A weather balloon has a volume of 200.0 L at a pressure of 760 mm Hg. As it rises, the pressure decreases to 282 mm Hg. What is the new volume of the balloon? (Assume constant temperature)

The new volume of the balloon is 539 L

Explanation:

As the volume increases, the gas particles (atoms or molecules) take longer to reach the walls of the container and therefore collide less times per unit time against them. This means that the pressure will be less because it represents the frequency of gas strikes against the walls. In this way, pressure and volume are related, determining Boyle's law that says:

"The volume occupied by a given gas mass at constant temperature is inversely proportional to the pressure"

Boyle's law is expressed mathematically as:

Pressure * Volume = constant

o P * V = k

Having an initial state 1 and an final state 2 will be fulfilled:

P1 * V1 = P2 * V2

So, in this case, you know:

Replacing:

760 mmHg*200 L= 282 mmHg*V2

Solving:

V2=539 L

The new volume of the balloon is 539 L