Could changing chairs be called for? How comfy is your chair? Would you like to try a different one? Sometimes the choice is easy, but other times you have to consider trade-offs between squirminess (enthalpy) & spread-out-ability (entropy). So you have to turn to Kelvin (temperature) to assist you in choosing which to care more about. But you’ll have to follow the store’s laws of thermodynamics!
Why Gibb a damn? A lot of times scientists want to know whether you have to “bribe” a reaction with energy, or whether it can instead occur spontaneously (i.e. you don’t have to give it energy to go). Energy is the ability to do work (like press my fingers down onto the keys of the keyboard to write these words or push a bowling ball up a hill or force protein letters (amino acids) to come together & link up). And change in free energy (ΔG) is like a measure of chemical “drive” that looks at whether the products or the reactants of a reaction are “happier”
I like to think of free energy as a sort of “couch shopping.” Say you’re sitting on a couch. It’s not a very comfortable couch; it’s cramped & hard so you’re squirming around a bit trying to get comfortable. There’s a more comfortable couch across the room. When you’re in that couch you sink right in & can relax & stop squirming. Aaahhh…
BUT in order to get to the comfy couch you have to overcome your laziness & get up off the 1st couch. Whether it’s “worth it” depends on how much comfier the 2nd couch is & this depends on how much less squirmy you’ll be there & how much you’ll be able to spread out
Similarly, whether a reaction will occur spontaneously (i.e. you don’t have to give it energy to go) depends on whether the products have more or less “free energy” than the reactants. We can think of this “free energy” aka Gibbs free energy (G) as overall “comfiness” – it takes into account squirminess (kinetic energy aka HEAT) in the ENTHALPY term (H) & spread-out-ability (randomness/freedom/disorder) in the ENTROPY term (S) and we can equation-size it as:
ΔG = ΔH-TΔS
Δ (delta) means “change in” so this equation looks at DIFFERENCES in H & S between reactants (couch 1) & products (couch 2)
Where’d that T come from? It stands for Temperature & it takes into account the “mood.”
Note on tricky terminology: heat is a type of energy and temperature is the average heat for a group of molecules. So, if you have glass of hot water and a hot tub at the same temperature, the hot tub’s gonna have a lot more heat because there are a lot more molecules with that same average heat.
Enthalpy is a special type of heat that involves energies required to break bonds & energies released when making bonds. The stronger a bond, the more energy required to break it and, going the other direction, the more energy released when making it (the molecules “give up” their squirming so they have less heat), so enthalpy depends on the “bond energies” of the specific bonds being made and broken. Enthalpy also takes into account pressure and volume, but if those are constant, you don’t have to worry about them.
ΔH & ΔS are “constant” because they’re calculated based on the reactants & products. But just like couch 1 & couch 2 don’t change with temperature, but when it’s hot, you care more about spreading out, at higher temps, ENTROPY becomes more & more important
NEGATIVE ΔG means products have LESS FREE ENERGY than reactants, so the “2nd couch is comfier” & the reaction is likely to proceed spontaneously. We call such reactions EXERGONIC
POSITIVE ΔG means products have MORE FREE ENERGY than reactants, so you’ll have to really bribe it to go… We call such reactions ENDERGONIC
How ‘bout enthalpy? That heat stuff? NEGATIVE ΔH means products have LESS HEAT than reactants. This can only happen if reactants give up heat to the “surroundings” & such heat-releasing reactions are called EXOTHERMIC.
POSITIVE ΔH means products have MORE HEAT than reactants, which means reactants “stole” heat from “surroundings.” Such heat-absorbing reactions are called ENDOTHERMIC.
And, finally, we have ΔS to consider – change in entropy. NEGATIVE ΔS means the products have LESS FREEDOM/RANDOMNESS, which can come from having more/stronger bonds tethering the molecules together
POSITIVE ΔS means the products have MORE FREEDOM/RANDOMNESS & can come from having fewer/weaker bonds tethering the molecules together, allowing them to move around more. It’s especially “good” if you can go from a liquid to a gas &/or break up a big thing (which has limited motion because it has to move as a group) into lots of smaller things which can move separately
Another way to think about entropy is the # of possible “states” some system can have. Say you have a group of friends sitting cramped together on one couch. If they split up and each take their own couch you can now have different seating arrangements. And the bigger the couches the more different ways they can sit on it (e.g. splayed out, feet up, etc.)
So reactions are more favorable if they let off heat (have a ➕ ΔH) &/or give the molecules more freedom/randomness (have a ➕ ΔS) BUT it’s the combination of those 2 (& temp) that’s the ultimate decider of whether reaction will occur spontaneously (have a ➖ ΔG).
If we go back to that “spontaneity test:” is ΔG = ΔH-TΔS negative? We can imagine a few different scenarios
Remember, ΔH is the change in enthalpy (heat) (assuming constant temperature and pressure). More specifically, we’re usually looking at “internal enthalpy” aka “enthalpy of the system” – changes of heat in the reacting molecules (system) not all the stuff around them (surroundings) – it will be negative if the reaction releases heat into the surroundings (exothermic) and positive if the reaction takes heat from the surroundings (endothermic).
Temperature (T) is in Kelvin, and in Kelvin, 0 is “absolute 0” meaning you can’t go any lower. So T can never be negative. So it can’t change the sign of the second half of the equation; the sign of that part will always be determined by ΔS. So the only way we can have a positive second half of the equation is if ΔS is negative.
Recall that ΔS is the change in entropy (randomness/disorder/# of possible states). If ΔS is negative it means that there’s lower entropy in the products (this is like having fewer or smaller couches).
If ΔH is negative (the reaction is exothermic) AND ΔS is positive, you can be “positive” the reaction is spontaneous – no matter what the temperature is, ΔG will be negative because a negative minus a positive is always negative. This is like having the option to move to a softer, bigger couch and/or having members of a group originally sitting cramped together on one couch get to each have a soft couch of their own. Yes please!
If ΔH is positive (the reaction is endothermic) AND ΔS is negative, the reaction is NOT spontaneous – no matter what the temperature is. ΔG will be positive because a positive minus a negative is like a positive plus a positive, which is always going to be a positive. This is like having the option to move to a hard, small couch. Or taking a bunch of people each lounging on their own personal couch and telling them they have to squish together on a hard single couch. No thank you!
Those are the “extremes” – the best & worst couch-shopping experiences (both enthalpy & entropy changes were either favorable or unfavorable). But often you have to make some trade-offs between enthalpy & entropy – and temperature acts as your sort of “sales assistant” convincing you which is more important.
T can NOT change the sign of the second half, but it CAN change its magnitude – so it can make ΔS more important (if T Is high) or less important (if T is low).
If ΔH is negative (the reaction is exothermic) BUT ΔS is positive, the sign of ΔG (and thus whether the reaction is spontaneous) depends on whether TΔS is bigger than TΔS. At low temps, ΔH “wins” and, since it’s negative, the reaction is spontaneous. But at high temps, ΔH “loses” and the reaction is not spontaneous. How low or how high T has to be to flip the sign depends on how big ΔH & ΔS are. For example, if you have a really negative ΔH (highly exothermic reaction) you’ll have to get things really hot and/or have a drastic decrease in entropy to make a dent in spontaneity. But if ΔH & ΔS are close, small temperature differences can have more of an impact.
Another way to think about this is to consider heat product or reactant of a reversible reaction and use Le Chatelier’s principle to think about what favors the forwards vs reverse reactions. more here: http://bit.ly/2Pz9O72
In an exothermic reaction like this, you can consider heat to be a “product” of a reversible reaction. And if you “add product” you push the equilibrium of the reaction towards reactants. So adding heat makes the forward reaction less favorable.
Way oversimplified, but it’s kinda like the surroundings “wanting” a certain amount of heat and if they get it from someplace else they don’t need to reaction to make it for them. But the reaction can’t just not give off heat, so the reaction just doesn’t happen.
You can also have a reaction that is endothermic (has a positive ΔH and is thus exothermically unfavorable) BUT is enthalpically favorable (has a positive ΔS). Once again, T will be the deciding factor. But now, it’s more like heat is a reactant. And we want TΔS to be bigger than ΔH (remember TΔS is getting subtracted).
At low temps, ΔH “wins” BUT ΔH is POSITIVE, so the reaction is NOT spontaneous. But at high enough temps, ΔH “loses” and the reaction IS spontaneous.
Don’t confuse “spontaneous” with “likely.” Free energy change is a “state function” – it doesn’t take into account the route between the initial G and the final G (it doesn’t care how you get from one couch to another) – you’re just comparing the 2. There could be a big wall between you and the other couch but moving would still be considered a “spontaneous reaction” if the second couch is more favorable.
And don’t confuse “spontaneous” with “fast” – thermodynamics does not tell you anything about reaction rates. For that sort of thing you have to look to kinetics. For example, rusting is spontaneous but it can be really slow.
And don’t count off endergonic” as “hopeless.” A LOT of the most important reactions that occur in our bodies are endergonic. They’re made to proceed by “coupling” them to an exergonic reaction. This allows us to do things like build proteins from amino acids (energetically unfavorable because it decreases entropy (you’re taking many molecules moving around “randomly” & forcing them together into fewer molecules w/less freedom). You have to put in some energy (in the form of ATP-splitting coupled reactions) but you really wouldn’t want the reaction to be “too easy” because you want to write the protein words you want to write – you don’t just want letters randomly connecting!
So organisms maintain internal order by taking in free energy (G)(from food or sunlight), using it to organize their stuff, then returning energy to the surroundings as heat (H) & entropy (S).
Biochemistry may seem wild, but it still has to follow laws – including LAWS OF THERMODYNAMICS! And they can seem somewhat confusing (especially the second one) unless you keep focus on your place in the universe! “Universe” can mean different things depending on the context and, when talking thermodynamics, universe can mean big U Universe, like the giant “everything” one you’d probably think of if you heard the word. But more commonly we use universe to refer something like a reaction happening in a container.
A UNIVERSE consists of a SYSTEM (e.g. reacting molecules) & their SURROUNDINGS. *We* can define “systems” at different scales and can have systems w/in systems (e.g. single reaction w/in a single cell w/in an organ within a whole person). The important thing is to keep track of system vs. surroundings and know “whose perspective” (that of the system or that of the surroundings) you’re looking from. It’s like how if you give $100 to the bank you’ve lost money but the bank’s gained money.
We can further define systems into a few different types:
- open systems: can exchange heat & matter (physical stuff) with the surroundings
- closed systems: can exchange heat but NOT matter with the surroundings
- isolated systems: can not exchange heat nor matter with the surroundings
When we think about reaction spontaneity, we’re usually looking at things from the system’s perspective, but it’s based on laws of thermodynamics that take into account the “universe”
1st law: CONSERVATION OF ENERGY: energy can’t be created or destroyed, it can only change form (e.g. potential to kinetic (think bowling ball at top of ramp (high potential energy) vs near base of ramp (energy was converted to kinetic energy)) or get “moved”
When we talk about “losing” or “gaining” energy, it’s from 1 perspective (usually the system’s). So when a system “loses” energy, it gives them to the surroundings. So the surroundings gain energy, total energy in the universe remains constant and thermodynamic law enforcement stays happy.
This might remind you of our talk of redox reactions – where molecules give and take electrons – and you can’t have oxidation (electron giving) without complementary reduction (electron taking). When 1 molecule gains e⁻ (is reduced) another molecule had to have lost e⁻ (been oxidized), so the total # of e⁻ didn’t change
2nd law: Entropy (S) of the universe is continuously increasing (Nature likes randomness/disorder (probably can’t say the same about the science journal Nature though…)
This law can seem confusing because reactions often form more stable products w/lower entropy. What Gibbs? Once again, it’s all in perspective. The 2nd law says an increase in S in the UNIVERSE must occur BUT universe = systems + surroundings. So an increase in S in surroundings can compensate for a decrease in S in the system and still lead to fulfillment of the law.
see the figures for an example