The pressure on a 240.0 \(\mathrm{mL}\) sample of helium gas is increased from 0.428 atm to 1.55 atm. What is the new volume, assuming constant temperature?

Understanding the different laws that govern the behavior of gases is crucial in the field of chemistry. Gas laws are a set of laws that describe the relationship between the pressure, temperature, and volume of a gas. These include Boyle's Law, Charles's Law, Gay-Lussac's Law, and the Combined Gas Law, among others. Boyle's Law, in particular, defines the inverse relationship between pressure and volume at a constant temperature for a fixed amount of gas.

When we examine gases under varying pressures and volumes while keeping the temperature constant, we are dealing with real-life applications of Boyle's Law. As the pressure on a gas increases, the volume decreases, and conversely, as the pressure decreases, the volume increases. This principle helps us in daily activities as simple as breathing and as complex as operating pneumatic systems.

The pressure-volume relationship of gases is a fascinating topic that allows us to predict how a gas will behave when subjected to changes in pressure. This relationship is an inverse one, as stated in Boyle's Law: when the volume of a gas increases, its pressure decreases, provided the temperature and the amount of gas remain constant. Similarly, decreasing the volume of a gas increases its pressure. This concept is relevant not just in laboratories but also in industrial processes, the medical field, and even in weather prediction.

At the heart of this concept is the ideal gas assumption, which posits that gas particles are small compared to the distances between them and do not attract or repel each other. Although real gases do not always follow this principle perfectly, the ideal gas law provides a reasonable approximation for many conditions. In essence, understanding the pressure-volume relationship is key to mastering the behavior of gases under different conditions.

Solving problems in chemistry, particularly those involving gas laws like Boyle's Law, requires a methodical approach. To adeptly navigate through these problems, it is essential to first identify the known values and the variables that need to be found. The next step involves applying the appropriate gas law and rearranging the formula to solve for the unknown variable. This systematic process ensures that students can find solutions to complex scenarios by breaking them down into smaller, more manageable parts.

In doing so, it promotes the development of critical thinking skills and a deeper understanding of the material. The exercise given earlier is a fitting example of applying problem-solving strategies to Boyle's Law. By recognizing the methodical steps—identification of variables, application of the law, rearrangement of the equation, and calculation—we can approach these problems with confidence. Furthermore, practicing these steps routinely will prepare students to tackle a wide range of chemistry problems, establishing a strong foundation in the subject.