Ideal Gases 7/6/19

By Richard Bleil

There is no such thing as an ideal gas. It’s like an ideal relationship; fun to think about, but unrealistic.

But there is a lot to be learned about the behavior of gases by understanding this model, and as it turns out, real gases behave enough like ideal gases that, except under the most extreme conditions, they behave enough like ideal gases that any deviation is typically inconsequential.

There are four basic assumptions of an ideal gas, some absolutely accurate, and some not so much. For example, an ideal gas is assumed to consist of small independent particles. This is absolutely true Gases are made of molecules (like carbon dioxide), elements (like helium) and allotropes (like oxygen, or O2). “Allotrope” is a term that is not frequently used. An element is any form that has only one element involved, like O2, or O3 commonly known as “ozone”. These are both considered to be elements because they only involve oxygen, but because they are different forms of the same element, we call them “allotropes”. Compounds always exist of at least two elements, and always in fixed whole-number ratios. For example, H2O is water, and H2O2 are both compounds comprised of the same two elements (hydrogen and oxygen), but because the ratios are different, they are different compounds. Water is essential to all life on earth (save viruses), and hydrogen peroxide will pretty much kill anything.

The second assumption of an ideal gas is that the volume of these particles is zero (they are called “point particles”). In reality, molecules and elements do have volume, so this assumption is incorrect. However, it’s a very good assumption for gases because the cumulative volume of gas molecules is very small compared to the volume of their container. This assumption begins to fail if the pressure is very very high because the molecules are being forced closer together. Liquids and solids are both considered to be the “condensed states” because the molecules are very close. This is one reason that the assumptions of ideal gas behavior do not work for other states.

Third, we assume there are no intermolecular forces between gas particles. This means molecules do not attract or repel one another. We make this assumption, very accurately, when playing billiards. But, the assumption fails for both billiards and elements and compounds. Billiards have mass, so there is gravitational attraction between them, but this force is so negligible that it has no impact. If there were no intermolecular forces, there would be no condensed states. Liquids and solids occur when intermolcular forces hold the molecules together. These forces are a form of potential energy, but for gases, kinetic energy is so high relative to these potential forces that they are negligible, just like the speed of the billiard ball moving so quickly that the gravitational force won’t affect them.

Finally, it is assumed that the higher the temperature of the gas, the higher the average kinetic energy. All gases will have the same kinetic energy at the same temperature, but some gases will travel faster because of the difference in the masses. Helium is very light, and so it travels faster than oxygen (O2). We see this in the summer and winter in our tires. At higher temperatures, molecules move faster, so they hit the walls of the tire faster causing higher pressure. At lower temperatures, the pressure will drop. This is why you’ll want to keep an eye on your tire pressure.

So the reader might be wondering why so much time is spent on a model of gases that cannot exist. There are a couple of reasons, First, models such as this helps us to understand the behavior of gases, but it also helps us develop laws, the best known of which is the Ideal Gas Law. There are four parameters that define the state of matter; volume (V, unit of space), temperature (T, measure of kinetic energy), pressure (P, force per unit area on container walls) and number of particles (n, called “moles”). The ideal gas model gives us, for example, Boyle’s law which tells is as pressure increases volume decreases (think of an air pump) and Charle’s law (or “Chuck’s Law” to his friends) which tells us that pressure increases as temperature increases (which I mentioned above). With these assumptions, these parameters come together to form the ideal gas law which the reader may or may not recognize, PV=nRT where R is the ideal gas law constant. This law is not only superb for predicting the properties of gases, but is also elegantly simple and is packed with additional knowledge of gases.

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