A gas‑filled weather balloon has a volume of 50.0 L at ground level, where the pressure is 769 mmHg and the temperature is 22.8 ∘C. After being released....

Question

A gas‑filled weather balloon has a volume of 50.0 L at ground level, where the pressure is 769 mmHg and the temperature is 22.8 *C. After being released, the balloon rises to an altitude where the temperature is -2.37*C  and the pressure is 0.0836 atm. What is the weather balloon's volume at the higher altitude?

Answer 1

What are we given, and what are we being asked to find?

Given:

V1 = initial volume = 50.0 L

P1 = initial pressure = 769 mm Hg

T1 = initial temperature = 22.8ºC

P2 = final pressure = 0.0836 atm

T2 = final temperature = -2.37ºC

Asked to find:

V2 = final volume

This requires us to use the combine gas law: P1V1/T1 = P2V2/T2

But before doing this, we must get all of our units correct. Temperatures have to be in Kelvin, so we will add 273 to the ºC

T1 = 22.8 + 273 = 295.8K

T2 = -2.37 + 273 = 270.6K

Also, we will change P1 to units of atmospheres to agree with P2.

P1 = 769 mm Hg x 1 atm / 760 mm Hg = 1.01 atm

Now plugging in the values and solving for V2, we have...

P1V1/T1 = P2V2/T2

(1.01 atm)(50.0 L) / 295.8K = (0.0836 atm)(V2) / 270.6K

V2 = 553 liters

(please be sure to check the math)