Getting the number out of thin air
You have a small vial of clear solvent and need its molar mass. The standard lab trick is to vaporize a known volume inside a flask, trap the gas, weigh it, and apply the ideal gas law. It works most of the time if you control the temperature and pressure precisely. I use this when preparing calibration standards for gas chromatography, usually targeting compounds in the 50 to 150 gram per mole range. The calculation rests on rearranging PV equals nRT. You measure the mass of the vapor, the volume of the flask, the temperature of the water bath, and the ambient pressure. Divide the mass by the number of moles you calculate from pressure and temperature, and you get the molar mass. The algebra is straightforward. The practical execution is where things usually go wrong. I set up a 125 milliliter Erlenmeyer flask with a piece of aluminum foil secured by a rubber band. The foil has a pinhole about one millimeter wide. You add roughly two milliliters of the liquid, seal the flask, and immerse it in a boiling water bath. The liquid vaporizes, pushes the air out through the pinhole, and then condenses back once you remove it. You dry the outside, weigh the flask with the condensed liquid, and record the bath temperature and barometric pressure.
One detail people miss is the initial mass. You need to weigh the empty flask, foil, and band before adding the liquid. Subtract that from the final mass to get the mass of the vapor alone. If you skip this step, your result will be off by several grams, which ruins the precision entirely. I also make sure the water level covers the lower third of the flask. Heating only the top creates a temperature gradient that skews the ideal gas calculation. I ran into a persistent issue a while back where my calculated masses were consistently low by about eight percent. The liquid was diethyl ether, and I assumed the vapor filled the entire flask volume. It turns out the vapor displaces air, but the air doesn't escape completely through a one millimeter hole. The partial pressure of the vapor is slightly less than atmospheric pressure because some air remains trapped. I fixed it by submerging the flask upside down in the water bath during heating. The vapor escapes through the pinhole while water enters, ensuring the flask contains only vapor at the end. That eliminated the displacement error and brought my results within two percent of the literature value. You should measure atmospheric pressure with a barometer, not rely on weather app readings. Lab pressures can drift by five millibars during a day, which translates to a one percent error in molar mass. Temperature should be measured with a calibrated thermometer placed directly in the water bath, not on the wall of the container. Water bath temperature stabilizes about three minutes after the bath reaches a gentle boil. Wait that long before recording.
The method breaks down for liquids that decompose near their boiling points. If your compound darkens or smells sharp when heated, do not use this approach. It also fails for hygroscopic liquids because the condensed mass will absorb water from the air, adding unaccounted weight. In those cases, switch to a mass spectrometer or use colligative property measurements like freezing point depression. Those methods are slower but avoid the vapor handling errors entirely. A typical result comes in around twenty minutes from start to finish if you run the bath first and prepare the flask simultaneously. With practice, you can get reproducibility within plus or minus three percent. Without careful technique, expect ten to fifteen percent variance. Keep a log of each run, note any condensation on the foil outside the flask, and reject data where visible droplets remain. The math only matters if the physical setup is clean.
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