[mscchephy]

Hello,
I'm desperate for some help.
I'm a high school chemistry teacher, and I love pushing my students and I love being as practical in my teaching as possible.
We discussed the Ideal Gas Law and practiced using it for a few days with sample problems from the textbook.
Today I wanted to use it to prove it works by calculating the volume of a balloon that I would blow up in class.
I massed the rubber balloon before and after blowing it up ( .129 gram difference), and I used the molar mass of exhaled air (29 g/mol) to find the number of moles of gas I put into the balloon.  ( 0.00445 moles )
I have a barometer in the room for the pressure.  ( 99.65 kPa )
I have the temperature of the balloon. ( 293 K )

So I put it into the formula where V = nRT/P
V =  0.0045 mol   ·  8.314  kPa  ·  L  ·  293 K  /  99.65 kPa  ·  mol  ·  K   =   0.108 L

BUT.. it's obvious that the balloon that I blew up is over a liter in volume, not a tenth of a liter.

Does anyone know why it would be off by a factor of 10?  It's very frustrating... (sigh)

[Corribus]

Well I can think of four possible problems.

First, you don't exhale air (more on that in a sec) so the molecular weight is probably off.

Second, I would bet weighing the balloon isn't a great way to determine the amount of air inside, because the gas pushes in all directions, not just down into the balance. (Another way to put this: the balance measures weight, not mass - in most cases this isn't an issue because the primary force acting on the weighed mass is downward, but this isn't the case in a balloon). If your calculation uses a much smaller amount of gas in the balloon than there actually is, your calculated volume will be much smaller than actual.

Third, the pressure inside the balloon is higher than atmospheric pressure because of the tension in the balloon. We know this: it takes work to blow up the balloon; if the pressure were the same as atmospheric... well, you get the idea. I tried to find out what the pressure inside a party balloon actually is... seems to be on the order of 1.1 atm, or 10% higher than atmospheric. If the pressure is higher on the inside than your assumption, the calculated volume will be less even if the ideal gas assumption holds.

Finally, are we sure the ideal gas assumption holds? Your breath contains a lot of water, which is frequently not ideal, especially under higher pressure situations.

Do those issues add up to a factor of 10? I'm guessing the balance issue is the biggest one. At STP, a mole of gas is about 22.4 liters. If we estimate that your filled balloon has 1 L of gas in it, and we assume standard conditions, then that's ~0.044 moles of gas, almost exactly 10 times more than you are calculating by your balance. Check!

The experiment isn't a bust though - a good class activity may be to brainstorm for reasons the experiment did not work in this case.

[Borek]

Have you accounted for buoyancy? IMHO the mass difference you observe tells us much more about the changed composition of the air in the balloon (higher fraction of CO₂) and the higher internal pressure (balloon squeezing the air) than about the air trapped inside.

[Borek]

the gas pushes in all directions, not just down into the balance

I don't see why it should matter. Balance is not reacting to the gas pressure, but to the weight of the balloon with its content.

[Corribus]

I don't see why it should matter. Balance is not reacting to the gas pressure, but to the weight of the balloon with its content.

LOL, I don't know. I was just thinking out loud. I agree buoyancy matters - certainly imagine if the balloon were filled with helium instead of air, where the reduced density of helium more than compensates for the mass/weight of the balloon. The balance wouldn't be able to record a weight at all, since the buoyant force upward would be larger than the force due to gravity. In the case of air, the density of air in the balloon is higher than the air outside the balloon, since as I've said the pressure in the balloon is higher than the pressure outside the balloon, so the balloon will sink until the density of air (plus balloon) is larger than the density of the atmosphere - but it will hit the ground/balance first unless the ground is in a really deep hole. Yes? I could be wrong but this seems to be more or less equivalent to the point I think I was trying to make. In the case of a balloon filled with a fluid (in this case a gas), there are more forces than just the downward force of gravity that come into play, and the balance is not equipped to account for them. Meaning that the weight recorded by the balance cannot easily be converted into a mass. (I imagine a scenario opposite of helium, this time where the balloon is instead filled with water - here the buoyancy force is so small compared to the force of gravity because of the huge density of water that buoyancy can be completely neglected and the weight recorded by the balance is easily correlated to the corresponding mass.)

Ultimately it's clear that weighing the balloon this way does not give anywhere near the correct mass of the air inside the balloon, and almost certainly dominates the error in the OP's experiment.

[Enthalpy]

Avoiding that buoyancy ruins this experiment is difficult. One possibility:
Use a bottle of pressured air, nitrogen, oxygen... to inflate the balloon.
Have the bottle on scales, weigh it before and after inflating the balloon.

You need scales sensitive enough despite carrying the heavy bottle. The gas' temperature in the balloon must also be stabilized and known, which isn't trivial after an expansion.

An other possibility is to have a void bottle on scales and let air in. Same difficulties.

[mscchephy]

Hello again,
I printed and addressed the items that each of you expressed and the class had a good discussion.
I always try to keep the quantities and units as practical as possible.  I try to avoid students just plugging numbers into formulas, etc.  This seemed like a good idea and it did force us to reexamine where we had inadvertently included error.

Again, I appreciate everyone who responded....

God bless,
Scott