Question

Explain why pressure increases as a gas is compressed into a smaller volume.

Short answer

Pressure increases as the gas volume decreases because the gas molecules collide more frequently with the container walls, increasing the force per unit area.

Step-by-step solution

- Understand the Relationship between Volume and Pressure

According to Boyle's Law, for a given amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. This means that if the volume decreases, the pressure increases.

- Analyze the Molecular Interactions

When the gas is compressed into a smaller volume, the gas molecules are forced closer together. This increases the frequency of collisions between the gas molecules and the walls of the container.

- Apply the Concept of Pressure

Pressure is defined as the force exerted by the gas molecules per unit area of the container walls. As the frequency and force of collisions increase with compression, the pressure exerted by the gas also increases.

Key concepts

Gas Compression

When you compress a gas, you are essentially squeezing it into a smaller space. Imagine you have a balloon filled with air. If you press on the balloon, it shrinks down in size. What you're doing is decreasing the volume of the gas inside without changing the amount of gas. This is what we refer to as gas compression.
In a more scientific context, when you compress a gas, this means reducing the volume it occupies. However, the amount of gas (number of molecules) remains constant. This action has significant effects on the pressure of the gas, which leads us to investigate how this pressure changes when the gas is compressed.

Pressure and Volume Relationship

The relationship between pressure and volume in gases is beautifully explained by Boyle's Law. Boyle's Law states:
\[ P_1 V_1 = P_2 V_2 \] Here, \( P \) represents the pressure of the gas, and \( V \) represents its volume. The subscripts 1 and 2 denote different states of the gas.
According to this principle, if you decrease the volume of a given amount of gas at a constant temperature, the pressure increases. This is because the gas molecules have less space to move around, causing them to collide more frequently with the walls of their container. Increased collisions mean more force is exerted on the container walls, which effectively increases the pressure.
For instance, if you were to halve the volume of a gas, the pressure would double, provided the temperature stays the same. This inverse relationship is crucial to understand why compressing a gas increases its pressure.

Molecular Interactions in Gases

Let's delve deeper into what happens at the molecular level when a gas is compressed. Gas molecules are in constant random motion, bouncing off each other and the walls of their container. This behavior follows the principles of the kinetic molecular theory.
When you compress a gas, the molecules are forced into a tighter space, increasing the frequency of their collisions. Every collision between gas molecules and the container walls transfers a tiny bit of momentum, which contributes to the overall pressure.
The more you compress the gas, the more frequently these collisions happen. Additionally, as the gas is compressed, the energy of these collisions increases, further boosting the pressure. It's like trying to fit more people into an already crowded room: not only does it get cramped, but the interactions become more intense.
Therefore, the increased collision frequency and energy among gas molecules are fundamental reasons why compressing a gas results in higher pressure.