The ideal gas law deserves a high five! And the bumbling biochemist is here to make it come alive – and put a whole new meaning to the 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. 

Note. adapted from past posts, added video⠀

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:

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 he 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:⠀

Therefore, gases act a lot alike, no matter what the molecules they’re made up of are.  

This has huge implications because it allows us to 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 mole (mol), which is a value like a “dozen” but that means 6×10²³ things instead of 12 
  • the temperature (T) – the higher the temperature, the more energy the molecules have and thus the faster they’ll move around – in these equations, we use temperature measured in Kelvins (K). The Kelvin system is the “same” as Celcius, but “zeroed” so that 0 K is “absolute zero” – you can 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 into the walls of the container (volume is usually in L) 
  • the pressure (p)(usually in units called atmospheres) 

These properties are interrelated, and we can describe the relationship mathematically with the ideal gas law: pV = nRT 

We saw most of those letters above. The one newbie is R, which is just a constant called 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 (one gets bigger as the other gets smaller) -> 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/V₂ = T₁/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 directly proportional to the # 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 (pressure is directly proportional to temperature) 

  • 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. more on that here: 

more about all sorts of things:  #365DaysOfScience All (with topics listed) 👉 or search blog:             

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