What is the pressure of a gas (in torr)

Question

What is the pressure of a gas (in torr) that undergoes isothermal expansion from 312 torr in a balloon of volume 1.61 L to a new volume of 3.56 L?

Answer 1

Hello, Iris,

We can use the gas laws in the following format:

P1V1/T1 = P2V2/T2

Where 1 and 2 represent initial and final.

Since the problem says "isothermal," the temperature stays constant, so T1 = T2, and we can cancel those out, and also rearrange to find P2:

P2 = P1V1/V2

We have the values for everything on the right side, in torr and Liters. So put those in the equation:

P2 = (312torr)*(1.61L)/(3.56L)

Liters cancel and we are left with 141 torr, to 3 sig figs.

Check to see if this makes sense. We took a set amount of gas and only allow it to expand at the same temperature. No gas is added or removed, so for it to expand, the pressure must be dropped. It expanded by almost twice the volume, and we have a pressure that drops by around the same amount, so it makes sense that an answer of 141 torr sounds reasonable.

I hope this helps,

Bob

Answer 2

Isothermal = constant temperature

Given:

P1 = initial pressure = 312 torr

V1 = initial volume = 1.61 L

V2 = final volume = 3.56 L

Asked for:

P2 = final pressure = ?

Consider Boyle's Law ... P1V1 = P2V2 (@ constant temperature)

(312 torr)(1.61 L) = (P2)(3.56 L)

P2 = (312)(1.61) / 3.56

P2 = 141 torr