A sample of air with volume \(6.6 \times 10^{7} \mathrm{L}\) changes pressure from 99.4 kPa to 88.8 \(\mathrm{kPa}\) . Assuming constant temperature, what is the new volume?

Understanding the gas laws is essential for students studying physics or chemistry, as they describe how gases behave under various conditions. Boyle's Law is one of the primary gas laws that depicts the behavior of a gas when the temperature remains constant. These laws are fundamental principles that govern the pressure, volume, and temperature of a given amount of gas. Being comfortable with gas laws allows students to predict how a gas will respond to changes in these conditions, which is crucial in many scientific and industrial applications.

Other important gas laws include Charles's Law, which describes the volume-temperature relationship at constant pressure, and Gay-Lussac's Law, which connects pressure and temperature at constant volume. For a more complete understanding, the combined gas law and the ideal gas law integrate all three variables (pressure, volume, and temperature) to describe the state of an ideal gas.

The pressure-volume relationship in gases is a key concept in understanding how gases interact with their containers and surroundings. According to Boyle's Law, this relationship is inversely proportional, meaning that as the pressure on a gas increases, the volume decreases, as long as the temperature stays the same. This is because gas particles exert less force on the walls of their container when compressed, occupying less space.

Boyle’s Law can be expressed with the formula: \( P1 \times V1 = P2 \times V2 \), where \( P1 \) and \( P2 \) represent initial and final pressures, and \( V1 \) and \( V2 \) represent initial and final volumes, respectively. Applications of this principle can be found in everything from breathing mechanisms to the behavior of gas in a piston.

When solving for the unknown volume in a gas law calculation, like in our exercise, it's essential to carefully rearrange the formula to isolate the variable you want to find. For instance, using Boyle's Law \( P1 \times V1 = P2 \times V2 \), and solving for \( V2 \) would involve dividing both sides of the equation by the final pressure \( P2 \).

The main steps include understanding the given variables, substituting them into the equation, and performing algebraic operations to solve for the unknown. In educational settings, being thorough in these steps can significantly help students in comprehending and solving problems based on the pressure-volume relationship of gases.

An inverse relationship is an essential concept in various scientific disciplines, especially in gas laws. As one value increases, the other decreases proportionally, and this is precisely what Boyle's Law demonstrates in the context of gases. At a constant temperature, the product of the pressure and volume of a gas remains constant. This means if the pressure goes up, the volume must go down, and vice versa.

This correlation enables scientists and engineers to manipulate gas conditions for various purposes, such as in balloon inflation, where reducing external pressure allows a balloon to expand. Similarly, deep-sea divers must understand how pressure changes with depth to avoid decompression sickness. The inverse relationship is not only theoretical but has real-world implications that affect how we work with gases in numerous scenarios.