Question

Use the kinetic molecular theory of gases to explain each of the following: a. Gases move faster at higher temperatures. b. Gases can be compressed much more than liquids or solids.

Short answer

a. Higher temperatures increase kinetic energy of gas particles, causing them to move faster. b. Gases are more compressible because their particles are spaced far apart.

Step-by-step solution

Explanation of Gases Moving Faster at Higher Temperatures

The kinetic molecular theory states that the kinetic energy of gas particles is directly proportional to the temperature. At higher temperatures, gas particles have more kinetic energy, which means they move faster. The mathematical expression for kinetic energy is given by \(\text{KE} = \frac{1}{2}mv^2\), where \(m\) is mass and \(v\) is velocity. As the temperature increases, the average velocity \(v\) of gas particles increases, causing them to move faster.

Explanation of the Compressibility of Gases

According to the kinetic molecular theory, gas particles are in constant motion and are spaced far apart from each other compared to the size of the particles. This large amount of empty space between gas particles allows gases to be easily compressed, as the particles can move closer together when pressure is applied. In contrast, liquids and solids have closely packed particles, leaving little room for compression.

Key concepts

gas particle motion

The kinetic molecular theory of gases offers a brilliant insight into understanding how gas particles move. According to this theory, gas particles are always in constant, random motion. They move in various directions and at different speeds.
What's fascinating is that these particles hardly interact with each other. They collide occasionally, but those collisions are elastic, meaning that there is no energy loss in the process.
Due to the high-speed movement and minimal interaction, gases can easily fill any container they are placed in. The motion of gas particles is essential for understanding other properties of gases, like temperature and pressure.

temperature and kinetic energy

The temperature of a gas is closely linked to the kinetic energy of its particles. Here’s how:

• Kinetic Energy: Kinetic energy is the energy that particles have due to their motion. The formula for kinetic energy of a gas particle is given by \(\text{KE} = \frac{1}{2}mv^2\).
• Direct Proportionality: According to the kinetic molecular theory, kinetic energy is directly proportional to temperature. This means that as the temperature increases, the kinetic energy of the gas particles also increases.

At higher temperatures, the average speed of gas particles rises, making them move faster.
This explains why gases behave more energetically and why they expand or exert more pressure when heated. In simple terms, if you heat a gas, its particles move faster and collide more frequently with the walls of the container, resulting in increased pressure.

compressibility of gases

Gases are unique among the states of matter because they are highly compressible. Let's understand why:

• Particle Spacing: Gas particles are much farther apart compared to those in liquids or solids. There is a lot of empty space between them.
• Easy Compression: This large amount of empty space means that gas particles can be squeezed closer together when pressure is applied. You can think of it as fitting many marbles into a jar; there’s plenty of space between each marble, making it easy to push them closer together.

This characteristic is what allows gases to be compressed much more than liquids or solids. For instance, you experience this every time you pump air into a tire.
In contrast, liquids and solids have particles that are closely packed, leaving little room for additional compression.