 So we've been talking about energy and enthalpy changes for a variety of different systems, but so far those have all been gaseous systems and they've all just involved pressure, volume, and temperature changes. So it's not just PVT changes for gases that have changes in their internal energy, changes in their enthalpy. Any system has an internal energy, has an enthalpy. If I change it in any way, there's some associated change in the energy or change in the enthalpy. So we can talk about delta U or delta H changes for any process including chemical reactions as well as all sorts of different types of processes. So that begins to open the discussion of this process called calorimetry. We can use these expressions that we've seen, the internal energy being related to the heat if we do something at constant volume or the enthalpy being related to the heat if we do it at constant pressure. Those give us a way to measure the change in internal energy or enthalpy if we measure the heat for a process under either constant volume or constant pressure. So this idea of calorimetry, so the word itself calor meaning heat and metric meaning measurement so the measurement of heat is a little bit of a misnomer. What we usually actually measure is the change in temperature for some process and we can relate that change in temperature to the heat using the heat capacity, maybe the constant volume heat capacity, maybe the constant pressure heat capacity depending on the conditions, constant volume or constant pressure. And then using these two expressions we can relate that heat either to the internal energy or the enthalpy depending on whether we've done the process at constant volume or constant pressure. So those two types of processes do something at constant volume, use the temperature increase or decrease to tell us something about the energy or do something at constant pressure, use that temperature increase to tell us something about the enthalpy. Those are calorimetry experiments, some examples of calorimeters that you may have seen, heard, read about, even used in a lab for example. Simple examples, there's a coffee cup calorimeter and we'll work an example that would be typical for a coffee cup calorimeter example in just a second. I guess I should say calorimeter is the device and so this is the constant pressure example, a coffee cup calorimeter, the constant volume equivalent would be something that's often called colloquially a bomb calorimeter. So let's do an example to see how this works in practice. We'll do a constant pressure example. So let's say that we have Mg2, MgSO4, magnesium sulfate. So let's say I've measured out some magnesium sulfate, it weighs 1.4 grams. The molar mass of magnesium sulfate is 120.4 grams per mole. So with that I can figure out how many moles of magnesium sulfate I have. I then dissolve that magnesium sulfate in water in, for example, a coffee cup, a styrofoam coffee cup. So if I dissolve solid MgSO4 in liquid water that will dissociate into ions, those ions will be aqueous in solution in the water. And if I've done that just pour the magnesium sulfate into a coffee cup open to the atmosphere, that process will happen at constant pressure because it's open to the atmosphere. That is an exothermic reaction. So that's going to actually change the temperature of the water in that coffee cup. Let's say I have exactly 100 grams of water. We're also going to need to know not just the molar mass for water, but I'll need to tell you the heat capacity. At constant pressure the heat capacity of water is 75.4 Joules per mole Kelvin. So if I do this, if I dissolve 1.4 grams of magnesium sulfate in 100 grams of water at constant pressure, the temperature will increase. If I start at a temperature of 25 Celsius, the amount of the temperature increase for that process with these amounts of the two substances is going to be 2.5 degrees Celsius. The temperature is going to go up from 25 to 27.5 degrees Celsius. So the question then becomes what is the enthalpy associated with that reaction when I dissolve the enthalpy per mole, when I dissolve a mole of magnesium sulfate in water, what's the enthalpy associated with that reaction? So to solve that we can start, we can go back to this diagram to remind ourselves what we're going to do. We're going to use that measured change in the temperature to learn something about the heat and then use the heat and this expression to learn something about the enthalpy. So the first step since we're at constant pressure, we know the heat is constant pressure heat capacity times change in temperature moles times a molar heat capacity. We have all these quantities or we can get them easily the number of moles. So this is the water that we're talking about that is increased in temperature by 2.5 degrees Celsius. So the amount of water we have, the moles of water we have is 100 grams divided by 18 grams per mole. That will give us the moles of water. If I multiply that by the heat capacity and by the change in temperature, 2.5 Celsius or Kelvin. To double check the units, my grams cancel, 1 over moles here, cancels the 1 over moles in the denominator there. Kelvin and degrees Celsius are the same thing if it's a delta T and so all I'm left with is joules and the calculator will tell me that the result of that arithmetic is 1,050 joules. So let's talk briefly about sines. Just remember what the sine of heat is when the sine is positive, positive 1,050 joules that means an input of heat and from the water's point of view that makes sense. This is the heat change for the water. The water increased in temperature from 25 to 27.5 because heat entered the water that was a transfer of energy into the water. That amount of heat was positive 1,050 joules. From the magnesium sulfates point of view however, this reaction is going to turn out to be an exothermic reaction. The reason there was heat available to be transferred in from the water's point of view is that that heat was evolved or generated by this chemical reaction. So from the magnesium sulfates point of view, the heat had a negative sign. So this, so I'm going to write down that the heat from the magnesium sulfates point of view is the negative of the heat from the water's point of view. That's just a reflection that depending on what I call the system. If I am the water, heat is flowing in. If I'm the magnesium sulfate, heat is flowing out. So whether the sine of q is positive or negative depends on your point of view. Whether you are considering the water to be the system or the magnesium sulfate to be the system. So in that case, the magnesium sulfate lost 1,050 joules worth of heat. The reaction took place, generated some energy and enthalpy that was transferred to the water in the form of heat. If what I want to know is the molar enthalpy of that chemical reaction. Luckily, I've done that reaction at constant pressure. So the enthalpy and the heat are exactly the same thing except so that would be the heat negative 1,050 joules. That would be, let's go ahead and say that is the enthalpy of the reaction. The total extensive amount of enthalpy for the reaction. But that was the reaction when I reacted 1.4 grams of magnesium sulfate. The molar enthalpy of that reaction, that's gonna be the change in the enthalpy divided by the number of moles. So that's gonna be negative 1,050 joules divided by the number of moles of magnesium sulfate. We have 1.4 grams of magnesium sulfate divided by its molecular mass. 120.4 grams per mole. So units of grams cancel. And if I divide 1,050 by 120.4, no, sorry, 1,050 divided by 1.4 over 120.4. The result I get is gonna be 90,000 joules per mole or 90 kilojoules per mole with the same negative sign that's been present since we changed our point of view to talk about the magnesium sulfate. So now that we've got an enthalpy, enthalpy is negative. That means this reaction is an exothermic reaction. Technically it's an exanthalpic reaction, meaning its enthalpy is negative. It gives off energy when the reaction takes place. And of course that's what heated up the water to begin with. But this general process of measuring the temperature change, relating that to a heat and then relating that in turn to either an enthalpy or an energy is this idea of calorimetry. This is an example with a constant pressure calorimeter, constant pressure process. Everything would proceed very similarly if we did a constant volume process, except the quantity we would have access to most directly is the internal energy. And it would take a little extra legwork to turn that internal energy into an enthalpy if that's what we were after. So that process is a little bit more involved when we do constant volume calorimetry, so that's what we'll explore next.