 So as we continue our quest to be able to predict whether a process is spontaneous or not, predict whether a chemical process is going to happen or won't happen. Our key tool at this point is the second law of thermodynamics, which tells us that a process will be spontaneous if the change in the entropy of the universe is positive. So second law is usually written in this form, change in the entropy of the universe must be greater than or equal to zero. For a spontaneous process and it'll be equal to zero for a process that's in equilibrium. And any process for which the entropy change of the universe is negative, that'll be a non-spontaneous process, that won't happen. That's fine. It's true and it's useful under some circumstances, but it's not as useful as it could be. Because if I think of the universe as being composed of the system and the surroundings, so I'll just rewrite the second law to say the sum of the entropy change of the system and the entropy change of the surroundings, that sum has to be either positive for a spontaneous process or equal if the process is in equilibrium. We can very often make measurements and know lots of details about the system that we're studying. It's pretty unusual that we have a lot of information about the surroundings, not just the beaker containing the solution that we're interested in perhaps the system, but also the beaker itself is part of the surroundings, the air in the room is part of the surroundings, the walls of the room, the other side of the city, the other side of the planet, stars light years away. Those are all parts of the surroundings. So in order to fully make a prediction about what's happening for the spontaneous process, we need to know the entropy of everything else in addition to just the system. And that's obviously fairly inconvenient. So just to give you an idea of what I mean that we can't fully make a prediction without knowing the entropy of the system and the surroundings, we can ask for various different combinations. Let's suppose the entropy of the system increases. So delta S has a positive sign. If the entropy change of the surroundings is also positive, the sum will be positive and that'll be a spontaneous process. So that's a fully spontaneous process. If I know both the system and the surroundings are increasing their entropy, that process is spontaneous. If the system is increasing its energy and the surroundings are decreasing their entropy, then that sum of a positive number and a negative number might be positive. If this number is larger in magnitude or it might be negative, if this number is larger in magnitude. So with just that information, I don't know whether that process is spontaneous or not. Likewise, if the system is losing entropy but the surroundings are gaining entropy, perhaps they're gaining more entropy than the system lost and that process would be spontaneous. Or perhaps they're gaining less than the system lost and the system would be not spontaneous. So it might be spontaneous or might not. The only time I know for absolute certain that the process will be not spontaneous is if the system is losing entropy and the surroundings are losing entropy. Then I know for sure that however I add these two numbers up, the sum is going to be negative and the process will be not spontaneous. So this illustrates if I know the entropy change for the system, if I know the entropy change of the system is positive, I don't know enough to know for sure if the process is spontaneous or not. It depends on what the entropy change of the surroundings is and it depends on how big the entropy change of the surroundings is. Likewise, even if the system has a negative change in the entropy, that would ordinarily suggest that the process might not be spontaneous, but it depends on the size of the entropy change of the surroundings. It's the sum of the two that matters, not just the system. So turns out what we'd really like to be able to do to predict whether a process is spontaneous or not is use, clearly we can't just use the entropy of the system, but we'd like to be able to use only the properties of the system so we don't have to study everything else in the system. We can focus our attention just on the system. So our goal will be to find some property of the system. It doesn't turn out to be the entropy as you guessed from the title of this video. It turns out to be something called the free energy that we haven't defined yet. We will soon. But if we define a new property called the free energy, it turns out that property for just the system itself will allow us to predict whether a process is spontaneous or not. So that's the direction we're heading next.