Question

Explain how increasing the volume of a gas decreases its pressure.

Short answer

Increasing the volume decreases the pressure because the gas molecules have more space, reducing collisions against the container walls.

Step-by-step solution

Understanding the Relationship

To solve this question, we need to refer to Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature and the number of gas molecules remain constant. Mathematically, it can be expressed as: \[ P \times V = k \] where \( P \) is the pressure, \( V \) is the volume, and \( k \) is a constant.

Rearranging the Equation

From Boyle's Law, we rearrange the equation to understand the relationship between pressure and volume: \[ P = \frac{k}{V} \] This equation shows that pressure is equal to a constant divided by the volume. This mathematical relationship indicates that as the volume (\( V \)) increases, the pressure (\( P \)) must decrease given that the constant \( k \) remains unchanged.

Explaining the Mechanism

The reason behind the decrease in pressure with an increase in volume is due to the fact that the gas molecules have more space to move around when the volume is increased. As volume increases, there are fewer molecules per unit volume, resulting in fewer collisions with the walls of the container, which decreases the overall pressure exerted by the gas.

Relating to Real-World Examples

Consider a syringe. When you pull back on the plunger, the volume inside the syringe increases, causing the gas pressure inside to decrease. This illustrates the practical application of Boyle's Law, where increasing the volume by pulling the plunger decreases the pressure inside.

Key concepts

Pressure and Volume Relationship

Boyle's Law captures the essence of the relationship between the pressure and volume of a gas. In simple terms, it tells us that if the volume of a gas increases, its pressure decreases, provided the temperature and amount of gas remain constant. This phenomenon is described as an inverse relationship. The reason it happens is because a larger volume means that gas molecules have more space to move around.
Let's take a closer look:

• When the volume expands, the gas molecules become more spread out.
• As a result, they collide with each other and the walls of the container less frequently.
• This decrease in collision frequency leads to a reduction in pressure.

These principles are elegantly summarized by the equation: \[ P \times V = k \]Here, \( P \) stands for pressure, \( V \) for volume, and \( k \) is a constant value specific to the amount and temperature of the gas.

Gas Law Principles

Gas laws provide us with a framework to understand how gases behave under different conditions. Boyle's Law is one of the central principles in this framework, emphasizing the pressure-volume relationship. This principle is based on the idea that gas behavior can be predicted and described mathematically.
Other important gas laws include:

• Charles's Law: It relates the volume of a gas to its temperature, stating that volume is directly proportional to temperature at constant pressure.
• Avogadro's Law: It tells us that the volume of a gas is directly proportional to the number of moles of gas, if the temperature and pressure remain constant.

These laws are part of the ideal gas law, which combines them into a single equation:\[ PV = nRT \]where \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. These gas law principles help us understand and predict gas behavior in various situations, from everyday scenarios to complex industrial processes.

Gas Behavior Explanation

Understanding how gases behave helps us interpret the world and make predictions in various scientific fields. Gases are composed of molecules that are in constant, random motion. This kinetic motion explains many properties of gases, including pressure and temperature interdependencies.
A few key points about gas behavior include:

• Gas molecules move faster at higher temperatures, which increases pressure if volume is constant.
• With increased volume, molecules have more space to move and spread out, resulting in reduced pressure.
• This spreading out decreases how often molecules hit the container walls, explaining lower pressure in larger volumes.

These ideas align with the kinetic-molecular theory, which explains the macroscopic properties of gases (like pressure) through molecular behavior. Observing these gas behaviors helps scientists and engineers design systems ranging from car engines to medical devices, effectively utilizing these principles to manage scenarios involving gases.