Understanding Boyle's Law: How Volume Changes with Pressure Variations

In the field of physics and chemistry, understanding how the behavior of gases changes in response to various pressures and temperatures is crucial. Boyle's Law, a fundamental principle of physics, provides a practical framework for predicting how the volume of a gas changes when the pressure is altered, assuming the temperature remains constant. Let's explore how this law can be applied to solve a specific problem involving a gas that initially occupies 450 mL under a pressure of 2 ATM and how its volume changes when the pressure is increased to 2.50 ATM.

Boyle's Law and the Ideal Gas Law

Boyle's Law, first stated in the 17th century, is one of the gas laws that describe the behavior of a gas kept at a constant temperature. According to Boyle's Law, for a given amount of gas at constant temperature, the product of the pressure and volume is a constant. Mathematically, Boyle's Law can be expressed as:

Boyle's Law Equation

Boyle's Law: PV k

Where:

P is the pressure of the gas, V is the volume of the gas, k is a constant for a given amount of gas at a constant temperature.

Since T, R, and n (amount of substance) are constant in the Ideal Gas Law PVnRT, we can equate the two expressions under constant temperature:

Boyle's Law in Context of Ideal Gas Law

Boyle's Law: PV nRT (assuming T, R, and n are constant) > PV k

Applying Boyle's Law to a Real-World Problem

Let's consider the problem of a gas that initially occupies a volume of 450 mL under a pressure of 2 ATM. We need to determine the final volume if the pressure is increased to 2.50 ATM, assuming the temperature remains constant.

Solving the Problem

The volume of the gas can be calculated using the form of Boyle's Law applied to pressure and volume changes:

Boyle's Law Equation: P_1V_1 P_2V_2

Let's denote:

P_1 2 atm V_1 450 mL P_2 2.50 atm V_2 ?

Solving for V_2:

Calculation

V_2 (P_1V_1) / P_2 (2 atm × 450 mL) / (2.50 atm) 360 mL

Interpreting the Result

The problem indicates that the volume of the gas decreases from 450 mL to 360 mL. This fall in volume is a direct consequence of the increase in pressure. Boyle's Law clearly shows that when the pressure is increased, the volume of the gas decreases proportionally, assuming the temperature remains constant.

Conclusion

This analysis demonstrates how Boyle's Law can be applied to real-world scenarios to calculate changes in gas volume under different pressures. Understanding this principle is essential for studies in chemistry, physics, and engineering, helping professionals in these fields to better predict and manipulate gas behavior in various applications.