You begin with 100mL of air at 1 atm of pressure. How would you change the pressure in your machine to accomplish you goal of 500mL?

P1V1 = P2V2

So what's the answer!?

To change the pressure in your machine while keeping the volume constant at 500 mL, you would need to follow Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant.

Boyle's Law can be mathematically represented as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In this case, you want to increase the volume from 100 mL to 500 mL while keeping the temperature constant. As a result, the pressure must decrease.

Using the Boyle's Law equation, you can calculate the final pressure:

P1V1 = P2V2

(1 atm)(100 mL) = (P2)(500 mL)

Simplifying the equation, you get:

100 mL atm = P2(500 mL)

Dividing both sides of the equation by 500 mL gives:

(100 mL atm) / (500 mL) = P2

Thus, the final pressure, P2, would be 0.2 atm.

To accomplish your goal of 500 mL of air at 0.2 atm of pressure, you would need to decrease the pressure in your machine while keeping the volume constant.