Introduction:

Every chemical and physical transformation involves some change in energy. These changes may involve heat, light, electricity, or some other form of energy. The branch of chemistry, which deals with the measurement of these changes is called thermochemistry. Enthalpy is a word which means ‘heat content’. Every substance has some characteristic enthalpy because of its chemical makeup. It depends upon several factors: the total number of subatomic particles in each atom and how they are arranged; the total number of atoms in the substance and how these atoms are arranged; and the total number of molecules and how they are arranged (including any interactions between them). Because it is impossible to know all of these factors, we can not calculate the absolute value for the heat content of a substance. However, we can measure the change in heat content, which accompany chemical or physical transformations.

The energy change of a reaction that occurs at constant pressure is termed the heat of reaction or the enthalpy change. The symbol H_rxn is used to denote the enthalpy change. If heat is evolved, the reaction is exothermic (H_rxn < 0) and if heat is absorbed the reaction is endothermic (H_rxn > 0).

If the transformation only involves a change in heat energy, it is a simple matter to monitor the energy change with a thermometer. The quantity of heat either evolved or absorbed may be calculated using the equation:

Where q is the quantity of heat, m is the mass of the substance undergoing the change, s is the specific heat of the substance, and T is the change in temperature in °C.

The quantity of heat is measured experimentally by allowing the reaction to take place in a thermally insulated vessel called a calorimeter . Ideally, the heat liberated in the reaction would only cause an increase in the temperature of the solution. However, because no calorimeter is perfect, some of the heat "leaks" out and we must calibrate it by determining its water equivalent, WE. This can be readily determined by measuring the temperature change that occurs when a known amount of hot water is added to a known amount of cold water in the calorimeter. The heat lost by the warm water is equal to the heat gained by the cold water and the calorimeter (we will assume no heat is lost to the laboratory). For example, if:

then the heat lost by the warmer water is

The specific heat of water is 4.18 J/g°C, and the density of water is assumed to be 1.00 g/mL. The heat gained by the room temperature water is

The heat lost to the calorimeter is the difference between the heat lost by the warmer water and that gained by the cooler water:

Thus, by measuring T₁, T₂, and T_f, the water equivalent (WE) of the calorimeter can be calculated:

Now lets look at some real numbers and see how the (WE) is determined and used. Assume that we mix 50 g of warm water with 30 g of cool water:  

Using this data, we can calculated the WE as:

So, now that we have the (WE), what do we do with it? Well, lets say that we want to determine the H_rxn  for the following reaction:

We first need to determine the amount of heat (q_rxn) that is evolved during this reaction.  For this we will add 20.00 g of 1.00 M reactant 'A' and 15.00 g of 2.00 M reactant 'B' into the calorimeter and monitor the temperature.  During the course of the reaction, the 35.0 g of solution increases in temperature by 6.5°C.  From this increase in temperature, we can calculated the true amount of heat, q_rxn , that was released:  

Now that we know the true amount of heat that was released, we can calculate H_rxn by simply dividing q_rxn by the moles of the limiting reagent (assume that the density of this solution is 1.000 g/mL):

Therefore 'A' is the limiting reagent, and the H_rxn is:

Purpose:

In this experiment, you will determine the enthalpy of combustion, H_comb for magnesium reacting with oxygen to form magnesium oxide:

The most straight forward method of determining this value would be to weigh a piece of magnesium, place it in a 'bomb' calorimeter with excess oxygen and initiate the reaction with a spark.  Unfortunately, we do not have such a sophisticated piece of equipment and so must be a little bit more clever.

Method:

Since we do not possess the technology to determine this H_comb directly, we will use Hess' law to determine it indirectly.  Basically, Hess' law states that it does not matter how many different steps a reaction goes through.  As long as the overall reactants and products are the same, then the enthalpy of reaction will be the same.  This of course is a very powerful tool since it allows us to calculate the H for reactions that would normally be difficult or impossible to measure directly.

For our study, we will need to determine the H_rxn of each of the following three reactions:  

Reaction #1:	Mg(s)	+	2 HCl(aq)		MgCl2(aq)	+	H2(g)
Reaction #2:	MgO(s)	+	2 HCl(aq)		MgCl2(aq)	+	H2O(l)
Reaction #3	H2(g)	+	½ O2(g)		H2O(l)

As written, the first reaction provides one of the reactants we needed, Mg_(s).  However, it requires HCl_(aq) as a reactant, and generates MgCl_2(aq) and H_2(g) as unwanted products.  Likewise, the third reaction provides us with the other reactant we need, O_2(g).  Unfortunately, it introduces H_2(g) as a reactant and generates H₂O_(l) as an unwanted product.  Fortunately, all of these problems are solved if we consider reversing of the Reaction #2:

Now we can see that the MgCl_2(aq) generated as a product in the first reaction is canceled by the reactant MgCl_2(aq) in the second reaction.  Also, the two moles of HCl_(aq) required as a reactant in the first reaction, are canceled by the two moles of HCl _(aq) generated as a product in the second reaction.  Finally, the H_2(g) generated as a product in the first reaction, is canceled by the H_2(g) required as a reactant in the third reaction.

Therefore, the overall H_comb for the reaction of Mg_(s) with O_2(g) to form MgO_(s) , can be calculated as:

In this experiment you will need to determine the temperature change or T for several reactions. Throughout this discussion we have referred to T as the change in temperature. One might assume that this was simply the difference between the beginning and final temperatures as determined with a thermometer. Unfortunately, things are slightly more complicated. For a variety of reasons, including the heat capacity of the thermometer, inefficient mixing of the solution, and heat losses to the calorimeter, the temperature difference determined by the thermometer is less than the actual temperature change of the solution (see Figure below).

To correct for this we must collect a series of temperature data over the course of the reaction. The graph above is a typical plot of temperature versus time for this type of calorimeter. Notice that the initial temperature is increasing slightly over time as it warms to room temperature. At 60 seconds into the experiment, the reactants were mixed and the temperature began to rise. The maximum temperature was seen at 3 minutes and slowly began to fall. To determine the true, instantaneous temperature rise, we must extrapolate this temperature data back to the instant they were mixed, 60 seconds (dotted line). The difference between these two temperatures is the true T we need for our calculations.

Procedure:

Construction of Calorimeters

1. Insert one Styrofoam cup into the an other to make a calorimeter.  You will need two of these calorimeters (one you will calibrate and use throughout the experiment, the other will be used to hold reagents until needed).
2. Add a stirring bar into the calorimeter to be calibrated and place it on a magnetic stirrer.
3. Place a block of Styrofoam on top of the calorimeter as a lid.
4. Insert the PASCO thermocouple through the lid and clamp to a vertical upright.
5. Adjust the height of the probe so that it does not come in contact with the stirring bar but will be totally immersed in the solution.

1. Accurately weigh approximately 50 g of room temperature water into your second (non-calibrated) calorimeter.
2. Start the DataStudio software monitor its temperature for several minutes.  It should not change significantly.
3. Use a microwave oven to heat approximately 200 mL of distilled water to 50-60 °C.
4. Accurately weigh approximately 50 g of this heated water into the calorimeter your are calibrating.
5. Assemble your calorimeter and start acquiring data with the DataStudio Software.
   
6. Adjust the rate of stirring so that good mixing is achieved but no water is splashing on the sides of the calorimeter.
7. After 2-3 minutes of readings, add the room temperature water to your calorimeter as quickly as possible without spilling or splashing.
8. Continue taking readings for another 5-10 minutes.  Then dump the solution, carefully rinse and dry the calorimeter.
9. Repeat a second time.
10. From the graphs of your time/temperature plots, determine an average T and calculate the (WE) for your calorimeter using the example above.

1. Dispense exactly 100.0 mL of 2.00 M HCl directly into your calibrated calorimeter. Take care not to splash the acid on the sides of the calorimeter.  Use this link to determine the density of your HCl:  Density of HCl Solutions.
   
2. Adjust the rate of stirring so that good mixing is achieved but no solution is splashing on the sides of the calorimeter.
3. Start the DataStudio software and acquire temperature data for several minutes.  This will establish the baseline temperature of your HCl.
   
4. After 2-3 minutes, add approximately 1.000 g of MgO to the calorimeter as quickly as possible without splashing the HCl or the powder on the sides of the calorimeter. Continue taking readings for an additional 5-10 minutes.  (Note:  MgO dust is mildly toxic by ingestion.  DO NOT INHALE the dust!)
5. After the reaction is complete, dump the solution down the drain, carefully rinse and dry the calorimeter.
6. Repeat a second time.
7. From the graphs of your time/temperature plots, determine an average T.  From this you should be able to calculate the q _rxn and H_rxn for this reaction.

1. Dispense exactly 100.0 mL of 2.00 M HCl directly into your calibrated calorimeter. Take care not to splash the acid on the sides of the calorimeter.  Use this link to determine the density of your HCl:  Density of HCl Solutions.
2. Adjust the rate of stirring so that good mixing is achieved but no solution is splashing on the sides of the calorimeter. 
3. Cut approximately 0.400 g of Mg into 0.25 inch pieces. Be sure to remove any oxide coating with sandpaper before you weigh the Mg. (DO NOT SAND ON YOUR BENCH!).
4. Start the DataStudio software and acquire temperature data for several minutes.  This will establish the baseline temperature of your HCl.  
5. After 2-3 minutes, add the Mg strips to the calorimeter as quickly as possible without splashing the HCl on the sides of the calorimeter. Continue taking readings for another 5-10 minutes.
6. After the reaction is complete, dump the solution down the drain, carefully rinse and dry the calorimeter.
7. Repeat a second time.
8. From the graphs of your time/temperature plots, determine an average T.  From this you should be able to calculate the q _rxn and H_rxn for this reaction.

1. Unfortunately, this reaction is so exothermic (Explosive, ala the 'Hindenburg') that it can not be safely studied in your calorimeter.  Therefore, we will use the literature value of -285.8 kJ/mol.

Use the following table as a guide for your data collection:  

From your time/temperature curves, calculate:

• The instantaneous change in temperature, T, for the room temperature water / hot water mixing.
• The instantaneous change in temperature, T, for the MgO-HCl reaction.
• The instantaneous change in temperature, T, for the Mg-HCl reaction.

From your T data calculate:

• The water equivalent (WE) for your calorimeter.
• The H_comb for the Mg-O₂ reaction.  How does this compare to the literature value?

• Report the average Water Equivalent for your calorimeter.
• Report the average H_rxn for the MgO-HCl reaction.
• Report the average H_rxn for the Mg-HCl reaction.
• What would be the effect on your calculated T if you took data at a faster or slower rate?
• What effect does the assumption that water has a density of 1.000 g/mL have on your calculations?
• Is the density of the reaction products the same as water? Why?
• How would you improve the design of the calorimeter to reduce heat loss?

(Updated 6/5/07 by C.R. Snelling)