# Calorimetry

Calorimetry is the scientific method that we use to measure the amount of heat in/out of a system. It is a pretty basic premise that follows these basic steps.

1. Run a process that absorbs (endothermic) or releases (exothermic) heat - this could be either a physical change or a chemical change.
2. "Catch" all the heat in/out of your process with a standard substance - like water.
3. Make calculations on the water to determine the amount of heat that was transferred ($$q_{\rm water}$$).
4. The same amount of heat had to have been delivered or accepted by your system you are testing - adjust the sign of $$q$$ and calculate $$\Delta H$$.
5. Divide the amount of heat by the amount of substance you were testing to either get a standard value of kJ/mol or kJ/g of substance.

### The Calorimeter

Lets just break a calorimeter down into TWO major components that we will track. The hardware and the wetware - ok, the wetware is just water. A calorimeter is a glorified nice insulating container with a bunch of water in it. It also has a way to measure the temperature of the water inside of it. The water and the hardware together are the whole calorimeter. So we can do the following mathematical treatment.

qcal = CcalΔT

That reads as the heat that flows in/out of the calorimeter (qcal) is equal to the heat capacity of the calorimeter (Ccal) times the change in temperature (ΔT). Pretty straight forward, although you do need to know the heat capacity of your particular calorimeter.

Well, we are going to SPLIT the heat capacity into two parts, the heat capacity of the hardware (Chardware) and the heat capacity of the wetware which is the water (Cwater). The hardware is SET and is what it is, but the water component is variable because we can put different amounts of water in the calorimeter. Therefore we will split the water heat capacity into its mass and the specific heat capacity - that is Cwater = mwater · Cs,water. So our equation above now expands to this

qcal   =   Chardware ΔT   +   mwater Cs,water ΔT

So that is it - that is where the main heat calculation takes place. Find the heat that the calorimeter gains, and you've got the amount of heat the system or reaction loses. They are identical in amount (the magnitude) but opposite in sign.

qsys   =   –qcal

So remember to change the sign before you switch over to the system. And system here means the chemical reaction you are studying. But you are still not done yet - ok, you are PROBABLY not done yet because we tend to want to communicate the result based on some standard amount - like a gram or a mole.

Normalize to Amount Asked For: So get the total number of J or kJ that the system delivered and then divide by either the number of grams or moles depending on what was asked for. Also remember that you can easily convert from kJ/g to kJ/mol simply by multiplying by the molar mass of the reactant. And FYI - in THIS chapter, the reactant is going to be a fuel of some sort.

READ the question you've been given to find the hardware component of the calorimeter it has to be given one way or another. If it is not given, then maybe it is a situation where the hardware is so minimal compared to the water, that you can just ignore it. Then you just do the water part and move on. Big expensive calorimeters made for burning real fuels tend to always have a significant hardware component and it will be given. Cheap DIY calorimeters made out of styrofoam cups tend to have no hardware component at all.

### More Lingo - but for Calorimeters

Bomb Calorimeter: That expensive calorimeter I mentioned - those are known as isochoric calorimeters or the more thrilling name of "bomb calorimeter". The isochoric in the name means at constant volume. Just know they have a lot of metal parts and you DO have to account for the hardware. Below are a couple of pictures of an entire Parr calorimeter and a blow up pic of the little "bomb" reaction chamber that goes inside it. You can see the "bomb" in the first pic to get an idea of scale.  Coffee-Cup Calorimeter: The cheap-ass DIY one made out of a styrofoam cup is called a "coffee-cup calorimeter" and it requires no hardware calculations. Notice my picture I just grabbed off the web of a coffee-cup calorimeter. Replace the straw with a thermometer and you are in business. The context of your questions will convey which type you have. Just know that if you are burning a fuel like gasoline or kerosine, you are NOT going to be in the cheap one. Burning food works the same way - you burn it in a bomb calorimeter and your calculations lead to finding out the number of Calories in that food. Bear in mind, you DO have to do a lot of initial preparing in order to burn food. It must be completely dehydrated and then homogenized in to basically a power. That powder will then burn nicely.

### Heat Capacities of Metals

Another common use of a coffee-cup calorimeter is to just use it to determine the heat capacity of another substance - like a metal. Heat your metal sample up to a known temperature (usually with boiling water at 100 °C) and then drop the warm/hot piece of metal into the cup containing your much cooler water. Watch and measure the temperature rise. Do the calculations and determine the specific heat capacity of the metal. In this case your heat leaving the metal enters the water - the the quantity of heat must be equal. Therefore:

qwater = –qmetal Note that there are three important temperatures to use here: the initial temperatures of both the water and the warm metal, AND the final equilibrium temperature which will be between the two. 