Exploring Boyle's Law: A Guide to Calculating Gas Volume under Constant Temperature

Understanding the behavior of gases is crucial in chemistry and physics. One fundamental principle that governs this behavior under specific conditions is Boyle's Law. This law, named after the 17th-century chemist Robert Boyle, describes the relationship between the pressure and volume of a gas when the temperature remains constant. This article delves into how to apply Boyle's Law to calculate gas volume changes and how the ideal gas law can be an alternative method for similar calculations.

Boyle's Law: A Basic Overview

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are kept constant. Mathematically, this is expressed as:

[ P_1V_1 P_2V_2 ]

Where:

( P_1 ) is the initial pressure of the gas, ( V_1 ) is the initial volume of the gas, ( P_2 ) is the final pressure of the gas, ( V_2 ) is the final volume of the gas.

Applying Boyle's Law to a Practical Example: Nitrogen Gas Compression

A cylinder contains 2.14 liters of nitrogen gas at a pressure of 76 mm Hg. A piston slowly compresses the gas to 90 mm Hg, with the temperature remaining constant. Using Boyle's Law, let's find the final volume of the gas.

The known values are:

( P_1 76 text{ mm Hg} ) ( V_1 2.14 text{ L} ) ( P_2 90 text{ mm Hg} ) ( V_2 ) is the unknown final volume.

Using the formula:

[ 76 times 2.14 90 times V_2 ]

Rearranging to solve for ( V_2 ):

[ 162.24 90 times V_2 ]

[ V_2 frac{162.24}{90} ]

[ V_2 1.8 text{ L} ]

Thus, the final volume of the gas is 1.8 liters. This calculation demonstrates the direct application of Boyle's Law to determine the volume of a compressed gas.

Using the Ideal Gas Law for Verification: An Alternative Approach

Additionally, the ideal gas law can be used to verify the calculation. The ideal gas law states:

[ P_2V_2 P_1V_1 ]

This can be rearranged to find the final volume:

[ V_2 frac{P_1V_1}{P_2} ]

Substituting the known values:

[ V_2 frac{76 times 2.14}{90} ]

[ V_2 1.81 text{ L} ]

This result closely matches the value we obtained using Boyle's Law, confirming the application of the ideal gas law for volume calculations under constant temperature.

Conclusion

Boyle's Law provides a straightforward method for understanding and calculating the volume changes of gases under constant temperature. Whether you use Boyle's Law directly or leverage the ideal gas law, the fundamental principles remain the same. Understanding these laws is essential for various fields, including engineering, environmental science, and physical chemistry. By mastering these concepts, you can apply them to real-world scenarios where gas behavior under different pressures and volumes needs to be analyzed.