What is the pressure when a gas originally at 1.81 atm and a volume of 1.80 L is expanded to 3.16 L?
The pressure when a gas is expanded from 1.80 L to 3.16 L can be calculated using Boyle's law. Boyle's law states that the pressure and volume of a gas are inversely proportional at constant temperature. This means that the product of pressure and volume remains constant when the temperature is constant.
Given:
Initial pressure (P1) = 1.81 atm
Initial volume (V1) = 1.80 L
Final volume (V2) = 3.16 L
To calculate the final pressure (P2) when the gas is expanded to 3.16 L, we can use the formula:
P1V1 = P2V2
Substitute the given values into the formula:
P2 = (P1V1) / V2
P2 = (1.81 atm * 1.80 L) / 3.16 L
P2 ≈ 1.034 atm
Therefore, when the gas is expanded from 1.80 L to 3.16 L, the pressure decreases to approximately 1.034 atm.
Understanding Boyle's Law
Boyle's law is a fundamental gas law named after the scientist Robert Boyle. It describes the inverse relationship between the pressure and volume of a gas at constant temperature. In simple terms, when the volume of a gas increases, the pressure decreases, and vice versa, as long as the temperature remains constant.
Boyle's Law Formula:
The mathematical expression of Boyle's law is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively. This formula is commonly used to calculate pressure changes when the volume of a gas is altered.
Application to the Given Scenario:
In the provided scenario, the gas initially has a pressure of 1.81 atm and a volume of 1.80 L. When the volume is expanded to 3.16 L, the pressure decreases to approximately 1.034 atm. This pressure change can be accurately predicted using Boyle's law.
Calculation Steps:
1. Identify the initial pressure (P1), initial volume (V1), and final volume (V2).
2. Substitute the values into the Boyle's law formula: P1V1 = P2V2.
3. Calculate the final pressure (P2) by rearranging the formula.
4. Solve for P2 to determine the pressure at the expanded volume.
By following these steps and applying Boyle's law, we can accurately calculate the pressure changes when a gas expands or compresses. This basic principle is crucial in understanding the behavior of gases under varying conditions and volumes.