A sample of oxygen occupies \(17.5 \mathrm{~L}\) at \(0.75 \mathrm{~atm}\) and \(298 \mathrm{~K}\). The temperature is raised to \(303 \mathrm{~K}\) and the pressure is increased to \(0.987\) atm. What is the final volume of the sample?

Understanding the behavior of gases is a fundamental part of chemistry and physics, and gas laws succinctly describe these behaviors. Gas laws help us predict the behavior of gases under varying conditions of pressure, volume, and temperature. The most commonly taught gas laws include Boyle's Law, Charles's Law, Avogadro's Law, Gay-Lussac's Law, and the Ideal Gas Law. Together, these laws provide a comprehensive description of gas behavior and are paramount when dealing with problems in chemistry. For instance, Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature, while Charles's Law asserts that the volume and temperature of a gas are directly proportional at constant pressure. The Combined Gas Law, which was used in the given exercise, integrates both Boyle's and Charles's Laws by showing the relationship between pressure, volume, and temperature when they are not held constant. Chemists and physicists use these laws to predict how gases will respond to changes in environmental conditions, which is crucial for everything from balloon inflation to predicting the behavior of the atmosphere.

The interconnection between pressure, volume, and temperature is essential in understanding gas behavior and is explained using the pressure-volume-temperature relationship. This relationship is embedded within the Combined Gas Law, which is expressed as \( \frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2} \). Here, P represents pressure, V signifies volume, and T indicates temperature.

Pressure is a measure of the force applied per unit area and is usually measured in atmospheres (atm) or Pascals (Pa). Volume is the amount of space that a gas occupies, typically measured in liters (L) or cubic meters (m³). Temperature must always be considered on an absolute scale, which is Kelvin in science, to provide accurate predictions. This relationship asserts that if a gas undergoes a change where no gas particles are added or removed, the initial state of the gas (P1, V1, T1) will be proportional to its final state (P2, V2, T2). In real-life applications, this law aids in calculating changes in one of the variables if the others are known, as demonstrated in the exercise provided.

While the term chemiosmotic variables may seem unfamiliar within the context of gas laws, it is related to the transport and energy conversion within cellular membranes found in the domain of biology. The concept of chemiosmosis refers to the movement of ions across a semipermeable membrane, down their electrochemical gradient. This process is crucial for the production of adenosine triphosphate (ATP), the energy currency of the cell. The key variables in chemiosmosis include the membrane potential, the pH gradient (or proton gradient), and the concentrations of different ions across the membrane. These variables are indeed environmental factors that affect the chemiosmotic process, similarly to how pressure, volume, and temperature influence gas behavior.

However, connecting chemiosmotic variables directly to the gas laws may be a bit of a stretch, as the principles governing chemiosmosis typically do not apply to the behavior of gases. Instructors should clarify that in the context of chemistry and physics, 'chemiosmotic' refers more broadly to variables affecting transport and energy, which diverges from the specific pressure-volume-temperature variables considered in the Combined Gas Law.