
  Part C can be done whenever you have a spare moment.
• The same Erlenmeyer flask must be used throughout the experiment. To hold the hot Erlenmeyer flask, clamp the neck of the Erlenmeyer flask (using a standard ring stand clamp) while holding the bottom using a cloth towel.
• This experiment should be done individually.
• Each student will be assigned a different liquid to study.

Special Equipment Needed

• Aluminum foil
• Digital thermometers (placed in hot water baths)
• Medicine dropper
• 500 mL graduated cylinder
• Hot water baths.
• Stand and clamp
• One computer with Vernier pressure sensor (for the class).
• Cloth towel.

Chemicals Needed

• Acetone: 10 mL
• Assigned Liquid: approximately 15 mL

Part A: Determining the Mass of Gas Present

Each student will be assigned an organic liquid to study.

1. Ensure that your Erlenmeyer flask is clean; wash with soap and water (and dry with paper towels) if not.
2. Clean your 250 mL Erlenmeyer flask with a small amount (5 mL) acetone. Allow the contents to dry until there is no residue.
   The primary purpose of rinsing with acetone is to remove any stray water.  Therefore, we swirl with a very small volume of acetone, making sure that it goes over all of the surface of the flask.
3. Trim a piece of aluminum foil to cover the Erlenmeyer flask. Put a rubber band around the neck of the Erlenmeyer flask, and punch a small needle hold on top of the foil.
4. Determine the mass of your empty Erlenmeyer flask, rubber band and tin foil.
5. Remove the tin foil and rubber band. Using a medicine dropper, place about 2 mL of the assigned organic liquid into the Erlenmeyer flask. Replace the tin foil and rubber band.
6. Clamp the Erlenmeyer flask in one of the hot water baths in the fume hood, being sure to submerge it as completely as possible into the water bath.
7. Allow all of the organic liquid to evaporate completely from the Erlenmeyer flask, including the pinhole. When all of the liquid has vaporized (driving out all of the air from your Erlenmeyer flask), record the temperature of the hot water bath and remove the Erlenmeyer flask from the water bath.
8. Allow the Erlenmeyer flask to air cool. You can finish it off by using cold water when the Erlenmeyer flask is cool enough to touch directly.
9. Dry the outside of the Erlenmeyer flask with a towel and weigh the flask with the aluminum foil attached to it.

10. Repeat this procedure (steps 5-9) one more time.  Note that you need not re-clean the flask.  You will use the mass of the empty flask you recorded at the beginning for both trials.

Part B: Determining the Volume of the Erlenmeyer Flask

1. Clean the Erlenmeyer flask with soap and water.
2. Fill the Erlenmeyer flask with water.
3. Pour the water into a 500 mL graduated cylinder^[2] and measure the volume of the water. This is the volume of the Erlenmeyer flask.
4. Repeat this procedure (steps 1-3) one more time.

Part C: Measuring the Atmospheric Pressure of the Room

1. Record the atmospheric pressure in the room from the pressure sensor provided.

Waste Disposal

All organic liquids should be collected and disposed of in the waste beaker.

Data Analysis

We will explore the deviation between the ideal gas and your organic vapor in two ways.

Using the Ideal Gas Law

We will use the ideal gas law to determine the molar mass of the gas in the sample, and compare this with the accepted molar mass of the sample (using relative atomic masses and the formula of the compound).

Recall that the molar mass is the mass per mole:

[latex]\mbox{molar mass} = \frac{\mbox{mass of sample (g)}}{\mbox{moles of sample}}[/latex]

The mass of the sample was determined in Part A of the experiment. The number of moles of sample can be determined by rearranging the ideal gas law

[latex]n = \frac{pV}{RT}[/latex]

where V is the volume (in L) of the Erlenmeyer flask you determined in part B of the experiment.

This can then be substituted back into the definition of molar mass to obtain a calculated value of the molar mass.

You can then compare this to the actual molar mass given the compound. The deviation between the molar mass and the actual mass can be used as a crude measure of the non-ideality of the vapor.

Using the van der Waals equation

Another way of analyzing the non-ideality of the gas is to use the van der Waals equation and estimate (using your data) values of the a and b parameters.

[latex]\left(p + \frac{n^2a}{V^2}\right)(V-nb) = nRT[/latex]

Estimating b from the Liquid Density

While we have no explicit way of measuring b, it is more instructive to estimate b from the density of the liquid by assuming that the liquid phase contains the molecules completely packed together.  The liquid density will be given to you on the electronic (MyOpenMath) report form.

Using this approximation, you can show that the b (in L/mol) is

[latex]b \approx \frac{1}{1000} \times \frac{\mathcal{M}}{d}[/latex]

where d is the density of the liquid (in g/mL) and [latex]\mathcal{M}[/latex] is the molar mass of the liquid (in g/mol).  The factor of 1000 takes into account unit conversions required for this problem.

Estimating a from the Experimental Data

It can be shown that the van der Waals equation can be rearranged such that

[latex]a = \left(\frac{V}{n}\right)^2 \left(\frac{nRT}{V-nb} - p\right)[/latex]

In this equation, we use the values from Trial 1 of Part A.  For that trial, you will need to calculate n using the mass of sample and the accepted molar mass.  The value of b is based on the part above.