Pressure gauge

Pressure gauge (malerapaso, iStockphoto)

Kinetic Molecular Theory of Gases

Digital Development Team

Summary

Learn about the Kinetic Molecular Theory of Gases as well as about the units and tools used to measure gases.

Kinetic Molecular Theory of Gases

Gases behave in certain ways that are described by so-called ‘gas laws.’ Laws in science are not the same as how we normally think about laws. These laws simply describe behaviour; they do not offer any explanations. To provide an explanation, a theory is needed. The theory used to explain how gases behave is called the Kinetic Molecular Theory of Gases.

This theory helps us understand the behaviour of gases. There are four assumptions (things we think are true) that form the basis for the theory:

  1. Particles (atoms or molecules) are constantly moving in straight lines until they either collide with other particles or with the walls of their container.
  2. There is no loss of energy when a particle collides with another particle or the wall of the container - this is known as an elastic collision in the world of molecules. In our world, collisions always result in some loss of energy due to friction. These are called inelastic collisions.
  3. The volume of the particles themselves is so small compared to the volume of the space they occupy that it is considered to be negligible (can be ignored).
  4. There are no forces of attraction between particles (because they are so far away from each other).
Pressure inside a container
Pressure inside a container (Source: Becarlson [CC BY-SA] via Wikimedia Commons).

So what can this theory explain? First, it explains pressure. The force of many collisions by many molecules against the walls of a container is what we call pressure. In Figure 5 you can see where the molecules are exerting an outward force on the container (shown by the red arrows). If the pressure becomes stronger than the container is able to withstand, there will be an explosion (rapid expansion of gas). You may have had this happen if you have shaken a can of pop or seen this happen when someone uncorked a bottle of champagne. 

Release of pressure from a champagne bottle
Release of pressure from a champagne bottle (Source: Niels Noordhoek [CC BY-SA] via Wikimedia Commons). 

All of the energy of a gas is in the form of kinetic energy (energy from movement). Since, according to the Kinetic Molecular Theory, molecules do not lose energy when they collide, this means the average kinetic energy of the molecules stays constant. Any change in kinetic energy is accompanied by a change in temperature (and vice versa – when there is a change in the temperature, there is a change in the kinetic energy).

Units for Measuring Gases

Before we can look at how gases behave, we need to know something about how we measure the physical properties of gases.

Volume

The amount of space a gas takes up is its volume. Volume is measured in units called capacity units. The most common examples of capacity units are millilitres (mL) and litres (L). Very small volumes can be measured in microlitres (μL) while very large volumes can be measured in kilolitres (kL).

Temperature

We are all familiar with the Celsius scale, which was named after Anders Celsius, a Swedish astronomer and physicist. We use this scale in day-to-day life for measuring the temperature outside, the temperature of water in a swimming pool, and our own body’s temperature. Both the Celsius scale (used in the metric system) and the Fahrenheit scale (used in the imperial system) are based on water because originally people were interested in knowing when water changes state (e.g., its freezing point and boiling point). These scales work well for many liquids and solids, but it turns out that neither of the scales works well for describing the behaviour of gases.

Celsius, Fahrenheit and Kelvin scales
Celsius, Fahrenheit and Kelvin scales (Let’s Talk Science using an image by ttsz via iStockphoto).

 

So why do the Celsius and Fahrenheit scales not work well for describing gases? If you remember from above, kinetic energy is related to temperature. A substance at a temperature of 0 ̊C does not mean it has zero kinetic energy. As we will see below, the particles of a substance at 0 ̊C still has a considerable amount of kinetic energy.

What is needed for gases is a temperature scale in which zero means the particles are not moving at all (i.e., have zero kinetic energy).

A temperature scale was created specifically for this purpose. It is called the absolute temperature scale or the Kelvin scale, named after its creator, Lord Kelvin of England. As you can see in Figure 7, absolute zero, or 0 K, is the lowest temperature. (Note that there is no degree sign when using the Kelvin scale). Thus, the freezing point of water can be written as 0 ̊C or 273.15 K.

To convert ˚C to K add 273.15 to the number in ˚C (e.g., 3 ˚C would be 3 + 273.15 = 276.15 K). 

Did you know?

Canada adopted the metric system for everyday use in the 1970’s. In all countries, the metric system is the most commonly used system for scientific applications.

Pressure

As we saw above in the Kinetic Molecular Theory, pressure is caused by the collision of molecules against the walls of the container. These collisions can be thought of as a force exerted upon an area of the wall. We can express this using the equation:

P = F/A

where P stands for pressure, F stands for force and A stands for area. Force is measured in units called Newtons (N) and area is measured in square metres (m2). The unit of pressure then can be stated as N/m2, which is called the pascal (Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. In the imperial system, pressure is given in pounds per square inch (lb/in2 or psi). This unit is still used in pressure gauges that measure the air pressure in car tires.

The most common unit for pressure in science is the kilopascal (kPa), which is 1000 Pa. Another commonly used unit is the bar, which is 100 kPa.

One way to measure air (atmospheric) pressure is with a pressure measuring device called a barometer. One of the first practical barometers - a type still used today - uses an upright tube that is partially filled with mercury and sits in a container of mercury. The tube is closed at the top and contains a vacuum, so that when air molecules from the atmosphere push down on the mercury in the container, the mercury is forced up into the tube. The mercury rises up the tube until its fluid pressure exactly matches the atmospheric pressure.

Mercury barometer
Mercury barometer (©2020 Let’s Talk Science).

The height (in mm) to which the mercury rises in the tube (above the level of mercury in the container), is equivalent to the pressure pushing down on the mercury by the atmosphere. The unit for this type of measurement is called mm Hg (millimetres of mercury) or torr (1 mm Hg = 1 torr). In more modern commercial barometers, the mercury sits in an enclosed well at the bottom and its height is measured in millimetres by a precise scale at the top.

A modern barometer
Modern barometer (Peter Bloch, used with permission).

 

A baseline measurement for atmospheric pressure uses the pressure at sea level. At sea level, the height of mercury in a barometer is 760 mm. This can also be expressed in psi (14.696 lb/in2) and kPa (101.325). The pressure at sea level is also known as one standard atmosphere, which uses the symbol atm. More recently, the atm has been replaced with the bar, which is a unit equivalent to 100 kPa (a nice round number to work with!). If you made a barometer with water instead of mercury, it would need to be more than 10 m tall to measure atmospheric pressure!

To measure the pressure of a gas inside a container, we use a different type of measuring device called a pressure gauge

The pressure gauges used to measure the pressure inside bicycle or car tires work in a similar way to the mercury, but instead of the air pushing a fluid through a tube, in a tire gauge, the air pushes on a piston attached to a spring inside a tube. 

Like the mercury, the distance the piston travels is relative to the pressure in the tire. A calibrated rod (essentially a ruler) tells you the pressure in psi.

Inside a tire pressure gauge
Inside a tire pressure gauge (©2020 Let’s Talk Science).

 

 

References