Boyle's Law: Applying Gas Laws to Calculate Volume Changes

What information do we need to calculate the new volume of propane?

Given that some propane occupies 2.00 m³ at 18.0°C at an absolute pressure of 3.50 x 10⁵ N/m², what factors do we need to consider to find the new volume when the absolute pressure is halved and the temperature is decreased to -12.0°C?

Answer:

To calculate the new volume of propane in this scenario, we need to consider the initial volume, initial pressure, final pressure, and temperature conditions of the gas.

To solve this problem, we can apply Boyle's Law, which relates the pressure and volume of an ideal gas at constant temperature. The law states that the product of pressure and volume at initial conditions is equal to the product at final conditions. Mathematically, it can be represented as: P1V1 = P2V2.

First, we need to identify the values for the initial pressure (P1), initial volume (V1), final pressure (P2), and final volume (V2). In this case, we have P1 = 3.50 x 10⁵ N/m², V1 = 2.00 m³, P2 = 3.50 x 10⁵ N/m² / 2 = 1.75 x 10⁵ N/m², T1 = 18.0°C = 18.0 + 273.15 K, and T2 = -12.0°C = -12.0 + 273.15 K.

By substituting these values into the Boyle's Law equation and solving for V2, we find that the new volume is 4.00 m³.

This calculation demonstrates how changes in pressure and temperature affect the volume of a gas, showcasing the practical application of gas laws in solving real-world problems.