Highschool Chem

Question

A certain flexible weather balloon contains helium gas at a volume of 855 L. Initially, the balloon is at sea level where the temperature is 25°C and the barometric pressure is .947atm

The balloon then rises to an altitude of 5500 ft, where the pressure is .758atm and the temperature is 15°C. What is the change in volume of the balloon (in L) as it ascends from sea level to 5500 ft?

If you can show work on how to actually solve it that would be great.

Answer 1

Look at what you are given, and what you are asked for.

Given:

Initial volume = V1 = 855 L

Initial pressure = P1 = 0.947 atm

Initial temperature = T1 = 25ºC + 273 = 298K (always work in K when dealing with gases)

Final pressure = P2 = 0.758 atm

Final temperature = T2 = 15ºC + 273 = 288K

Asked for:

Final volume = V2 = ?

For this problem, you can used the Combined Gas Law: P1V1/T1 = P2V2/T2

Calculations:

(0.947)(855) / (298) = (0.758)(V2) / 288

V2 = (0.947)(855)(288) / (298)(0.758)

V2 = 1032 L

Since the problem actually asks for the CHANGE in volume, it would be ...

1032 L - 855 L = 177 L = change in volume

Answer 2

Hi Bill O.,

One way you could set a problem like this up is by using the Universal Gas Law:

pV = nRT

Since you are dealing simultaneously with changes in pressure, temperature, and volume, move these three variables to the same side of the equation, and everything else to the opposite side:

pV/T = nR

Now you know that there has been no loss of He (n in this case), and that R is a constant.

So therefore, p1V1/T1 = p2V2/T2

Convert those temperatures into K (as you always must!), plug in and crank.

That's a sure-fire method.

But you can set it up as an immediate calculation also by starting with your initial volume and multiplying by ratios of the altered variables. To do this, you have to have immediate grasp of what temperature and pressure do to volume, namely, T has a direct relationship and p has an inverse relationship. Again, you need to convert the temperatures to K first (well, you could convert them to any other scale that runs up from absolute zero -- such as Rankine -- but why bother). So V2 = V1*(T2/T1)*(p1/p2) . And crank.

-- Cheers, --Mr. d.