A sample of gas has an initial volume of \(3.95 \mathrm{~L}\) at a pressure of \(705 \mathrm{~mm} \mathrm{Hg}\). If the volume of the gas is increased to \(5.38 \mathrm{~L}\), what is the pressure? (Assume constant temperature.)

Gas laws are fundamental principles that describe the behavior of gases under various conditions of pressure, volume, and temperature. They are essential for understanding how gases will react when subjected to changes in their environment. One of the most basic and widely taught gas laws is Boyle's Law, which focuses specifically on the relationship between the pressure and volume of a gas when its temperature is held constant. Boyle's Law alongside Charles's Law, Gay-Lussac's Law, and Avogadro's Law make up the combined gas law. These principles not only inform academic studies in chemistry and physics but are also critical in real-world applications such as respiratory mechanics, syringe design, and the workings of internal combustion engines.
Understanding these gas laws is fundamental to studying chemistry and provides a basis for more complex concepts like the ideal gas law. When dealing with any gas law, remembering the conditions kept constant (such as temperature in Boyle's Law) is crucial to properly applying the law and predicting the gas's behavior.

The pressure-volume relationship is an important consideration in the study of gases. Boyle's Law describes this relationship, establishing that for a given mass of gas at a constant temperature, the pressure and volume are inversely related. This means that if the volume of a gas increases, the pressure decreases, provided the temperature does not change, and vice versa.
This concept can be illustrated using everyday examples, such as pressing on a syringe: when the volume within the syringe decreases due to the plunger being pushed, the pressure of the gas inside increases. This relationship is critical not only in chemistry but also in many industrial and medical applications where gases are used or produced.

Inverse proportionality is a type of mathematical relationship found throughout science, especially in gas laws like Boyle's Law. If two variables are inversely proportional, it means that as one variable increases, the other decreases at a rate that maintains a consistent product. The formula for Boyle's Law, which is expressed as P1 * V1 = P2 * V2, showcases this relationship.
When trying to visualize inverse proportionality, think of a balloon: as you compress it (decrease volume), the air inside gets squeezed (pressure increases), and when you let it expand, the pressure drops. Mathematically, if you plot this relationship, you'd get a hyperbola, with pressure on one axis and volume on the other, demonstrating that as one increases, the other decreases, and the product of the two remains the same.

Step by Step Analysis

Chemistry problem solving often involves a series of logical steps to find a solution to a problem, as seen with the application of Boyle's Law. The first step usually includes identifying the correct law or formula that applies to the situation. After understanding the variables and their relationship, setting up the equation with the existing values is the next essential step.

Finding the Solution

Then, rearranging the equation to solve for the unknown variable follows. In the case of the provided exercise, P2 was the unknown which required solving. Finally, the calculation is done using correct units and significant figures. These steps can be applied to a myriad of problems in chemistry, and mastering them is fundamental for any student wishing to excel in the subject.