0.10 The ideal gas law

Foundation

We assume as our starting point the atomic molecular theory. That is, we assume that all matter is composed ofdiscrete particles. The elements consist of identical atoms, and compounds consist of identical molecules, which are particlescontaining small whole number ratios of atoms. We also assume that we have determined a complete set of relative atomic weights,allowing us to determine the molecular formula for any compound.

Goals

The individual molecules of different compounds have characteristic properties, such as mass, structure,geometry, bond lengths, bond angles, polarity, diamagnetism or paramagnetism. We have not yet considered the properties of massquantities of matter, such as density, phase (solid, liquid or gas) at room temperature, boiling and melting points, reactivity, and soforth. These are properties which are not exhibited by individual molecules. It makes no sense to ask what the boiling point of onemolecule is, nor does an individual molecule exist as a gas, solid, or liquid. However, we do expect that these material or bulkproperties are related to the properties of the individual molecules. Our ultimate goal is to relate the properties of theatoms and molecules to the properties of the materials which they comprise.

Achieving this goal will require considerable analysis. In this Concept Development Study, we begin at a somewhatmore fundamental level, with our goal to know more about the nature of gases, liquids and solids. We need to study the relationshipsbetween the physical properties of materials, such as density and temperature. We begin our study by examining these properties ingases.

Observation 1: pressure-volume measurements on gases

It is an elementary observation that air has a "spring" to it: if you squeeze a balloon, the balloon rebounds toits original shape. As you pump air into a bicycle tire, the air pushes back against the piston of the pump. Furthermore, thisresistance of the air against the piston clearly increases as the piston is pushed farther in. The "spring" of the air ismeasured as a pressure, where the pressure $P$ is defined

$F$ is the force exerted by the air on the surface of the piston head and $A$ is the surface area of the piston head.

For our purposes, a simple pressure gauge is sufficient. We trap a small quantity of air in a syringe (a pistoninside a cylinder) connected to the pressure gauge, and measure both the volume of air trapped inside the syringe and the pressurereading on the gauge. In one such sample measurement, we might find that, at atmospheric pressure (760 torr), the volume of gas trappedinside the syringe is 29.0 ml. We then compress the syringe slightly, so that the volume is now 23.0 ml. We feel the increasedspring of the air, and this is registered on the gauge as an increase in pressure to 960 torr. It is simple to make manymeasurements in this manner. A sample set of data appears in . We note that, in agreement with our experience with gases, the pressure increases asthe volume decreases. These data are plotted here .