How does the ideal gas law help determine the molar mass of an unknown liquid?

The ideal gas law states that for a given pressure, temperature, and volume, the number of moles of gas is always the same. By vaporizing an unknown liquid in a Dumas tube, measuring its mass after condensation, and using the ideal gas law to calculate moles, you can divide the mass by moles to find molar mass. Since molar mass doesn't change with phase, the condensed liquid mass equals the vapor mass.

What is the purpose of immersing the Dumas tube in boiling water during this experiment?

Immersing the Dumas tube in boiling water vaporizes the unknown liquid inside. The vapor then equilibrates with its surroundings at the boiling water temperature and room pressure. After waiting 3–5 minutes for complete vaporization and an additional 3 minutes for equilibration, you remove the tube and allow it to cool so the vapor condenses back into liquid for mass measurement.

Why is it important to cool the Dumas tube to room temperature before measuring its final mass?

Cooling the tube to room temperature ensures the vapor fully condenses into liquid. If measured while still warm, residual heat could cause incomplete condensation or water droplets on the exterior to remain, adding unwanted mass. Allowing 2–3 minutes of cooling in ambient air and drying the outside with paper towels ensures an accurate mass measurement of only the condensed unknown liquid.

How do you determine the volume of the Dumas tube in this experiment?

You fill the Dumas tube completely with deionized water using a syringe, ensuring no air bubbles remain. After drying the outside, you weigh the water-filled tube and subtract the empty tube mass to find the water mass. Since water density is approximately 1 g/cm³, the mass in grams equals the volume in cubic centimeters, giving you the tube's volume for ideal gas law calculations.

What does the difference between calculated and theoretical gas constant values indicate?

After determining the actual molar mass of your unknown compound, you can recalculate the number of moles and solve for the gas constant using your experimental pressure, volume, and temperature. The difference between your calculated gas constant and the universal constant (8.314 × 10⁴ hPa·cm³/mol·K) represents the deviation from ideal gas behavior, showing how closely your unknown behaved as an ideal gas under the experimental conditions.

Why are multiple trials performed when measuring the mass of the unknown liquid?

Performing four trials allows you to calculate an average mass and standard deviation, which indicate the consistency and reliability of your results. By comparing individual trial masses and calculating standard deviation, you can assess measurement precision. The average mass is then used with the calculated moles to determine molar mass, and percent error is calculated by comparing your result to the literature value.

What safety precautions are necessary when working with the unknown liquid in this experiment?

The unknown liquids are volatile, toxic, and potentially flammable, so you must work in a fume hood and wear a lab coat, safety glasses, and two pairs of nitrile gloves. Keep the Dumas tube pointed away from yourself and others. Since acetone and unknowns rapidly permeate nitrile gloves, replace gloves if contaminated. Additionally, exercise caution around the Bunsen burner flame and hot water to prevent burns.

Ideal Gas Law

Concepts Instructor Prep Student Protocol

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A gas is simply a dispersed sample of matter that is fluid and expands freely to occupy available space. However, a certain number of gas molecules occupy a specific volume under a defined temperature and pressure. We can describe the behavior of a gas under these parameters using the ideal gas law, which uses the universal gas constant, R, to relate all of these variables.

The universal gas constant is equal to 8.314 joules per mole Kelvin. This equation enables us to understand state relationships in a gaseous system. For example, in a system of constant temperature and pressure, we know that the addition of more moles of gas results in an increase in volume. Similarly, we can look at a system of constant temperature and moles and see that a decrease in volume results in an increase in pressure.

One challenge is that the ideal gas law describes gases behaving ideally. So what do we mean by that? Ideal behavior assumes that first, the molecules themselves are infinitesimally small and essentially have no volume and that the distance between the molecules is significantly larger than the size of the individual molecule.

Second, we assume that the molecules are constantly in motion. Any collisions occurring between the molecules are elastic, and their motion is frictionless, meaning that the molecules do not lose energy. Finally, we assume that there are no intermolecular forces acting between the molecules and their surroundings.

Unfortunately, most gases do not behave ideally. At very low temperature or high pressure, molecules are very close together and slow-moving, so intermolecular interactions are significant. Similarly, gases with a high molecular weight experience increased interactions due to their large size and mass. However, the ideal gas relationship serves as a good approximation in general.

So how do we use the ideal gas law to study the behavior of a gas in the laboratory? Pressure, volume, and temperature are generally more easily measured, but how about moles, and by extension, mass?

One of the simplest ways to measure the mass of a gas is by the Dumas method. To perform this test, a small amount of a volatile compound in its liquid phase is placed inside a Dumas tube, and the tube is then placed in boiling water.

A volatile compound has a high vapor pressure at room temperature. The vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. Thus, a volatile compound with high vapor pressure transitions from liquid to gas rapidly.

When this happens, the newly formed gas forces the air out of the Dumas tube so that it is solely filled with gas. Once the tube is removed from the water bath and left at room temperature, the gas condenses to form a liquid again. Since mass is conserved, we know that the mass of the condensed liquid is equal to the mass of the gas that filled the known volume of the Dumas tube.

In this lab, you'll explore the ideal gas law by using the Dumas Method to determine the molar mass of an unknown volatile substance. You'll then measure the temperature, pressure, and volume of the system and see how much this gas deviates from ideality.

Print Procedure Steps

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Source: Smaa Koraym at Johns Hopkins University, MD, USA

Determining the Mass of the Unknown Liquid

According to the ideal gas law for a given pressure, temperature, and volume, the number of moles of gas in that volume is always the same. In this lab, you will use that relationship to calculate the molar mass of an unknown liquid. You will immerse a Dumas tube containing the unknown liquid in boiling water to vaporize the solvent. After waiting a few minutes for the vapor to equilibrate with its surroundings, you will let the vapor condense and then measure the mass of the liquid in the tube. Molar mass doesn't change with phase, so the mass of the condensed liquid is the same as the mass of the vapor.

The unknown liquids are volatile, toxic, and may be flammable, so you will work in a fume hood. Your instructor will dispense your assigned unknown into your Dumas tube for you. Always keep the Dumas tube pointed away from yourself and others. This section of the lab uses a Bunsen burner to boil water. Take care to keep your sleeves, hair, and the unknown liquid away from the flame and use caution when working around hot liquids, glass, and metal.

Before starting the lab, put on a lab coat, safety glasses, and two pairs of nitrile gloves. Note: Acetone and the unknown liquids rapidly permeate nitrile gloves, so get new gloves if you touch any of these liquids. Let the old gloves dry in the hood before throwing them out.
Connect one end of a piece of latex tubing to the barbed inlet of a Bunsen burner. Connect the other end of the tubing to the gas jet in your hood. Confirm that the collar at the base of the Bunsen burner is closed.
With the Bunsen burner on the base of the lab stand, fit a ring fixture onto the lab stand over the Bunsen burner and adjust the rings so that it is centered 2 inches above the flame. Tighten the clamp to fix the ring in position. Place a square of wire gauze on the ring to make a platform.
Then, clamp a 500-mL Erlenmeyer flask on the platform with a 3-prong clamp. Fix a thermometer clamp above the three-prong clamp and rotated away from the flask.
Once the clamps are in position, remove the Erlenmeyer flask. Place several boiling chips in the flask and fill it to the 500 mL mark with deionized water.
Fill a 400-mL beaker with deionized water. Clamp the filled flask back in place on the wire platform.
Obtain several paper towels. Tear one paper towel into strips about as wide as the length of the elongated neck of the Dumas tube. Note: Move the paper towels out of the way before you light the Bunsen burner.
Ensure that your fire striker is within easy reach. Then, open the gas jet, hold the striking end close to the top of the Bunsen burner, and rapidly squeeze the movable handle to strike a spark, which will ignite the gas.
Once you have lit the flame, turn the collar at the base of the barrel to increase the airflow, which will make the flame hotter. Turn the gas valve to increase the height of the flame to about 4 – 6 inches. Note: One student must remain at the workstation while the Bunsen burner is in use.
Place the Dumas tube in a clean 100-mL beaker and bring it to an analytical balance.
Tare the 250-mL plastic beaker. Use a laboratory wipe to remove traces of dust and oils from the entire surface of the tube.

Hold the clean tube in a fresh laboratory wipe and carefully transfer it to the plastic beaker. Record the mass of the empty Dumas tube in your lab notebook.

Table 1: Molar Mass of Unknown Liquid

Trial	Mass_{Dumas Tube} _{+ Unknown}	Mass_{Empty Dumas Tube}	Mass_Unknown
1
2
3
4
Average Mass_Unknown
Standard deviation

Pressure (hPa)
Temperature (ºC)
Temperature (K)
Mass_{tube filled with water} (g)
Mass_water (g)
Density_water(g/cm³)	1
Volume_gas (cm³)
Moles_gas (n)
Molar mass_unknown(g/mol)
Percent error (%)
Theoretical R (hPa·cm³/mol·K)	8.314 × 10⁴
Calculated R (hPa·cm³/mol·K)
Difference between theoretical and calculated R

Click Here to download Table 1

Use a laboratory wipe to transfer the tube back in your 100-mL beaker.
When your instructor calls you, bring the Dumas tube in the beaker to the designated dispensing hood where your instructor will add a small volume of the unknown to the tube.
Wrap the neck of the Dumas tube with paper towels to help maintain a constant temperature.
Once the water in the Erlenmeyer flask boils, secure the Dumas tube in the thermometer clamp. Carefully rotate the clamp so that the tube is lined up with the Erlenmeyer flask neck and slowly lower the clamp until the body of the Dumas tube is fully immersed in the boiling water. Note: Do not touch the flask.
Once the Dumas tube is in position, fix the thermometer clamp in place and note the time.
Now, wait for your unknown liquid to vaporize, which should take 3 – 5 minutes. Note: Top off the water in the flask whenever the water level goes down.
Once you can't see any liquid in the tube, note the time and wait another 3 minutes to let the vapor temperature and pressure equilibrate with its surroundings.
Raise the thermometer clamp to lift the Dumas tube from the boiling water. Rotate the clamp away from the flask so that the tube can cool in ambient air.
After 2 – 3 minutes, carefully dry the outside of the tube with paper towels. Note: The drops of water may still be hot.
Wait for the tube to cool to room temperature so that the vapor fully condenses. Once cooled, remove the tube from the clamp and dry any remaining traces of water on the tube before placing it in the 100-mL beaker. Note: Residual water will add mass.
Carry the beaker to a balance and clean the outside of the tube with a laboratory wipe. Measure the mass. Record this in your lab notebook as the post-trial one mass.
Perform three more trials in the same way. To find the mass of the remaining unknown after each trial, subtract the mass of the empty Dumas tube from each post-trial mass.
When you finish the 4th trial, turn off the gas to extinguish the Bunsen burner. Wait 5 minutes before disassembling the ring, gauze, and Bunsen burner from the ring stand.

Determining the Volume of the Dumas Tube
- Fill a 400-mL beaker with deionized water and obtain a few paper towels.
- Measure the temperature of the water and record the temperature in your lab notebook.
- At the instructor's hood, fill a 20-mL syringe with water from the beaker and connect a needle to the syringe.
- Carefully insert the needle into the Dumas tube and push the water into the tube. Note: Avoid forming air bubbles as all air must eventually be eliminated from the tube.
- Once the syringe is empty, remove the needle, refill the syringe with water, reconnect the syringe, and add the water to the tube. Repeat this process until the Dumas tube is full, with no visible air bubbles.
- Thoroughly dry the outside of the Dumas tube. Then, weigh the water-filled tube and subtract the mass of the empty tube to find the mass of the water.
- Record the air pressure in the room from the lab barometer.
- Connect the barbed side arm of the Büchner flask to the vacuum pump or house vacuum using silicone tubing.
- Clamp the filter flask upright in the hood. Insert a single hole stopper with a tubing adapter into the mouth of the Büchner flask and fit one end of a piece of latex tubing over the adapter. Fit the other end of the latex tubing over the elongated end of the Dumas tube.
- Use the thermometer clamp to hold the Dumas tube upside down, then open the vacuum line to rapidly drain the water into the filter flask. Once the Dumas tube is empty, close the vacuum line and open the filter flask and Dumas tube to air.
- Place the Dumas tube back in the 100-mL beaker and carefully bring it to your instructor, who will dispense 1 mL of acetone into the tube.
- Shake the tube until all the water droplets in the tube have mixed with the acetone and the inside of the tube appears dry. Return the dry tube to your instructor. Note: If any liquid is still visible in the tube, hold the tube upside down over an empty beaker until the acetone evaporates or drips out of the tube.
- Disassemble the vacuum suction apparatus and dispose of organic and organohalide-contaminated waste in the appropriate container. Pour leftover deionized water down the drain and wash your glassware according to your lab standard procedures.
Results
- Determine the molar mass of your unknown compound. Start by determining the moles of vapor using the ideal gas law. Note: When the vapor in the tube is at equilibrium with its surroundings, it has the same pressure as the room and the same temperature as the boiling water.
- For the volume, determine the mass of water that filled the Dumas tube. Note: The density of water is about 1 g/cm³.
- Select the value of the ideal gas constant with the closest units to the ones that you used and convert any mismatched units, such as temperature.
- Solve to get the number of moles of gas under those conditions.
- Find the average mass of the unknown from the four trials.
- Calculate the standard deviation to see how consistent your results were. Divide the average mass by the calculated number of moles to find the approximate molar mass of your unknown.
- Compare that value to the molar masses of the three candidates for your unknown-- trichloroethylene, 1,2-dichloroethane, and 2-bromopropane.
- Identify the candidate with the closest molar mass and calculate the percent error. Note: Gases tend to mimic ideal behavior at atmospheric pressure, so you should be within 10% of the literature value.
- Now that you know the actual molar mass of your compound, recalculate the number of moles from your average mass. Using the same pressure, volume, and temperature as before, solve for the gas constant. The difference between the calculated constant and the universal constant represents the deviation from ideal gas behavior.

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