In the previous lecture, we began our study of the energetics of chemical reactions by developing a method by which we could measure the energy changes of chemical reactions, by taking advantage of known heat capacities. So we had to define and measure those heat capacities. The approach that we developed, which we called Calorimetry, is based upon the simple idea of either capturing the energy released by a chemical reaction in a water bath and watching its temperature rise, or allowing the water bath to provide energy needed for a chemical reaction to take place and watching the temperature drop. In either circumstance we would measure the change in the temperature delta t. Use that to calculate the change in the energy, the heat flow for the water. And then way, by conservation of energy, we would set that energy flow for the water to be the negative of the energy change during the course of the chemical reaction. That process seemed perfectly reasonable until we encounter certain circumstances. Here's a reaction we might want to know the energy for. Let's imagine we're trying to convert graphite into diamond. It's actually possible to carry out this chemical reaction, but only under some fairly extreme conditions. Very high temperature and pressure, for example. If we were simply to put some graphite into our calorimeter, and wait for it to turn into diamond, we will wait essentially an infinite period of time. And there will be no way to measure the temperature change associated with the reaction because the reaction is basically not taking place. Consequently, even though we would like to know the energy change for this reaction, calorimetry is just not going to get us there. We need to develop another method. That method is actually is based upon doing something that we're going to call energy algebra. We'll give it a different name in just a moment. Let's imagine that we have measured the chemical reaction, or the energy of the following chemical reaction. We have taken solid carbon and we are in fact converting it into, into gaseous hydrogen. So in some regards what we have done is to take one fuel, and turn it into another fuel here. And in the process of carrying that, that chemical reaction. We can actually make measurements. And we'll determine that 90.1 kilojoules per mole of reactant will turn, the carbon into the water. We're actually going to study this in comparison to 2 other chemical reactions involving those fuel sources. Carbon and hydrogen. Here they are. Here's the same carbon, serving as a fuel by burning with oxygen here to form carbon dioxide. That's a common chemical reaction and in fact, it releases an enormous amount of energy per mole of carbon, 393.5 kilojoules per mol of carbon. If we burn hydrogen in oxygen, that's actually expressed here in the reverse reaction. There's an enormous amount of energy released there as well, 483.6 kilojoules per mol. What's fascination about these number, however, if we stare at them for just a little while, we discover the sum of these 2 numbers for these 2 chemical reactions is exactly equal to the energy of that reaction. And these reactions are actually relatively simply related to one another. Let's see if we can figure out why. We're going to draw a simple energy diagram over here, in which we relate the energy of the reactants over here. Carbon solid and 2H2O gas. To the energy associated with the products. Notice that it's clearly up because there is an increase in energy here as we go to the products. So we have to rise to get to the products of the reactants here which are carbon dioxide and hydrogen. For reasons it'll be clear in just a second, I'm going to add to the reactants and the products some oxygen, O2. The process of going from reactants to products involves an increase in energy of 90.1% kilojoules per mol of carbon. On the other hand, if I were to take this carbon and oxygen and turn it into carbon dioxide, it's quite clear from what we have here, that in fact, I would release an enormous amount of energy. So let's draw a line down below here that include carbon dioxide and H2O, 2 H2O. Clearly, the process of moving down, from the reactants, to this new set of circumstances, releases minus 393.5, kilojoules. Now, you might wonder, why did we do this? The answer is because now, using the third reaction, we can take this H2O, and notice that what we would be able to do is turn it into hydrogen and oxygen, which are in fact the products up above. And the process of taking the carbon dioxide in water and turn it into carbon dioxide, hydrogen gas and oxygen gas according to third reaction over there is 483.6 kilojoules. Drawn in this diagram that makes it clear why the bottom 2 reactions on the slide here add up in energy to the top reaction. Because the process of moving on the energy scale from here to here must be the same, regardless of whether we do the con, direct conversion, or whether we first create carbon dioxide and then create hydrogen and oxygen. In either circumstance it appears quite clear that we are first releasing an amount of energy and then absorbing an amount of energy. And the difference between those 2, is exactly equal to the amount of energy required to move from one step to the other. This is actually a general result. We've only illustrated in one case. But its a general result referred to as Hess' Law. Hess' Law says that the overall reaction energy, for example, 90.1 kj here, is equal to the sum of the reaction energies. For any sequence of reactions which lead to the overall reaction. In other words, here's a sequence of reactions go from one to the other, sum the reaction energies along that alternative pathway minus 393.5 plus 483.6 is exactly equal to 90.1. So either path, in fact, produces the exactly the energy change, that is Hess' law. Here it is sort of diagrammatically here. I can either follow the direct path from reactants to products, or I can follow the alternative path that carries me through an intermediate. And in either circumstance the path does not in fact affect the energy of the reaction. We'll actually build upon the concept of Hess's law to introduce something else. Well, actually we're going to solve a problem first involving Hess's law. We're going to illustrate that using a similar kind of a diagram. Remember, we were trying to solve this problem of turning graphite into diamond. So here's our energy diagram again here. Here is the carbon in the form of graphite. You don't know it yet, but it turns out that the diamond is slightly higher in energy, so I'm going to write it above. If I wrote it below we would figure out quickly that we had done the wrong thing. We are interested in the q of this particular reaction, but we've concluded that we can't measure it experimentally. Instead what we could do is add some oxygen to both sides of the reactant and the product. Let the graphite an oxygen reactant and in the process turn into carbon dioxide. And according to this diagram for the slide here, the amount of energy released when we do that is -393.5 kilojoules per mol of carbon. And then we can take that carbon dioxide and turn it into diamond. In doing so, we would reverse the energy associated with the reaction, so we will now go up by 395.4 kilojoules. And according to Hess's law, we can get the energy in going from reactant to product by going first to carbon dioxide and then taking the carbon dioxide and turning it in to diamond and the energy would be the same. So the q of the reaction is minus 393.5 kilojoules plus 395.4 kilojoules, and the result of that is a difference of 1.9 kilojoules per mole of carbon reactant. And that is the energy of the overall reaction that we're interested in. In the circumstance that q is greater than 0, as it is here, we refer to that as an endothermic reaction, meaning that energy must go into the reaction. If q had been less than 0, we would have referred to that as an exothermic reaction. Alright, I mentioned a second ago that we're going to build on the idea of Hess's law to define a new quantity we're going to call the enthalpy commonly used in chemistry. The Enthalpy is an example of a state function. State function is a function of value that depends only upon the state of the materials that we are looking at. What are the materials, what are their temperature, what are their pressure, or, in some other circumstances, what are their concentration? But that does not matter how we achieved that particular state, doesn't make any difference what path was followed to get to those materials, whether they were originally in that form or were the product of a reaction. In either circumstance, the energy is exactly the same. That would be, for example, the energy associated with carbon graphite, that does not depend, for example, on whether I go from carbon graphite to carbon dioxide to diamond, and then turn back around and go to graphite. If I sum the energy going all the way around the cycle here, it's clear that I get 0. That means that the energy associated with the carbon graphite does not depend upon whether the carbon graphite just sat there or whether in fact carried out a set of chemical reactions. That means that energy is a state function. If the energy depends only upon the fact that we are starting in that state or winding up in a different state, then the energy change between those two, cannot depend upon the path where I started. It's a bit like saying that the elevation, where I sit right now on the 3rd floor, higher than the 1st floor is independent of the path that I take to get from, the 1st floor to the 3rd floor. I could go to the fourth floor and come down to the third floor. I could go to the roof and come down to the third floor. I could go to the second floor, wander around the second floor, and go to the third floor. The difference is going to be exactly the same because my elevation on the third floor is a state function. It depends only on the fact that I am sitting on the third floor and therefore the elevation difference is independent of any path. So the advantage of defining the state function is it's a path independent property. We're going to define a particular state function, H, the chemists call the Enthalpy. We define it specifically so that the change in the state function, over the course of a chemical reaction is equal to the heat flow of the chemical reaction provided that the reaction is carried out at constant pressure which is the way most interesting chemical reactions occur. Delta H then is the change of the reaction, a change in energy of the reaction and we constant we, we, we will often use the term the Enthalpy of the reaction or the heat of the reaction. According to Hess's law, we can calculate delta H, the change in energy, in any path that we want that carries us from reactant product. So for example, back over here, we might refer to the enthalpy of the carbon dioxide and water, and the enthalpy of the diamond and, and, and oxygen. And in this circumstance, assuming we carried this added constant pressure, then delta H for this reaction is equal to the heat of the reaction, provided that we carried it out at constant pressure. We would then, in fact, say that delta H of this reaction is 1.9 kilojoules per mol. We're going to use the fact that the enthalpy is a state function to be able to make a number of calculations, involving chemical reactions. In fact, we're going to develop an entire machinery around the enthalpy that allows us to predict the heats of chemical reactions.
