The kinetic-molecular model of gases1 describes the gaseous state as one in which gas particles are spaced out relative to one another and are moving around with rapid, random motion.
Calculations based on this model reveal a number of interesting facts:
- The average distance between particles is about 10 times the particle2 diameter – for oxygen3, this distance is 3.54 nm.
- There is a wide range of particle speeds within this rapid random motion, and it is possible to calculate an average value, which depends on the temperature4 of the gas and the mass5 of the gas particle. For example, at standard temperature (0°C) and pressure6 (101.3 kPa), referred to as STP7, the average speed of an oxygen molecule8 is 425 m/s and the average speed of a hydrogen9 molecule is 1845 m/s. These are staggeringly high speeds!
- The mean free path is the distance a given gas particle moves before colliding either with the walls of the container or with another particle. For oxygen at STP, the mean free path is 63 nm. This is an exceptionally small distance.
- The number of collisions occurring per second for a given molecule can be calculated by dividing the average speed by the mean free path. For an oxygen molecule at STP, this is close to 7 billion collisions per second!
Properties of gases explained
Relationship between gas pressure and gas volume
While studying the compressibility of gases, Robert Boyle (1627–1691) discovered that, for a fixed amount of gas at a given temperature, if the pressure acting on it is doubled, the volume10 of the gas is halved.
This inverse relationship between the pressure acting on a gas and its volume is known as Boyle’s Law, which takes the mathematical form P1V1=P2V2. In each case, the product of the pressure and the volume is a constant.
Relationship between gas volume and gas temperature
In 1787, French scientist Jacques Charles discovered that the volume of a fixed amount of gas held at constant pressure decreased with decreasing temperature. If the temperature is measured in kelvin11 rather than °C, the relationship is a directly proportional one. Charles’s Law takes the mathematical form V1/T1 = V2/T2.
Combining Boyle’s Law and Charles’s Law
For a fixed amount of gas, these three relationships can be combined to give the form P1V1/T1 = P2V2/T2. This equation is known as the general gas law.
Here is an example of how the general gas law is applied. Weather12 balloons are filled with helium13 (or less expensive hydrogen) gas. When released, they move up through the troposphere14, and the attached instruments send back information about temperature, pressure, wind speed and humidity15.
Suppose a 5000 L balloon is launched when the temperature is 17°C and the pressure 1000 hPa. If it ascends to a height of 35 km where the temperature is -33°C and the pressure 150 hPa, what will the volume of the balloon now be?
Now P1V1/T1 = P2V2/T2 and P1= 1000 hPa; V1 = 5000 L; T1 = 17 + 273 = 290 K
P2= 150 hPa; V2 = ? L; T2 = -33 + 273 = 240 K
Rearranging for V2 gives:
V2 = P1V1T2/P2T1
= (1000 x 5000 x 240)/150 x 290
= 27586.2 L
The balloon has expanded to 5.5 times its original volume. It is most likely that the balloon would have burst before reaching this altitude16.
Nature of science
A scientific law is a statement of fact meant to explain, in simple terms, an action or set of actions. It is generally accepted to be true and universal and can sometimes be expressed in terms of a single mathematical equation. For example, the changing volume of a gas with changing pressure embodied in Boyle’s Law can be expressed as P1V1=P2V2.
Related content
Use this timeline for a look at some of the historical aspects in the development of our understanding of gases and plasmas.
Activity ideas
Try these activities with your students, to help them understand more about fases and plasmas
- Diffusion and effusion – students complete a laboratory experiment to gain a basic understanding of diffusion17 and effusion18 and then investigate carbon monoxide19 and hydrogen sulfide20.
- Gas properties – students investigate gas compressibility and gas expansion in a quantitative21 way – the end result will be an appreciation of Boyle’s Law and Charles’s Law.
- Atmospheric pressure – students indirectly measure atmospheric pressure22 using a plastic23 drink bottle and a ping pong ball, they will then use this measure to calculate the force24 acting on the outside of a soft drink can.
- Relative humidity and thermal comfort – students measure the relative humidity25 in their classroom and in a sheltered playground location and relate the relative humidity and temperature in the classroom to thermal comfort levels.
- gases: The state of matter distinguished from the solid and liquid states. Gases have the ability to diffuse readily and to become distributed uniformly throughout any container.
- particle: A tiny piece of matter. A particle may refer to an atom, part of an atom, a molecule or an ion.
- oxygen: A non-metal – symbol O, atomic number 8. Oxygen is a gas found in the air. It is needed for aerobic cellular respiration in cells.
- temperature: A measure of the degree of hotness or coldness of an object or substance. Temperature is measured with a thermometer calibrated in one or more temperature scales. Kelvin scale temperature is a measure of the average energy of the molecules of a body.
- mass: The amount of matter an object has, measured in kilograms.
- pressure: The force per unit area that acts on the surface of an object.
- STP: Standard temperature and pressure is taken as a temperature of 0°C (273 K) and a pressure of 101.3 kPa.
- molecule: Two or more atoms bonded together. The molecule of an element has all its atoms the same. The molecule of a compound has two or more different atoms.
- hydrogen: First element on the periodic table – symbol H, with the atomic number of 1, meaning that it has a single proton in its nucleus.
- volume: 1. The quantity of space occupied by a liquid, solid or gas. Common units used to display volume include cubic metres, litres, millilitres, tablespoons and teaspoons. (Volume can refer to a large quanity of something). 2. The degree of sound intensity or audibility; loudness.
- Kelvin: 1. Kelvin temperature scale – An SI (international system of units) temperature scale used by scientists. It goes up in the same steps as the Celsius scale, but starts at absolute zero (-273.15 °C).
2. kelvin – A unit of temperature named after William Thomson (1824–1907), known as Lord Kelvin. It is equivalent in size to a degree Celsius and forms the basis of the Kelvin temperature scale. The starting point of this scale, absolute zero, is the lowest temperature that can be achieved. - weather: Daily or short-term conditions like temperature, cloud cover, precipitation and wind affecting a certain area.
- helium: (He) A colourless, odourless inert gaseous element occurring in natural gas and with radioactive ores.
- troposphere: The lowest layer of the Earth’s atmosphere. We live in the troposphere. All weather happens in this layer.
- humidity: The amount of water vapour in the air.
- altitude: 1. The height of something, usually height above sea level. 2. In astronomy, the angular distance of a natural or artificial satellite above the horizon.
- diffusion: The movement of atoms or molecules from an area of higher concentration to an area of lower concentration. Atoms and small molecules can move across a cell membrane by diffusion.
- effusion: A process that involves gas molecules escaping through a small hole in a containing vessel. It explains why inflated toy balloons deflate when left alone for several days.
- carbon monoxide: Carbon monoxide consists of one carbon atom and one oxygen atom. It is an odorless, colourless, tasteless, flammable gas.
- hydrogen sulfide: A colourless gas with a characteristic rotten-egg smell. Exposure to high levels (>100 ppm) can cause convulsions, coma and death.
- quantitative: Looking at numerical aspects of something; measuring and comparing something in units.
- atmospheric pressure: The force per unit area at a given location on the Earth caused by the weight of the air above it. At sea level, this pressure is about 10 N per cm2 (101.3 kPa in SI units).
- plastic: A synthetic material made from a wide range of organic polymers (such as polyethylene, PVC and nylon) that can be moulded into shape while soft and then set into a rigid or slightly elastic form.
- force: A push or a pull that causes an object to change its shape, direction and/or motion.
- relative humidity: The ratio of the amount of water vapour in a given parcel of air, at a set temperature and pressure, to the maximum amount that the parcel of air could hold under the same conditions. It is expressed as a percentage.
