Properties of Gases

Introduction

There are several basic properties of gases which differentiate gases from liquids and solids:

• A gas has no definite shape or volume, it will expand to fill its container
• A gas is easily compressible
• Gases form homogeneous mixtures with each other (without exception)

These properties are a consequence of the microscopic state of a gas:

• Individual molecules (atoms for the noble gases) are far apart. The distance between atoms is such that only about 0.1% of the volume of a gas at room temperature and pressure is occupied by molecules. This compares with ~70% of the volume occupied by molecules in a liquid.
• There is very little interaction between molecules.

Pressure

The state of a gas can be completely defined by specifying its temperature, volume, number of moles and pressure. We have previously discussed all of these quantities except pressure.

Pressure is equal to the force per unit area.

P = F/A

Atmospheric pressure results from the force exerted by the weight of air above us. If we were to measure the mass of a column of air extending all the way to the top of the atmosphere with a cross sectional area of 1 m2 its mass would be ~ 10,000 kg. We can use this to calculate atmospheric pressure:

P = F/A = mg/A = (10,000 kg)(9.81 m/s2)/(1 m2)

P = 1 ´ 105 kg-m/s2-m2 = 1 ´ 105 N/m2 = 1 ´ 105 Pa

The SI unit for pressure is a Pascal, Pa, which is equal to the pressure exerted by 1 N of force on an area of 1 m2.

Many of you may also have observed that when lift a glass of water (bottom end down) out of the sink, the water in the cup will not flow out until the rim is above the surface of the water. This is because the pressure exerted downward by the weight of the water in the cup is less than pressure atmospheric pressure (exerted upward).

We can use this same principle to measure the atmospheric pressure. We simply increase the weight of the liquid in the cup until it is equal to atmospheric pressure. We can reduce the height of the liquid if we use a very heavy liquid, such as mercury.

Example

Mercury (density, r = 13,594 kg/m3) is added to a cylinder which is closed on one end. The cylinder is then inverted into a resevior of liquid mercury. What is the maximum height of mercury that can be supported by atmospheric pressure?

Patm = 1.01325 ´ 105 Pa

PHg = F/A = mg/A = Vrg/A = hArg/A = hrg

Patm = PHg = hrg

h = Patm/rg = (1.01325 ´ 105 N/m2)/[( 13,594 kg/m3)(9.81 m/s2)

h = 0.760 m Hg = 760 mm Hg

The above principle illustrates how a barometer works. We can and will report pressures in several different units.

1 atm = 1.01325 ´ 105 Pa = 101.325 kPa = 760 mm Hg = 760 torr