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Pressure is the force exerted by gas particles when they collide with the walls of their container. In the context of the Ideal Gas Law, pressure is an essential variable to understand how gases behave under various conditions. In the given problem, we start with an initial pressure (P1) of 5.20 atm inside the aerosol can. As the gas expands into the plastic bag, the volume increases, and the pressure decreases accordingly, assuming temperature remains constant. This relationship is represented by Boyle's Law, which states that the pressure of a gas is inversely related to its volume when temperature is constant.

The final step is to calculate the new pressure (P2) in the plastic bag. This is done using the formula derived from the Ideal Gas Law, where the Pressure-Volume Relationship can be simplified to:

• P1 x V1 = P2 x V2

This formula helps us understand how changes in volume can affect pressure, given a constant temperature. By substituting known values, the pressure in the bag is found to be approximately 0.97 atm.

When working with gases, converting volumes into consistent units is crucial. In this exercise, the gas initially occupies a volume of 400 mL inside the aerosol can. But, when dealing with equations rooted in the Ideal Gas Law, we need these volumes in liters to work consistently with common pressure-volume equations.

1 liter (L) equals 1000 milliliters (mL). To make the conversion from milliliters to liters, divide the volume in milliliters by 1000:

• 400 mL = 0.4 L

By converting the initial volume to 0.4 L, all volumes in the equation are comparable. It ensures accurate calculations when determining the new pressure after expansion. Incorrect volume units can lead to inaccuracies in calculations, so always check units carefully.

A key assumption in this problem is that the temperature remains constant as the gas moves from the aerosol can to the plastic bag. This assumption is central to applying Boyle's Law, which allows us to link changes in pressure and volume directly, without worrying about temperature changes.

When temperature is constant, we can simplify the Ideal Gas Law to a form that relates only pressure and volume:

• T1 = T2 âž” so, P1 x V1 = P2 x V2

No temperature terms appear in the equation because temperature's constancy ensures that it doesn't affect the relationship of pressure and volume. In real-life scenarios, especially when gases undergo quick expansions or compressions, temperature changes could impact outcomes. But in this controlled problem, focusing on pressure and volume gives clear results.