# Molar Mass of a Volatile Liquid by the Dumas Method

## Objectives

• Determine the molar mass of a volatile liquid.
• Use the ideal gas law in connection with an experiment.

## Background: ideal gas law

A volatile liquid (or solid, for that matter) is one which evaporates easily. [Note: volatile is not a synonym of reactive.] We will evaporate the liquid in this lab, and make use of the properties of the resulting vapor (gas).

From the 17th through the early 19th centuries, a number of scientists discovered simple relationships among the temperature, pressure, volume, and amounts of gases:

• Robert Boyle: volume of a gas inversely proportional to its pressure; or
pV = constant.
• Jacques Charles and Joseph Gay-Lussac: pressure of a gas proportional to its temperature;
p = constant x T
• Amedeo Avogadro: equal volumes of gas contain equal numbers of molecules;
n = constant x V, with the same constant for all gases.
These relationships can be combined into a single equation which describes the relationship among temperature, pressure, volume, and amount (number of moles) of all gases under ordinary conditions. The equation is the ideal gas law:
pV = nRT ,
where
• p = pressure
• V = volume
• n = number of moles
• R = ideal gas constant (8.21x10-2 L atm mol-1 K-1)
• T = absolute temperature (i.e., temperature in Kelvin) .

The ideal gas law has wide applicability in chemistry. One can use it to compute any one of the four variables if the other three are known or can be measured. In this week's experiment, we will determine the pressure, volume, and temperature of a sample of gas (our evaporated volatile liquid), which means that we can solve for the number of moles:

number of moles = n = pV/RT .

But we go one step further, because we will also measure the mass of the evaporated liquid. Knowing the mass and the number of moles will allow us to compute the molar mass of the liquid:
molar mass = (mass)/(number of moles).

## Procedure Overview

I won't go over the procedure in step-by-step detail, but I will stress some points of safety and (in bold color) some places where our procedure differs from that in the lab packet. The main difference is to measure the volume of the flask last, not first.

Work in pairs (no triples).

We will heat a volatile liquid to evaporate it so that its vapor just fills a flask whose volume we can measure; we will also know the temperature and pressure of the vapor, and the mass of the vapor.

1. Determine the mass of flask, boiling stone, and foil cap
• This is done before adding the liquid so we can weigh the amount of vapor by difference between this and a later measurement; it is done before the first trial only.
• Make a small pin-hole in the foil cap.
• Use narrow-neck 250 mL pyrex flasks only; examine flask for cracks.
2. Add volatile liquid
• About 5 mL is sufficient. It is not crucial to get exactly 5 mL.
3. Heat to vaporize liquid
• We will use Bunsen burner flames to heat the water baths. Be careful not to let your flames get too high, because our volatile liquids are flammable.
• Put a boiling stone in the water bath too (but you don't have to know its mass).
• Keep the flask slightly tilted; it will be easier to notice when the liquid disappears.
• Keep as much of the flask under water as possible.
4. Measure water bath temperature and atmospheric pressure
• Heat the water bath gently. The assumption that the water bath and the vaporized liquid have the same temperature is only reasonable if the water is being heated gently (with the temperature not rising rapidly). Don't let the water boil.
• Measure the temperature quickly once the liquid vaporizes, but keep the wires of the thermal probe away from the flame and iron ring.
• You may measure the atmospheric pressure any time during the lab period. Your instructor will show you how to use the barometer in the lab.
5. Condense vapor in flask
• Run cold water over flask.
6. Determine mass of flask, boiling stone, foil cap, and condensed vapor
• There will be less volatile liquid left than there was initially; that is what we expect. You put in more than enough liquid so its vapor would fill the flask and the excess left through the pinhole. The condensed vapor (i.e., the remaining liquid) has the same mass as the vapor which exactly filled the flask.
• Be sure the foil cap is not wet from boiling water or condensed water vapor. Dry the neck of the flask, if necessary, keeping the foil cover on.
7. Determine volume of flask The flasks are nominally 250 mL, but 250 mL is not an exact measurement; furthermore, it refers to the volume of liquid it holds in normal use, so it excludes the volume of the flask's neck.
• After you are finished with all determinations, rinse the flask with acetone, and then with water, to remove all remnants of the oily volatile liquids.
• Now fill your flask (to overflowing) with tap water, and measure with a 500-mL graduated cylinder the volume it contains.