Understanding Gas Behavior with Boyle's Law: Solving a Pressure and Volume Relationship

Boyle's Law is a fundamental principle in the study of gases, describing the relationship between the pressure and volume of a gas when its temperature is kept constant. This law is pivotal in various fields, including chemistry, physics, and engineering. The relationship can be mathematically expressed as:

Boyle's Law: P1V1 P2V2

Solving a Practical Problem Using Boyle's Law

Consider a sample of gas with an initial volume of 750 milliliters (ml) at a pressure of 700 Torr. If the pressure is increased to 100 Torr, what will be the new volume of the gas?

This change in pressure from 700 Torr to 100 Torr represents a decrease in pressure, not an increase. However, to follow through with a practical example, we can still solve this problem using Boyle's Law:

To find the new volume V2:

Initial conditions: P1 700 Torr, V1 750 ml

Final conditions: P2 100 Torr, V2 ?

Using the formula P1V1 P2V2:

700 Torr × 750 ml 100 Torr × V2

Solving for V2:

V2 (700 Torr × 750 ml) / 100 Torr

V2 5250 ml / 100

V2 52.5 ml (or 5250 ml if you prefer milliliters)

Thus, the new volume of the gas will be 5250 ml under the given conditions.

Common Misconceptions and Clarifications

There are a few common misconceptions related to this problem:

Temperature is Constant: Boyle's Law assumes that the temperature remains constant. It is a critical condition that must be maintained for the calculation to be valid. Liquid vs. Gas: The statement that the volume in the USA would remain 750 ml because "gas" is a liquid is incorrect. The term "gas" refers to a state of matter, not a liquid. Therefore, the behavior of a gas under these conditions is correctly described by Boyle's Law. Direction of Pressure Change: The problem explicitly states that the pressure has increased from 700 Torr to 100 Torr, which is a decrease. This is a common error in problem statements, and understanding the direction of change is crucial.

Practical Applications of Boyle's Law

Boyle's Law has numerous practical applications. Some of these include:

Scuba Diving: Understanding how pressure affects the volume of air in diving tanks. Pneumatic Tools: Designing tools that utilize air pressure to operate. Meteorology: Studying the altitude-based changes in atmospheric pressure and volume. Chemical Reactions: Predicting the behavior of gases in different pressure conditions.

Conclusion

Boyle's Law is a crucial concept in understanding the behavior of gases. By applying the formula P1V1 P2V2, we can solve problems related to changes in gas pressure and volume. It is essential to keep in mind the conditions and precise values given in the problem statement to accurately apply this law. Understanding these principles can help in a wide range of scientific and engineering applications.