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### Course: Biology archive > Unit 5

Lesson 3: Free energy# Gibbs free energy and spontaneous reactions

Gibbs free energy and spontaneous reactions.

## Want to join the conversation?

- At several points of the video Sal describes things as being "spontaneous." What exactly does this mean? It seems like spontaneous would be synonymous with random, aka disorder or entropy. What is a good definition of spontaneous on a molecular level?(28 votes)
- Spontaneous just means something happens of itself.

Wiki defines it as: "performed or occurring as a result of a sudden inner impulse or inclination and without premeditation or external stimulus."(24 votes)

- i did not understand what is really gibbs free energy?(15 votes)
- Strictly speaking, Gibbs free energy change determines if a reaction is spontaneous under the conditions of constant pressure and constant temperature, which is usually the situation in biology. Under constant volume for example, then it's something else called the Helmholtz free energy. You really have to take a thermodynamics course to make sense of it. Just try to get the basic idea that going downhill in energy and increasing entropy both favor a reaction happening, and the entropy part becomes more important the higher the temperature.

For most chemical reactions at ordinary temperatues, the enthalpy term is much more important, being on the order of 100,000 cal/mole while the TdeltaS term is on the order of a few cal/mole.(14 votes)

- How do you use this Gibbs equation if you don't know the exact numbers to plug in?(8 votes)
- If I give you an expression E = a * b, and I tell you that a and b are positive, you don't need to know the values of a and b to predict that E is going to be positive (since positive * positive = positive). Similarly, in the Gibbs equation, all that matters is the sign of ΔG, you can use the various rules of signs to infer what the sign of ΔG will be.(6 votes)

- What does entropy-enthalpy mean? Can this lead to something?(6 votes)
- I think you should start here: https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/enthalpy-chemistry-sal/v/enthalpy

and here: https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/entropy-chemistry-sal/v/chem20-entropy (1st video only)

before you have a look at Gibbs Free Energy :)(7 votes)

- What are the numbers for low T and high T? Low and high are not sufficiently defined. And buzz? Too technical for me.(5 votes)
- Good question! 'Low T' and 'High T' relate to the specific thermodynamic process being discussed and whether or not Gibbs free energy is negative (spontaneous) or positive (non-spontaneous) for each of the different possible combinations (i.e. G, H, T, S). For example, when Mr. Khan was talking about a spontaneous Gibbs free energy process - if delta H (enthalpy) was positive and delta S (entropy) was positive, the temperature would need to have a "High T" or high enough to make delta G (Gibbs free energy) negative overall and thus a spontaneous process. So, what Mr. Khan is describing regarding temperature is that it is either low or high enough for the specific example he is describing to either be a spontaneous or non-spontaneous Gibbs free energy process. I hope this helps to answer your question!(5 votes)

- How can a reaction releases energy (negative delta H) but gains free workable energy (positive delta G)? Does enthalpy not represent the total energy of a system? Or does it mean free energy is not a sub group of total energy.(5 votes)
- the type of reaction in which energy is released is called exothermic reaction you may take an example of acid...you might have added water to acid in laboratory the reaction of water with acid release heat(thats what energy is) and by touching the beaker you will feel something really hot...the energy utalized in the reaction is called enthalpy change..and therefore it explains that is energy released(exothermic) in the reaction or absorbed(endothermic)...(3 votes)

- Hmmm this video was over my head. :((4 votes)
- I recommend reading the Free energy article on here (Biology Library > Unit 7 > Lesson 3) as I think it does a better job defining terms, though I will admit this is certainly one of the toughest sections on here and I didn't completely grasp all the concepts. It also has a table of all 4 combinations (which I believe Sal also does in the next video) which is helpful.

As for the math, it's all arithmetic. For example, subtracting something positive from a negative number is always negative. For the two cases where the arithmetic could go either way, that's where T matters. For example, if both DeltaH and DeltaS are negative, the sign of DeltaG will depend on how big T is.(2 votes)

- In the first example that Sal did, there were 5 atoms, to begin with, and then once they collided I only saw four atoms. Where did that atom go?(3 votes)
- How does knowing the spontaneity of a reaction help a scientist? What are the applications?(4 votes)
- That is a quite interesting question!

The first thing which comes to my mind is that it helps you in order if you want to simulate it (do it experimentally in a lab).

The second is that you*have*to know if a reaction happens spontaneously so you can predict or prevent a resulting reaction. Imagine what would it be if people could spontaneously combust under certain circumstances? We would avoid them, right?

Also, you have to knwo if reaction is ponatenous in terms of efficacy of work (such as electric circuits). If reactions happen spontaneously means it emits lots of thermal energy, therefore, you require a cooling system to prevent overheating.(1 vote)

- How can you quantitatively measure entropy?(2 votes)
- S = k * log W

where: S is entropy, k = Boltzmann constant, W = number of thermodynamic microstates for given system(3 votes)

## Video transcript

- [Voiceover] We're going
to explore Gibbs Free Energy a little bit in this video. And, in particular, its
usefulness in determining whether a reaction is going
to be spontaneous or not, which is super useful in
chemistry and biology. And, it was defined by
Josiah Willard Gibbs. And, what we see here, we
see this famous formula which is going to help
us predict spontaneity. And, it says that the
change in Gibbs Free Energy is equal to the change, and
this 'H' here is enthalpy. So, this is a change in enthalpy which you could view as heat content, especially because this formula applies if we're dealing with constant
pressure and temperature. So, that's a change in enthaply minus temperature times change in entropy, change in entropy. So, 'S' is entropy and it seems like this bizarre formula that's
hard to really understand. But, as we'll see, it makes
a lot of intuitive sense. Now, Gibbs Free, Gibbs,
Josiah Willard Gibbs, he defined this to think about, well, how much enthalpy is going to be useful for actually doing work? How much is free to do useful things? But, in this video, we're
gonna think about it in the context of how we can
use change in Gibbs Free Energy to predict whether a reaction is going to spontaneously happen, whether it's going to be spontaneous. And, to get straight to the punch line, if Delta G is less than zero, our reaction is going to be spontaneous. It's going to be spontaneous. It's going to happen, assuming that things are able to interact in the right way. It's going to be spontaneous. Now, let's think a little bit
about why that makes sense. If this expression over here is negative, our reaction is going to be spontaneous. So, let's think about all
of the different scenarios. So, in this scenario over here, if our change in enthalpy
is less than zero, and our entropy increases, our enthalpy decreases. So, this means we're going to release, we're going to release energy here. We're gonna release enthalpy. And, you could think about this as, so let's see, we're gonna release energy. So, release. I'll just draw it. This is a release of enthalpy over here. I end up with less enthalpy
than I started with. But, entropy increases. Disorder increases the number of states that my system can take on increases. Well, this makes a lot of sense. This makes a lot of sense that this is going to
happen spontaneously, regardless of what the temperature is. I have these two molecules. They are about to bump into each other. And, when they get close to each other, their electrons may be, say hey, "Wait, there's a better configuration here "where we can go into lower energy states, "where we can release energy "and in doing so, "these different
constituents can part ways." And so, you actually
have more constituents. They've parted ways. You've had energy released. Entropy increases. And, makes a lot of sense
that this is a natural thing that would actually occur. This over here, this is spontaneous. Delta G is, not just Delta, Delta G is less than zero. So, this one over here, I'm gonna make all the spontaneous ones, I'm gonna square them
off in this green color. Now, what about this one down here? This one down here, Delta
H is greater than zero. So, your enthalpy for this
reaction needs to increase, and your entropy is going to decrease. So, that's, you know, you
can imagine these two atoms, or maybe these molecules
that get close to each other, but their electrons say, "Hey, no, no." In order for us to bond, we would have to get to
a higher energy state. We would require some energy, and the disorder is going to go down. This isn't going to happen. And so, of course, and
this is a combination, if Delta H is greater than zero, and if this is less than zero, than this entire term
is gonna be positive. And so, Delta G is going
to be greater than zero. So, here, Delta G is going
to be greater than zero. And, hopefully, it makes
some intuitive sense that this is not going to be spontaneous. So, this one, this one does not happen. Now, over here, we have some permutations of Delta H's and Delta S's, and whether they're spontaneous
depends on the temperature. So, over here, if we are dealing, our Delta H is less than zero. So, we're going to have
a release of energy here, but our entropy decreases. What's gonna happen? Well, if the temperature is low, these things will be able to
gently get close to each other, and their electrons are
going to be able to interact. Maybe they get to a lower energy state, and they can release energy. They're releasing energy, and the electrons will
spontaneously do this. But, the entropy has gone down. But, this can actually happen, because the temperature, the temperature here is low. And, some of you might be saying, "Wait, doesn't that violate "The Second Law of Thermodynamics?" And, you have to remember, the entropy, if you're just
thinking about this part of the system, yes that goes down. But, you have heat being released. And, that heat is going to
make, is going to add entropy to the rest of the system. So, still, The Second Law
of Thermodynamics holds that the entropy of the
universe is going to increase, because of this released heat. But, if you just look at
the constituents here, the entropy went down. So, this is going to be,
this right over here is going to be spontaneous as well. And, we're always wanting
to back to the formula. If this is negative and this is negative, well, this is going to be a positive term. But, if 'T' low enough, this term isn't going to matter. 'T' is, you confuse it as the
weighing factor on entropy. So, if 'T' is low, the entropy
doesn't matter as much. Then, enthalpy really takes over. So, in this situation, Delta G, we're assuming 'T' is low enough to make Delta G negative. And, this is going to be spontaneous. Now, if you took that same scenario, but you had a high temperature, well now, you have these
same two molecules. Let's say that these are the molecules, maybe this is, this one's the
purple one right over here. You have the same two molecules here. Hey, they could get to a more kind of a, they could release energy. But over here, you're saying, "Well, look, they could." The change in enthalpy is negative. But, they're buzzing past each other so fast that they're
not gonna have a chance. Their electrons aren't gonna have a chance to actually interact in the right way for the reaction to actually go on. And so, this is a situation
where it won't be spontaneous, because they're just gonna
buzz past each other. They're not gonna have a
chance to interact properly. And so, you can imagine if 'T' is high, if 'T' is high, this term's
going to matter a lot. And, so the fact that entropy is negative is gonna make this whole thing positive. And, this is gonna be more positive than this is going to be negative. So, this is a situation where our Delta G is greater than zero. So, once again, not spontaneous. And, everything I'm doing
is just to get an intuition for why this formula for
Gibbs Free Energy makes sense. And, remember, this is true
under constant pressure and temperature. But, those are reasonable assumptions if we're dealing with, you know, things in a test tube, or if we're dealing with a
lot of biological systems. Now, let's go over here. So, our enthalpy, our change in enthalpy is positive. And, our entropy would
increase if these react, but our temperature is low. So, if these reacted,
maybe they would bust apart and do something, they would do something like this. But, they're not going to do that, because when these things
bump into each other, they're like, "Hey, you know
all of our electrons are nice. "There are nice little
stable configurations here. "I don't see any reason to react." Even though, if we did react, we were able to increase the entropy. Hey, no reason to react here. And, if you look at these
different variables, if this is positive,
even if this is positive, if 'T' is low, this isn't going to be able to overwhelm that. And so, you have a Delta G
that is greater than zero, not spontaneous. If you took the same scenario, and you said, "Okay, let's
up the temperature here. "Let's up the average kinetic energy." None of these things are going to be able to slam into each other. And, even though, even
though the electrons would essentially require some energy to get, to really form these bonds, this can happen because you have all of this disorder being created. You have these more states. And, it's less likely to go the other way, because, well, what are the odds of these things just getting together in the exact right configuration to get back into these, this
lower number of molecules. And, once again, you look
at these variables here. Even if Delta H is greater than zero, even if this is positive, if Delta S is greater than zero and 'T' is high, this thing is going to become, especially with the negative sign here, this is going to overwhelm the enthalpy, and the change in enthalpy, and make the whole expression negative. So, over here, Delta G is
going to be less than zero. And, this is going to be spontaneous. Hopefully, this gives you some intuition for the formula for Gibbs Free Energy. And, once again, you have to caveat it. It's under, it assumes constant
pressure and temperature. But, it is useful for thinking about whether a reaction is spontaneous. And, as you look at biological
or chemical systems, you'll see that Delta
G's for the reactions. And so, you'll say, "Oh,
it's a negative Delta G? "That's going to be a
spontaneous reaction. "It's a zero Delta G. "That's gonna be an equilibrium." Or, you could say, "That's
a positive Delta G. "That's not going to be spontaneous."