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Chemistry: Gibbs Free Energy

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About this Lesson

  • Type: Video Tutorial
  • Length: 10:58
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 118 MB
  • Posted: 07/15/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Thermodynamics (8 lessons, $14.85)
Chemistry: Gibbs Free Energy, Free Energy Change (2 lessons, $3.96)

This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidation-reduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.

Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electron-rich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.

Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies molecule-based magnetism.

Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.

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Thinkwell
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As chemists, it's going to be really important for us to understand whether a chemical reaction is spontaneous or not. That tells us whether at least it has the potential to occur. It doesn't tell us anything about rate, but it tells us if the reaction could occur, at least, given enough time.
Now, as we saw with the second law of thermodynamics, what determines whether something will be spontaneous or not is entropy - the entropy of the universe. A spontaneous process must be accompanied by an increase in the entropy of the universe, if it's a real process at least.
So we arrived at a mathematical relationship that said that S had to be larger than the q - the heat - involved divided by temperature in order for the process to be spontaneous. Now remember that q at constant pressure we define as H - the enthalpy of the reaction. And so this translates to S must be larger than H divided by temperature if the reaction is going to be spontaneous. And then simply rearranging that got us to the end of our discussion from last time, which is H - TS must be less than zero if the reaction is going to be spontaneous. Well, that's really valuable to know, because we can measure H or look up values of H. Using Hess's law, we can calculate values of H. Well, you know that we can look up or calculate values for S. And so that tells us whether or not the reaction we're trying to do - or we're trying to get our graduate students to do - will ever happen or not, because if it's not spontaneous, what's the point? Right? So, it would be really nice if H - TS, which doesn't exactly roll off the tip of your tongue - if we had a way to talk about that in a nice concise package. And in fact, it was Josiah Willard Gibbs who was actually the first scientist to be granted a PhD from an American university, back in 1863 from Yale. Anyway, Dr. Gibbs came up with the relationship that G = H - TS. Now this is actually a definition. He defined the Gibbs free energy - or maybe others defined it using his name later. I don't know the history of that. But at any rate, we, as chemists collectively, talk about free energy as being H - TS. And again, it gives us a concise package for this notion of entropy and enthalpy and how their relative weighting affects whether a reaction will be spontaneous or not.
Okay, then. So just taking that one step further, if G < 0, if our free energy is less than zero, then the forward reaction is going to be spontaneous. For a reaction in the forward direction, that would be a spontaneous reaction. If G > 0, the forward reaction would not be spontaneous, but that means that the back reaction would then be spontaneous. And finally, if G = 0, well then the system must be at equilibrium. So this gives us a numerical indicator for where we are with respect to the equilibrium of a chemical reaction. And all we need to know, to get that number, is values for H and S and whatever the temperature is that we're at.
Now to understand how this works, let's look at a relatively simple process - the process of fusion - in this case freezing a liquid and making it a solid. We'll talk, in particular, about water here, because that's a process we're all very familiar with - the notion than when liquid water turns to ice, we can describe that reaction as a free energy that is H of fusion. So talking about H for this reaction, which would have to be negative - because we're going to have heat released in this process as we make new bonds - minus TS. Well S also must be a negative value, because we're decreasing the disorder of this. We're increasing the order, in other words. So we know, qualitatively, what these values are and we can look up the quantitative value. We can look up the value for these two numbers. And it turns at that at 273° Kelvin is the exact point where these two terms cancel each other out. In other words, where H is exactly equal to TS. Well, if that's true, G is going to be zero, and as a result, we're at equilibrium. We're right at that balance point between water as a solid and water as a liquid, and at that temperature, both can coexist in equilibrium.
Now, again, let me just point out, this red line is indicating the term "TS" and this term is "H". So if S is negative, you'll notice that temperature times S is increasing as we decrease the temperature. Now, what I mean by increasing is it's becoming less negative. It's approaching zero as we go to lower temperatures now, because S was a negative value. So as we go away from equilibrium, in this direction - as we lower our temperature - this term becomes larger than H. As it becomes larger than H, then this difference here, G, becomes negative. Well, what does it mean with G negative? Remember, that means the reaction will be spontaneous. So that tells us as we drop our temperature, then water will spontaneously freeze, but the reverse process would not be spontaneous.
So let's go ahead, and actually look at an example involving numbers with this system. Once again, we're talking about the process now going from liquid to solid, for water. And here are the numbers. At 273 Kelvins, H - remember I said it was going to be negative. It's, in fact, about 6 kilojoules negative, or 6007 joules. S for the process also is negative, because again, more ordered. It's 22 joules per mole Kelvin. And G then at that temperature - remember, that was the balance point, where those two curves intersected - so G is zero, meaning we're at equilibrium.
Now, watch what happens when we go to a lower temperature. Going 10 degrees lower, H stays essentially the same. This is a little bit of an assumption. We're assuming H and S are going to be independent of temperature, which is not exactly true, but is a reasonably good assumption as long as we don't go through huge temperature changes. So we're only going through 10 Kelvins here. S also, we're assuming, is a constant. But of course, what's changing is the temperature. So, when we plug in those numbers, again, we end up now with a G of minus 220 joules. The minus sign indicates that the reaction is spontaneous - that the reaction will spontaneously freeze now - that the water will spontaneously freeze. And it gives us a measure of how far away we are from the equilibrium value - the 220 joules. So it gives us, in terms of energy units, some indication of how far we are from that equilibrium point.
So, what have we learned? We have introduced a new term - Gibbs free energy - defined as H - TS. And this is a convenient way to compare the notion of the enthalpy of a reaction with the entropy of a reaction and combine those ideas together to determine whether a reaction will be spontaneous or not. At this stage, what we're going to do - eventually at least, after defining a couple other things - is we're going to relate G to equilibrium and come full circle, in a sense that we'll be tying together the ideas of energy with an equilibrium of a chemical reaction.
Thermochemistry
Gibbs Free Energy and Free Energy Change
Gibbs Free Energy Page [2 of 2]

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