### Learning Objectives

By the end of this section, you will be able to:

- Calculate molar mass using the ideal gas law and laboratory data.
- Determine the identity of an unknown from a list of choices.
- Determine how sources of error affect your measurements.

**Introduction**

You may remember from unit one that all matter has mass and takes up space. It may be difficult to visualize a vapor occupying space or to feel the mass of the atmospheric gases pressing against you now. This laboratory takes advantage of several properties of gases including their mass and ability to occupy the entire volume of a container to allow the calculation of the molar mass for an unknown compound.

The gas laws in discussed in class relate other properties of gases. Boyles law demonstrates how pressure and volume of a gas are inversely related at constant T and n. Charles’ Law shows how temperature and volume of a gas are directly proportional when pressure and n are constant. Avogadro’s Law shows how all gasses occupy the same volume per mol (or number of particles). This means that regardless of the identity the compound, all gas samples of the same number of mol occupy the same volume. These concepts are combined in the ideal gas law which states:

[latex]\text{PV}=\text{nRT}[/latex]

Where P is pressure in atm, V is volume in L, n is the mols of the gas, R is the gas constant (0.0821 Latm/molK), and T is the temperature in Kelvin. This equation can be rearranged to calculate any variable. In this lab you are interested in finding the mol of an unknown sample so we can rearrange the equation to find n by

[latex]\text{n}=\frac{\text{PV}}{\text{RT}}[/latex]

Ideal gases should behave ideally. This means that we assume the gas will occupy the entire volume of a container. The particles will be moving rapidly, randomly and constantly. Any collisions between gas particles are elastic leaving kinetic energy intact.

During this lab you will be measuring out several mL of an unknown volatile compound. You will add this small volume to a flask and then cover it loosely with foil. Poking a few holes in the foil will allow some of the compound to leave as it is heated. When the flask is heated, the volatile liquid will vaporize and occupy the entire space of the flask. Because gases occupy MUCH larger volumes than liquids, the volume of liquid you measure out will be more than sufficient to occupy the whole flask once it is vaporized. The pressure of the gas in the flask will be the much higher than the pressure of the gas in the laboratory at first. However as you heat the sample, some of the rapidly moving particles will eventually leave the flask through opening at the top of the flask. This will continue to happen until the pressure in the laboratory and the flask are the same (when all liquid has been vaporized).

You can use the temperature you heated the flask to, the pressure of the laboratory, the volume of the flask and the gas constant to find the mol of the unknown compound you are using. At the end of the experiment when you cool down the compound, you can also get the mass of the liquid in grams. This will allow you to calculate the molar mass (g/mol) of the unknown compound. Using a list of possible choices (listed in Table 1), determine the identity of your unknown.

**Table 1: Possible Unknowns Used in Lab**

Possible Unknown |
Chemical Formula |
Molar Mass (g/mol) |

Methane | CH_{4} |
16.04 |

Ethane | C_{2}H_{6} |
30.07 |

Methanol | CH_{4}O |
32.04 |

Ethanol | C_{2}H_{6}O |
46.07 |

Acetone | C_{3}H_{6}O |
58.08 |

Benzene | C_{6}H_{6} |
78.11 |

Ethyl Acetoacetate | C_{6}H_{10}O_{3} |
130.12 |