A sample of nitrous oxide gas, \(\mathrm{N}_{2} \mathrm{O}\), occupies a volume of \(832 \mathrm{~L}\) at a pressure of \(0.204 \mathrm{~atm}\). What volume (L) will the gas occupy if the pressure is increased to \(8.02 \mathrm{~atm}\) ?

Gas laws describe how gases behave under different conditions, such as changes in pressure, volume, and temperature. These laws are essential for understanding many everyday phenomena. They also help in various scientific and engineering applications. One of the crucial gas laws is Boyle's Law, which relates pressure and volume of a gas at constant temperature.

Key gas laws include:

• Boyle's Law: Relates pressure and volume.
• Charles's Law: Relates volume and temperature.
• Avogadro's Law: Relates volume and number of gas particles.

These principles are based on the Kinetic Molecular Theory, which describes the behavior of gas particles in motion.

In our example with nitrous oxide gas, we focus on Boyle's Law, demonstrating the relationship between pressure and volume when temperature and the amount of gas are constant.

The pressure-volume relationship is a fundamental concept in the study of gases. According to Boyle's Law, for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This means that if you increase the pressure on a gas, its volume decreases, and vice versa.

Mathematically, Boyle's Law is expressed as:
P_1 V_1 = P_2 V_2

Here,

• P_1 and V_1 are the initial pressure and volume of the gas.
• P_2 and V_2 are the final pressure and volume after a change.

In our example, the initial volume ( V_1 ) is 832 L and the initial pressure ( P_1 ) is 0.204 atm. The final pressure ( P_2 ) is increased to 8.02 atm. To find the final volume ( V_2 ), we used the relationship described by Boyle's Law, performed the calculations, and found that the final volume is approximately 21.16 L.

Inverse proportionality is a key concept in understanding Boyle's Law. When two variables are inversely proportional, as one variable increases, the other decreases. In the context of gases, this relationship explains why increasing the pressure on a gas reduces its volume, while decreasing the pressure allows the gas to expand and occupy a larger volume.

Visualizing inverse proportionality can be helpful. Imagine compressing a balloon. As you push on it, the air particles inside get packed closer together, causing the balloon to shrink. This is an everyday example of Boyle's Law in action.

Knowing how to apply this principle, we used it to solve the problem with our N_2O gas. The initial pressure was low (0.204 atm), and then it was increased significantly (8.02 atm). According to inverse proportionality and Boyle's Law, this increase in pressure caused a notable decrease in volume, shrinking the gas to 21.16 L from its initial 832 L.

By understanding these concepts, students can apply gas laws to a variety of real-world and theoretical problems, making them essential tools in any science toolkit.