The IDEAL GAS LAW #thebumblingbiochemist-style puts a new meaning to words “jumping off the page!” Ever had to write a paper and there’s a page limit so you either increase the spacing to fill the page or (if you’re like me and always write too much) you squishthewords closer together to cram them in?
Dealing with the behavior of gases is kinda like that. Gas molecules will spread out to fill the container they’re in, with the “word spacing” and “page limit” (volume) being decided by the temperature, pressure, and # of words. And we can convert between them using the IDEAL GAS LAW pV = nRT. Ideally, you wouldn’t have to worry about page limits but things are never ideal. But a lot about gases can be explained if we assume that they are.
There are 3 common states of matter – solid, liquid, & gas – & the difference between them is how much energy the molecules have & whether that’s enough for them to overcome the attractions from nearby molecules. more here: http://bit.ly/2BrRhki
Even in solids, molecules are vibrating, trying to break free. If they can’t, they’re stuck in place, bound to the molecules they can’t escape. If they get some more energy, then can slide around, breaking off some bonds but quickly getting grabbed by other molecules. Only in a gas do the molecules have enough energy to break free. And since they’re free, they’re no longer as influenced by the molecules around them. So gases act a lot alike, no matter what the molecules they’re made up of are.
Gas molecules move around so quickly they’re more like a “blur” than individual words and even with the strictest page limits, the words are so far apart that their actual identity doesn’t matter. So instead of dealing with individual words it’s more like you’re dealing with dots or “point particles.”
These particles spread themselves out so that (although they’re constantly moving around) for any give set of conditions (temperature, pressure, volume) the average distance between any 2 of them (the “word spacing”) is constant. So, for any temperature (T) & pressure (P) you can determine the “page limit” (volume, (V)) and from the “page limit” you can determine how many words would fill it.
The higher the temperature and/or lower the pressure, the “looser” the limit so you have more writing space to fill. The higher the pressure and/or lower the temperature, the “stricter” the limit – you have to squish the words together more.
If you squish them together too closely and/or remove too much energy they will start to interact – and if they can’t overcome those interactions, they can go from a gas to a liquid to a solid.
There are a few assumptions you have to make and perhaps the most confusing is the assumption that the actual “words” don’t matter because you assume that…
They don’t interact with one another – unlike in real life, “cats” and “dogs” kinda ignore one another – they’re running around so fast they don’t have time to get distracted.
The molecules are considered to be moving kinda like billiard balls – they move in straight lines until they hit something (like another molecule or a container wall) and then they bounce of in an “elastic collision” (the energy doesn’t get transferred to the other molecule it just gets used to “change direction”
The size of the words doesn’t matter – “cat” and “supercalifragilisticexpialidocious” behave the same because, although supercalifragilisticexpialidocious might look huge on paper, it’s tiny compared to the distance between it and the closest other words
This sort of assumption might remind you of colligative properties – things like boiling point elevation & freezing point depression – in those cases you’re dealing with solutions & the identity of the dissolved thing (solute) doesn’t matter. More here: http://bit.ly/2HyAwqe
So we can describe and predict the properties of any gas just by knowing a few things:
- how many molecules of gas there are (n) (measured in a quantity called the mol – a value like a “dozen” but that means 6×10^23 things instead of 12)
- the temperature (T) – the higher the temperature, the more energy the molecules have and the faster they’ll move around – in these equations, we use temperature measured in Kelvins (K) – same as Celcius, but “zeroed” so that 0 K is “absolute zero” – convert from C to K by adding 273.15
- the volume (V) – the smaller the volume, the more the molecules are likely to bump into one another or the walls of the container (usually in L)
- the pressure (p)(usually in atmospheres)
These properties are interrelated, and we can describe the relationship mathematically with the IDEAL GAS LAW: pV = nRT
(R is just a constant, the “ideal gas constant,” – 0.0821 L × atm × mol-1 × K-1)
There are different names for different arrangements of the variables👇
Boyle’s law -> P1V1 = P2V2
👉 says if you keep temperature constant, pressure & volume are inversely related -> if you squish the same amount of stuff together more, you compress it, so it takes up less space
Basically, Boyle’s Law says if you wad up a piece of paper, the words on it get closer together and the paper takes up less space.
Charles’s law -> V1/T1 = TV/T2
👉 says if you keep pressure constant, gas expands when heated because the molecules have more energy to move around and venture farther away from one another -> take up more space
Basically, Charles’s Law says if you increase the spacing between words, the same # of words will take up more pages
Avogadro’s law -> V∝ n (volume is proportional to # of molecules)
👉 if temp & pressure are the same, the same volume of gas will have the same number of gas molecules, no matter what those molecules are (you can only fit a certain amount of gas molecules into a certain volume -> to add more you have to increase the volume)
👉👉 if you increase the number of gas molecules (n), you increase the volume (V) -> because gas molecules can move farther apart from one another than liquid or solid molecules, the same number of gas molecules will take up more room than that number of solid or liquid molecule
Basically, Avogadro’s Law says if you add words without changing the word spacing, your “essay” will be longer & take up more pages
Gay-Lussac’s Law-> P∝ T
👉 at a constant volume, pressure & temperature are directly related -> higher temperature means molecules are more likely to run into each other and walls of container, putting pressure on them
Basically, Gay-Lussac’s Law Law says if you add heat without increasing the page limit, the words will really want to “jump off the page” – but they can’t, so they just increase the pressure on the book binding as they try to!
A fun demonstration of the ideal gas laws is Peeps dueling. Marshmallows are sugar, water, corn syrup, and gelatin, whipped together to trap in air. Marshmallows get their “original” size by whipping (mechanical process) with air getting locked into place by the gelatin (a mix of polypeptides (protein strands) that come from chopping up the protein collagen (the protein that gives your skin strength)). Even though the air is trapped in your marshmallow, you can get it to try to escape by heating it up. The molecules start banging harder agains the mallow trap. They can’t get out, but they do “deform” their walls – push them out, making the marshmallow expand. And you get more molecules to join – water molecules gain energy and they want to be gasses to so they join in.
You’re dealing with 3 states of matter in these chicks – solid (sugar & gelatin), liquid (water trapped in & keeping things moist), & gas (the air molecules trapped in pockets). When you microwave a Peep, it gets a lot bigger, demonstrating Charles’ law (the trapped air molecules heat up and start banging against their gooey case, pushing them out, and Avogrado’s law – water molecules enter the gas phase, so you add more moles of gas (increase n)
When you remove the heat, the Peep shrinks back down (Charles’ law). And it hardens because you’ve evaporated out that water that was keeping it moist.
If you want some Peeps humor, Atlanta’s Emory University has a really funny website http://peepresearch.org/ . Also check outhttps://students.millikin.edu/~acs/HTML/peep_revenge.html
If you’ve been following along, this might remind you of our discussion of bread leavening. In bread, the bubbles are made “in place” by yeast as byproducts from fermentation, and locked into place by gluten proteins http://bit.ly/2Zm7KAa