12.3. BEHAVIOUR OF GASES

Properties of gases are easier to understand than those of solids and liquids. This is mainly because in a gas, molecules are far from each other and their mutual interactions are negligible except when two molecules collide.

Gases behave quite differently than solids and liquids because the molecules in gases are much farther apart. This spacing allows us to ignore the interactions between molecules except when they collide with one another. In solids, the molecules are closely packed together, which increases the significance of these interactions. Therefore, when studying gases, we can simplify our understanding by focusing primarily on how they behave during collisions rather than dealing with complex interactions prevalent in solids or liquids.

Think of it like a crowded concert versus an empty auditorium. In the crowded concert (like solids and liquids), individual people bump into each other frequently, making movement complicated. In the empty auditorium (like gases), people can move around freely without much interference from others, allowing for simpler interactions.

Gases at low pressures and high temperatures much above that at which they liquefy (or solidify) approximately satisfy a simple relation between their pressure, temperature, and volume given by: PV = KT (12.1)

Under conditions of low pressure and high temperature, gases tend to follow a simplified relationship known as the Ideal Gas Law. This equation, PV = KT, connects the pressure (P), volume (V), and absolute temperature (T) of a gas. Here, K is a constant for a given gas that varies according to the number of molecules in that gas. Understanding this relationship helps in predicting how gases will behave under different conditions, ideally providing insights into their compressibility and expansibility.

Imagine a balloon filled with air. When you heat the balloon (increasing temperature), the air inside expands, causing the balloon to inflate (increased volume) and the surrounding pressure to slightly change. This is an everyday example of how the Ideal Gas Law operates.

Observation tells us that this k is the same for all gases. It is called Boltzmann constant and is denoted by kB. If P, V, and T are same, then N is also the same for all gases. This is Avogadro's hypothesis: that the number of molecules per unit volume is the same for all gases at a fixed temperature and pressure.

Avogadro's Hypothesis is a fundamental concept in chemistry stating that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This implies that the properties of the gases can be compared directly based on their volume. For example, if you have 1 liter of hydrogen and 1 liter of oxygen at the same conditions, both will have the same number of molecules, allowing us to infer that they have similar behaviors under those conditions.

Think of it as sharing a pizza. If you and a friend each have a slice of pizza from the same pizza pie, you both have an equal share, regardless of how big the slices look from the outside. Similarly, in Avogadro's Hypothesis, each gas has an equal 'share' or number of molecules in a given volume under the same conditions.

If we fix μ and T in the ideal gas equation, we get PV = constant (12.6), meaning that the pressure of a gas varies inversely with its volume.

This part of the Ideal Gas Law signifies Boyle's Law, which states that if the temperature and amount of gas are held constant, increasing the volume of a gas will result in a decrease in pressure, and vice versa. The relationship is inversely proportional, meaning when one increases, the other must decrease, illustrating how gases expand or contract when the volume changes.

Consider a bicycle pump: when you pull the handle out (increasing volume), the pressure inside decreases, making it easier to pull (you can feel it get lighter). Conversely, when you push the handle in (decreasing volume), the pressure rises, making it much harder to push — a classical example of Boyle's Law at work.

Next, if you fix P, the equation shows that V ∝ T i.e., for a fixed pressure, the volume of a gas is proportional to its absolute temperature T (Charles’ law).

Charles' Law emphasizes that if the pressure of a gas remains constant, its volume will expand as the temperature increases. As we heat a gas, the kinetic energy of its molecules increases, causing them to move more vigorously and occupy a greater volume. This could be used to explain why hot air balloons rise; the heated air inside the balloon expands, increasing its volume and decreasing its density relative to the cooler air outside.

Think of a hot-air balloon: when the air inside the balloon is heated, it expands, taking up more space, thus making the balloon lighter than the surrounding cooler air, allowing it to float. This is a practical demonstration of Charles' Law in action.

For mixtures of non-interacting ideal gases, the total pressure is the sum of the individual partial pressures of each gas.

Dalton's Law states that in a mixture of gases, each gas exerts pressure independently of others. The total pressure is simply the sum of all partial pressures exerted by the individual gases in the mixture. For instance, in a balloon filled with both oxygen and nitrogen, the total pressure is the cumulative pressure contributed by both gases. This law allows us to analyze complex gas mixtures by breaking them down into simpler components.

Imagine a group of friends talking simultaneously at a party. Each person's voice contributes to the overall noise you hear. If two of your friends are talking, you hear the combination of their voices, but if you listen carefully, you can identify which voice belongs to whom — similar to how each gas in a mixture contributes to the total pressure.

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