[BLANK_AUDIO]. In this video, I shall endeavor to clarify various topics concerning the spontaneity of chemical reactions that confused me when I studied thermodynamics as an undergraduate. Firstly, what is actually meant when we say a chemical reaction is spontaneous, and secondly, what exactly governs the spontaneity of chemical reactions? I'm sure that my physical chemistry lecturers did a fine job of trying to explain these topics to me, and my failure to understand almost certainly derives from a lack of reading on my part. However, if I can make this lecture make sense to you, then it will have served great purpose. I want to start by considering the word spontaneous, so, I turn to the authority on the English language and look the word up in the Oxford English dictionary. Part of the definition is given here. Meanings of the word spontaneous that I find confusing from a thermodynamic point of view are sudden, and without apparent external cause. The reason for potential confusion is that a spontaneous reaction need not be sudden, or without apparent external cause at all. Take for example the reaction between hydrogen gas and oxygen gas. As far as thermodynamics is concerned, this reaction is spontaneous. One mole of hydrogen gas burns in half a mole of oxygen gas, to produce half a mole of water, usually with a bright orange flame. However, with suitable care, hydrogen gas and oxygen gas can be stored in the same balloon together, and they will not react with one another. The reason for this apparent lack of spontaneity lies in the domain of chemical kinetics, which determines that chemical reactions have an energy barrier called the activation energy. You will learn about this in detail with Professor Underson later on in the second part of the course. So, despite the spontaneous nature of this reaction, it takes a small amount of energy, either in the form of a flame or possibly just static electricity to ignite the gaseous mixture. Once a reaction starts, then its spontaneity becomes all too evident. So, hopefully this gives you a clear picture in your mind of why a spontaneous reaction doesn't necessarily react spontaneously. After much consideration, in my opinion, the best way way to think of the word spontaneous, with regard to thermodynamics, is to think of the word feasible. Okay. So having cleared up one potential source of confusion, let's tackle an even bigger one. What makes a chemical process spontaneous? The reason for confusion here is that, as far as I could determine as an undergraduate, there are actually two criteria for this one outcome. Do both have to be true for a reaction to be spontaneous? What happens if one is true and the other is false? As an undergraduate, I had no idea. So, let us consider what the criteria are. First, in any spontaneous chemical process, the entropy of the Universe must increase. Second, in any spontaneous chemical process, the Gibbs energy must decrease. If you aren't sure what Gibbs energy is for the moment, don't worry, as I will explain it in this lecture. Clearly, these two statements appear different. And so, once again, how can there be two distinct criteria for one phenomenon? The answer to this problem, is that the two criteria are not independent. The second one is both defined and derived from the first one, and absolutely depends on it. So, in other words, if one criterion is true, then the other one must also be true. It is impossible for one to be true without the other. So, in order to derive the second criterion, and in doing so to define Gibbs energy, we need to start with the first criterion. The first criterion states that for any spontaneous chemical process the entropy of the universe must increase. So, this is where we begin. The change in entropy of the universe, caused by a chemical process, is equal to the change in entropy of the system plus the change in entropy of its surroundings. Remember, from the second lecture on definitions, that the system plus its surroundings make up the entire universe. We now rely on the definition of entropy itself, given as equation ten in the last lecture. The change in entropy of the surroundings is equal to the reversible heat exchanged to the surroundings, divided by the temperature at which the transfer occurs. So, we can replace delta S surroundings by q surroundings divided by T. Now, crucially, whatever heat energy flows into the surroundings as a consequence of mechanical process, must have flowed out of the system. Thus, the heat flow into the surroundings equals the heat flow out of the system, which is the minus the heat flow into the system. This step is vital because it enables us to describe the total entropy change of the universe based purely on parameters of the system. Okay, so we can replace Q surroundings divided by temperature, by minus Q system divided by temperature. And the right hand side of our equation is now purely system based. Next, we recall equation four, which states that for an isobaric process, the heat energy supplied to the system is equal to the enthalpy change of the system. Replacing minus q system divided by t, behind minus delta H system divided by T, leads to the equation, delta S universe equals delta S system minus delta H system divided by T. Multiplying the equation through by temperature, and negating it, leads to minus T delta S universe equals delta H system minus T delta S system. We need to keep in mind the right hand side of this equation, as it is important for the next section, so you may wish to write this down. In 1873, the American Josiah Gibbs defined a new state function, G which is equal to H minus TS. And this Gibbs energy, or historically Gibbs free energy, entered the thermodynamic vernacular for the first time. Change in the Gibbs energy, delta G therefore, equals delta H, minus delta TS. Remembering that delta TS is a product and needs to be differentiated accordingly, delta G equals delta H minus T delta S minus S delta T. But if we consider an isothermal process, S delta T equals zero, and thus, delta G equals delta H minus T delta S. This is an equation of fundamental importance, and we denote it equation 11. So now, if delta G equals delta H minus T delta S, delta G system equals delta H system minus T delta S system. And it should hopefully be apparent why Gibbs energy was defined in this way. Because the right hand side of this equation is exactly the same as the right hand side of the equation at the top of the slide. Thus, we have now forged a link between the total entropy change of the universe, and the Gibbs energy of the system. Minus T delta S universe equals delta G system. The last part is now trivial, dividing both sides of the equation by minus T yields delta S universe, equals minus delta G system over T. Since T is absolute, and hence positive, we can now see that for spontaneous chemical process necessitating an increase in the entropy of the universe, the Gibbs energy of the system must be negative. Moreover, the changing Gibbs energy of the system is defined based on the change in enthalpy and entropy of this system, and the temperature which the reaction is carried out. It was originally thought that only reactions that were exothermic i.e., that give out heat, could be spontaneous. Then, it became apparent that some endothermic reactions, i.e., that draw in heat, were also spontaneous. Three examples of such processes are: the dissolution of potassium chloride in water, which has an enthalpy change of plus 19 kilojoules per mole, the melting of ice, which has an enthalpy change of plus six kilojoules per mol, and the decomposition of ammonium carbonate, which as an enthalpy change of plus 68 kilojoules per mol. As we have shown, delta G equals delta H minus T delta S. So, if delta H is positive, then delta S must be sufficiently positive to make minus T delta S outweigh delta H are the temperature of the reaction, thus making delta G negative and rendering the process spontaneous. In all three of the reactions shown above, there is a significant increase in entropy or disorder. Potassium chloride exists as a highly ordered crystalline ionic lattice of alternating potassium cations and chloride anions. Dissolution dismantles the structure, to leave hydrated ions moving around in solution. The melting of ice again causes the dismantling of a highly ordered crystalline solid. The decomposition of ammonium carbonate, sees one mole of highly regular ionic crystalline solid, transformed into multiple moles of gas and liquid. Gases have significantly higher entropies than solids as we shall see in lecture ten. In actual fact there are four possible situations. Reactions with negative enthalpy change and positive entropy change will be spontaneous regardless of temperature. Reactions with positive enthalpy change and negative entropy change will never be spontaneous. Reactions with negative enthalpy change and negative entropy change will switch from spontaneous to non-spontaneous as temperature rises, and reactions with positive enthalpy change and positive entropy change will switch from non-spontaneous to spontaneous as temperature rises. In order calculate the point at which a reaction switches spontaneity, we are looking for the Gibbs energy to change sign, and consequently, we need the point where it passes through zero. At this point, T delta S equals delta H, and thus, T equals delta H over delta S. On this slide, we're going to work an example calculation for a reaction with an enthalpy change of 19 kilojoules per mole and an entropy change of 45 joules per Kelvin per mole. The simplest way to get such a calculation wrong is to forget the units. Remember, enthalpy changes are usually quoted in kilojoules per mole rather than joules per mole. Also, remember the resulting temperature will be in Kelvin. So, we divide 19,000 joules per mole by 45 joules per Kelvin per mole and we get 422 Kelvin. Subtraction of 273 yields a temperature of 149 degrees Centigrade. The reaction becomes spontaneous above 149 degrees Centigrade. So, just to finish this lecture, I should like to make one final comment regarding spontaneity. That is that there is no such thing as a degree of spontaneity of a reaction. Reactions can not be highly spontaneous, or mildly spontaneous, or slightly spontaneous. They simply are spontaneous or they are not. Okay, so now hopefully we understand the somewhat enigmatic term spontaneous, and we understand that spontaneity is driven by an increase in universal entropy, which absolutely necessitates a decrease in the Gibbs energy of the system. The two criteria are effectively just one criterion. In the next lecture, we shall look at how Gibbs energy controls chemical equilibrium. [BLANK_AUDIO]