CO2 escapes a balloon faster than helium! – when Graham’s Law doesn’t apply

I thought it would be nice to do a little demonstration about the relative sizes of different atoms and molecules. Naively I thought I could demonstrate Graham’s law with the use of a few party Balloons and a couple of readily available gasses, little did I know just how deep the rabbit hole would go.

So starting out I thought it would be simplest to use great big balloons and take data over a long period of time. But to do this I knew I would need a lot of gas, helium was easy enough and nitrogen was all around me but I needed another gas. At the time I did not have any idea that CO2 would react differently so I went about making a Recipe for the full 10 liters needed to fill the great big balloon. While the recipe worked splendidly the results were not what I expected. The helium seemed fine and even though the Nitrogen didn’t change much it seemed okay, but the CO2 deflated very rapidly. I figured it was something specific to the CO2 and the latex, so I went for other materials. In this case I found Condoms could work since they were at least a different kind of rubber or possibly an organic material. I also swapped in another gas. Little did I guess that these changes would not change the overall result, that bigger molecules have a way of escaping faster than smaller ones. Only after a great deal more research did I figure out that there were more factors acting on the gas passing through the balloons than I had accounted for. With this knew knowledge I tried to get a wide range of gasses, that were either more driven by the molar mass (Helium, Nitrogen and Oxygen) and others that were likely to be more solubility driven (difluoroethane, Butane and CO2 ). Also With this many gasses (and potentially very flammable ones) I didn’t want to have to fill large balloons so I chose water balloons since they are readily available. This final setup is the experiment that follows but I will also show the Data from the first two attempts.

Materials:
At least three sources of simple gases likely to be primarily driven by their molar mass, I used Helium, Nitrogen and Oxygen (Other good candidates are Hydrogen, and Argon). All of these gasses are readily available from welding supply outlets but I chose the three I did because I could get them with little cost. Depending on the source you may need additional equipment, like a reaction chamber of you are doing chemistry to get the gasses.

You will also need a few gases that are likely to be more solubility driven, I used difluoroethane (the chemical in canned air canisters), butane and carbon dioxide (Other good candidates are methane, acetylene, propane ). Again I chose the ones I did because they are easily available.

A package of water balloons, at least 18 so you can do an average of three different balloons but preferably more since some of them can be poorly made.Again you may need special equipment to get these depending on the source, I had to modify the canisters I had so that they could be used with a balloon.

Flexible tape measure (like for measuring cloth) to keep track of the balloon size.

Marker for writing on the balloons.
Experimental steps:

  1. The first step is going to be picking your gasses and making sure you have a way to fill the balloons. For helium you can probably get a small tank from the store and use as directed. Nitrogen is also easy since the air is about 95% nitrogen and you can simply blow up the balloons. The other gases will vary in complexity and may require modifying dispensing mechanisms or making a reaction chamber.
  2. Order the gasses from most soluble to least soluble. You can look this up specifically in some cases but as a general like dissolves like. That is things with carbon and hydrogen will dissolve easily into rubbers while things that do not have these will dissolve less easily. This can be additionally modified by the relative mass of the gas (CO2 going faster than Butane for instance) but small differences will not cause too much of a problem.
  3. Fill 3 or more balloons of each gas starting with the least soluble. If you start with the more soluble gasses they will begin to deflate before you have finished filling the other gasses and interfere with the size comparison. Also the reason to do a few is to account for variation in exact volume and manufacturing quality of the balloons.
  4. Mark each balloon when filled to keep track of what is inside.
  5. After all the balloons are filled measure the circumference of the balloons to get an estimate for the volume. The balloons are nearly spherical and with a small amount of algebra one can find the volume from this one number.
  6. Continue measuring the balloon’s circumference at approximately 10 minute intervals for the first hour. Afterward the speed of deflation slows for most gases and the  frequency of measurement can be reduced if desired (like for sleeping).
  7. Keep measuring until balloons are nearly flat or stabilized at some small value.Calculate the change in volume over time and compare.

Data:

Original Three balloon’s measurements and volume change:

BigBalloons_FullTable

Condom change in volume over time:

CondomsTableData

Water balloon’s with various gases volume over time:

SmallBalloonsRaw

Water balloon’s with various gases volume over time adjusted for difference in starting volume:

SmallBalloonsAdjusted

Graphs:

Original balloons:
BigBalloons_Graph

Non-LatexGraph

Lambskin-Graph

SmallBalloonsRaw_Graph

SmallBalloonsAdjusted_Graph

Results and Interpretation: As described in the video the initial hypothesis based off of graham’s law of effusion predicted that carbon dioxide gas should escape 3.3 times slower than the helium. This turned out to be wildly wrong. Across all trials and different experimental design the carbon dioxide was far and away escaped the fastest.

The reason for this is that the carbon dioxide has a solubility factor that greatly affects its permeation through the rubber that isn’t taken into account with Graham’s law. While many of us have been taught at least a bit about graham’s law in chemistry class, like so many of these simple laws they only apply to special cases and most of the time the true behavior of a gas or chemical process is far more complicated. Yet time and again these laws are presented as completely explaining all there is to know about a subject. Where it is possible to find the values of solubility a more accurate predictive model would be to use Fick’s law, as mentioned in the video.

FullFick'sLaw.png

This is somewhat more complicated but in the case of the balloon many of the terms can be ignored. For instance while the pressure difference between inside and outside the balloon is small it will be essentially the same for all gases. Likewise if the balloons are about the same size we can ignore the area, and the thickness is similarly consistent. In other words there is some number but since the number is shared between all the gases that information can be dropped from the examination. as such Fick’s law just simplifies to essentially the diffusivity constant which consists of both the solubility and the square root of the molar mass:

SimplifiedFick's.png

Note this version of Fick’s law is not how it’s always written, you will often see it in a compacted form where the flux, that is the amount of gas leaving per unit area per unit time is equal to the diffusivity constant times the change in concentration across the change in thickness of the membrane, which is written like this.

CalcFick's

Here the J represents the flux. D is the solubility divided by the square root of the molar mass and when called for also includes the temperature. dc/dx just means how much gass is where in the thickness of the material.

The long and the short of this though is that gas passing through a membrane requires a more complex modeling of the behavior than we are led to believe by our introduction to chemistry examples. In truth this is an entire field of study with lots and lots of papers with different models explaining the behavior of the various gasses, some more analytically and others more empirically but there is a lot to learn. If you would like to try some out check out the sources in the linkography.

Linkography:

Baking Soda and Vinegar stoichiometry

http://www.webqc.org/balance.php?reaction=C2H4O2+%2B+NaHCO3+%3D+NaC2H2O2+%2B+H2O+%2B+CO2
http://antoine.frostburg.edu/chem/senese/101/gases/faq/co2-from-vinegar-and-baking-soda.shtml

Oh man apparently the diffusivity and solubility of CO2 are important. It’s like every serious mountain biker knows about this. Woah.
http://www.sciencedirect.com/science/article/pii/S037673880600202X
http://www.madsci.org/posts/archives/may98/895552329.Ch.r.html
http://stayfill.com/faq/
http://stayfill.com/wp-content/uploads/STAYFILLmsds2_09.pdf
http://velonews.competitor.com/2009/02/bikes-and-tech/technical-qa-with-lennard-zinn-large-molecules-and-short-frames_87175
http://www.sisweb.com/referenc/msds/dustoff.pdf
http://perfectdata.com/products/msds/PD-105842-1%20%28M-5670.01%29%20PERFECT%20DATA%20DUSTERS%20OSHA%20GHS%20100314.pdf

——-Condoms —–
https://en.wikipedia.org/wiki/Condom
https://en.wikipedia.org/wiki/AT-10_resin
https://en.wikipedia.org/wiki/Synthetic_rubber
https://en.wikipedia.org/wiki/File:Condoomgebruik_in_de_19e_eeuw.png

Oh gawd!! Condoms not working either…need to do more research.
http://www.thenakedscientists.com/forum/index.php?topic=39542.0
http://www.madsci.org/posts/archives/may98/895552329.Ch.r.html
https://en.wikipedia.org/wiki/Solubility
https://en.wikipedia.org/wiki/Flory–Huggins_solution_theory
https://en.wikipedia.org/wiki/Entropy_of_mixing#Gibbs_free_energy_of_mixing
https://www.youtube.com/watch?v=SL1qwsQMp_8
https://www.youtube.com/watch?v=l244A_6BJno
http://ac.els-cdn.com/S1877705812034236/1-s2.0-S1877705812034236-main.pdf?_tid=030e1b7e-41d2-11e5-8714-00000aab0f01&acdnat=1439480775_c215334f73d8cc3296d8bcb85b925726
http://www.google.com/patents/US2966235
http://journals.lww.com/anesthesia-analgesia/Citation/1929/09000/The_Diffusibility_of_Anesthetic_Gases_Through.22.aspx
http://users.encs.concordia.ca/~woodadam/GCH6101/Diffusion%20and%20permeability%20in%20polymers.pdf
ftp://ftp.bgc-jena.mpg.de/pub/outgoing/athuille/Publications/2004/Sturm_JoGR_2004.pdf
http://www.nist.gov/srd/upload/jpcrd567.pdf
http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291099-0488%2820000201%2938:3%3C415::AID-POLB8%3E3.0.CO;2-Z/pdf   — This is the paper I was holding in the video,Page 6/420

Graham’s Law and Fick’s Law and absorption
https://www.youtube.com/watch?v=Cg4KlmI_acs
https://www.youtube.com/watch?v=rKJ8gTGcYGw
https://www.youtube.com/watch?v=aNAWy60Q384
https://www.youtube.com/watch?v=cmh1nKCAggA

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