In this lecture, we're going to begin our study on the energetics of chemical reactions, the changes of energy that take place over the course of a chemical reaction. We're going to be, studying Material Concept Development Study 12, which is related to measuring energy changes during the courses of chemical reactions. In other words first, we're going to figure out how to qualify and measure in the laboratory how those energy changes. And then we're going to analyze why those energy changes take place in subsequent lectures. Of course, it's easy to observe that energy changes do take place, during the course of the chemical reaction. in fact, in a vast majority of cases, in many cases at least, energy chemical reactions take place specifically. So, that we can either, either capture and use the energy, which is released during the chemical reaction. Or to perhaps store energy in chemicals for later use. So, for example, and these are the primary ones it's commonly observed that chemical reactions can be used to produce heat. This is probably the first use of controlled chemical reactions in history. Perhaps we are burning materials to gain the heat that comes from that, the thermal energy to keep us warm or to cook our food. We can also, in a more sophisticated way, carry out chemical reactions in a controlled fashion. That allows us to capture the energy in the form of work, maybe by using an internal combustion engine or a turbine. We can use chemical reactions to provide illumination, light, as a form of energy that can come out of chemical reactions. And we can also in electric chemical processes, use the chemical reaction to separate a potential. And thereby to drive an electric current and to use that to be able to do electrical work. Primarily, we're going to focus on heat and the measurement of heat associated with chemical reactions. Now, the thing that we most commonly observe is that when we use the heat that comes from a chemical reaction to perform, to heat something. There's a temperature variation that occurs as a consequence of the chemical reaction. I might, for example, attempt to burn, say, a gram of propane to heat a pot of water on the stove. And in the process, I could measure that some temperature change had taken place in that pot of water. Let's say that it goes up by 15 degrees centigrade. I might be inclined to say that the amount of energy that came out of burning that gram of propane was 15 degrees centigrade. That turns out to not be completely incorrect, but it's misleading. Because the change in the temperature is actually not a good measure of the energy. Because the change in the temperature is going to depend both upon what we heat with the energy which is released and how much of that we heat. So, for example, if I use the amount of energy released by burning a gram of propane to heat just water, I will get a very different temperature change. A much smaller temperature change, than if I were to use that to heat, say the equivalent mass of iron. In fact, I'd observe that the iron goes up by dramatically more maybe about a factor of nine times greater temperature increase as a consequence of heating iron relative to heating water. Clearly, also, the temperature change depends upon how much of what of the substance is that I'm heating. If I burn that gram of propane in attempt to elevate the temperature of say, ten grams of water, I'll get a very much larger result. Than if tried to, for example, use that same gram of propane to elevate the temperature of say of a swimming pool. Consequently, we need to do more than simply measure temperature changes. What we do know that the temperature changes, in fact, related to the energy which is released during the chemical reaction. And, in fact, we're going to regard the heat change q to be proportional to the temperature change delta T. With the proportionality constant being called the heat capacity, that's this number C, which is here. However, it should be clear to us that since delta T is different for the same amount of energy for the same chemical reaction, depending upon what is heated. And depending on how much is heated, then C in turn must also depend upon what is heated and how much is heated. But we define this quantity as the heat capacity. The heat capacity relates, the amount of the energy which is absorbed by a material, to the temperature change of that material. But the heat capacity itself does depend upon what the substance is. It will depend upon whether we're talking about iron, or water, or any other substance, and will depend upon how much of that substance that we are in fact heating. Commonly, chemists referred to two different kinds of heat capacity. The first kind of heat capacity is called the Specific Heat Capacity. Takes into account the fact that heat capacity is general, proportional to the mass of the material for a pure substance. Consequently, we can describe the heat capacity, per gram as the specific heat capacity denoted here as C sub s. Notice that then the heat is given by taking the mass multiplied by this specific key capacity. Give the overall the capacity multiplied by delta T. So when you see the term specific heat capacity. It's referring sometimes even just specific heat. It's referring to the heat capacity per gram. There's also a molar heat capacity, which is the heat capacity per mole. And in that circumstance, what I would want to do to find the heat of the reaction. I would in fact take the temperature change associated with that reaction, multiply it by the molar heat capacity of whatever it was I was heating, multiplied by the number of moles of the material. All of these is just kind of formal, unless we know what those heat capacities are. So we need to have some means by which we can measure heat capacity. And here is one such approach. Let's imagine that we wanted to heat a gram of water by one degrees centigrade. So maybe we started off at 25 degrees C and we want to elevate that temperature. We can actually do work by stirring to measure the temperature change. And we can watch the temperature rise. And we can measure how much work we're doing. It turns out experimentally, that exactly 4.14 joules of work are required to elevate one degree centigrade one gram of water by 1 degree centigrade. Well, let's talk about work, and stop talking about heat. But if energy is conserved, then I have to be able to elevate the energy of the water by doing work on it, or by heating it. The amount of energy necessary to raise the 1 gram of water by 1 degree centigrade turns out to be the same whether we are heating the water or doing work on the water. Consequently, it takes an equivalent amount of heat, that is 4.184 joules of heat to raise one gram of water by one degree centigrade. That's the experimental observation. Consequently, we can say then, that the specific heat capacity of water, is 4.184 joules. Per gram heated per degree centigrade that we heat, and we now in fact have one such measure of the heat capacity. Notice that this required us to be able to do work on the water, which we can do, because water's fluid. But what if we were trying to measure the heat capacity of something else? Let's say we were trying to measure the heat capacity of iron. All we have to start with is that the heat capacity of the water is 4.184 joules per gram centigrade. So perhaps what we could do is to take a bucket of water. And into the water, we're going to put a kilogram of water. So a thousand grams of water, an then we're going to drop a piece of iron into that. We're going to take the water, to be 25 degrees centigrade. We're going to put a chunk, of iron in here, weighing 500 grams, starting at 90 degrees centigrade. Of course if we do this, we know what's going to happen, is eventually, we're going to wind up with a much cooler piece of iron. At a different temperature, that will be the same temperature as the temperature of the water. And that temperature experimentally, to be measured to turn out to be 28.3 degrees centigrade. So the final temperature in this process is 28.3 degrees centigrade. What we'd like to do is figure out from this, what is the heat capacity of the iron?` How could we do that? Well, one thing we could do is to measure the heat which goes into the water as a consequence of being in contact with the hot iron. Clearly, we know that it has gained energy because we went from 25 degrees centigrade to 28.3 degree centigrade. So according to our formula before, we take the mass of the water and we multiply by the specific heat of the water which is known and we multiply by the temperature change of the water which is now being measured. Lets see we have a thousand grams of water, the specific heat capacity is 4.184 joule per gram degree centigrade. And the temperature change can be measured as 3.3 degree centigrade because it is 28.3 minus 25 multiplying those numbers together, we get 13,800 joules. So I'm going to write that as 13.8 kilojoules of heat absorbed by this kilogram of water as a consequence of being in contact with the hot iron. How much energy does the iron lose? Certainly it loses energy, because it went from 90 degrees centigrade to 28.3 degrees centigrade. So, it's temperature has dropped by 61.7 degrees. The amount of energy that it lost must be exactly equal to the amount of energy which was gained by the water. And that must be minus 13.8 kilojoules. But that must also then be equal to the mass of the iron times the specific heat of the iron, times the temperature change of the iron. The, let's see, minus 13.8 kilojoules, must therefore be equal to 500 grams of iron. We don't know the specific heat of iron. That's what we're trying to find out. And the temperature change of the iron is minus 61.7 degrees centigrade. That's an equation with is relatively straightforward. So we can just find then by dividing up that the specific heat of the iron turns out to be 0.447 joules per gram degree centigrade. This method could actually be fairly easily used for a variety of substances to determine what the specific heat capacity is for any substance. Consequently, we can actually tabulate a set of specific heat capacities. Here is a table showing the rather great variations that occur as we move from one substance to the next. There's the iron calculation that we've just done. There's methane. We've got water is in here as well. Notice that the heat capacity of the water does depend upon the temperature of the water and varies somewhat over those ranges. In each of these circumstances, remember that the heat capacity is the proportionality constant between the heat and the temperature change. That is sometimes a confusing fact because what it actually tells us is that there is an inverse relationship between the heat capacity and the temperature change for a fixed amount of heat. So, any time I provide a fixed amount of heat so a substance, the smaller its heat capacity, the larger its temperature change. Or, conversely, the smaller the temperature change the smaller is heat capacity. Substances with high heat capacities have a tendency to resist temperature changes and will undergo small temperature changes. So when your'e dealing with a substance that doesn't seem to heat up very much, what you're observing is something which has a high heat capacity. All right, we spent quite a bit of time here talking now about heat capacities. What about, getting back to chemical reactions? The process of measuring the energy of a chemical reaction by using the heat capacity of the known substance and measuring the temperature change, is a process called calorimetry. It is a means by which we can measure the chemical reaction's energy by measuring temperature changes for a substance that has a known heat capacity. Let's see, how would we do this? Let's imagine that instead of putting that piece of hot iron in there, we burn a gram of methane, right? So we're going to take methane, react it with oxygen, and form carbon dioxide and water. And we are interested in the energy of this particular chemical reaction. So we'll burn a fixed quantity of methane. 1 gram, that's 1 16th of a mole of methane. We're going to use the heat that comes out of that and capture that again in a bucket of water which has 1 kg of water in it. And which therefore has a known heat capacity. If we know the energy, the, the energy absorbed by the water, or the temperature change of the water, we can measure the energy change absorbed by the water, from the mass of the water. Times the specific heat capacity of the water Times the temperature change of the water. The mass, again, is a thousand grams, the specific heat capacity is 4.184 joules per gram-degree centigrade, and the temperature change is given to be, 13.3 degrees Centigrade. Consequently, we can measure the energy just by multiplying these numbers together. We get, I'm going to put this in terms of kilojoules, 55.6 kilojoules of energy absorbed by the water. The energy released by the reaction must be the negative of the energy absorbed by the water. Because all the energy that came into the water came out of the reaction. So the energy of the reaction, it's exothermic because the energy is less than 0, so it's releasing energy to us in an amount 55.6 kilojoules. That is for 1 gram of methane burned. From this, we can actually then measure the chemical reaction, the energy associated within a chemical reaction, that is sufficiently fast that I can capture the energy released or absorbed by the amount of water by measuring the temperature change there. That's the essence of calorimetry. There are some limitations associated with this, including the fact that we have to carry out a chemical reaction every time we would like to measure the energy. We're going to actually develop an expansion beyond this to make it possible for us to measure energies more simply in the next lecture.
