# Calorimetry and Hess’s Law

Elemental magnesium is one of the principal components of flares used to illuminate nighttime activities, or to aid in signaling one’s location to aircraft and ships. Your instructor may ignite a strip of magnesium ribbon to demonstrate the combustion of magnesium in air. It will be evident that a great deal of light energy is released from this reaction. A direct method for measuring the heat produced by this reaction would be difficult, so we shall resort to an indirect method in this experiment as discussed below. Some chemical reactions (including the one above) are associated with the evolution of thermal energy and are called exothermic reactions. When there is absorption of energy in a chemical reaction, the process is called endothermic.

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The magnitude of the energy change is determined by the particular reaction as well as the amount of product(s) formed. The thermal energy transferred in a balanced chemical reaction carried out at constant pressure is called the enthalpy of reaction (or heat of reaction) and is given the symbol ΔHrxn. ΔHrxn is often expressed in units of kJ/mole where mole refers to the amount of a reactant or a product involved in the reaction. In general, the reactant or product must be specified. In this experiment, you will measure the enthalpy changes of several exothermic reactions utilizing a simple calorimeter. This calorimeter consists of an insulated vessel (a Styrofoam cup), a thermometer, and a lid (which is loose fitting to allow the pressure to remain constant. The energy given off by any reaction carried out in the calorimeter is absorbed by both the calorimeter and the solvent (water). This causes an increase in the temperature of the calorimeter and solvent that can be measured by a thermometer. The heat that is absorbed by the calorimeter and solvent is calculated from the equation: qcal = C ⋅ ΔT (1)

where C is the heat capacity of the calorimeter and solvent, and ΔT is the change in temperature of the water (the solvent) in the calorimeter. Heat capacity is defined as the amount of energy required to raise the temperature of an object by 1 °C. In this experiment, the vessel and the amount of solvent remain constant, so C is a constant. Enthalpy is an extensive quantity, so the amount of heat generated by the reaction is given by the expression: qrxn = n ⋅ ΔH (2) where n is the number of moles of a specific reactant or product and ΔH is the enthalpy change of the reaction in kJ/mol. Since the energy of the universe is conserved, the total energy change of the system (the reaction) and surroundings (calorimeter and solvent) is equal to zero. These relationships can be combined as shown in equation (3).

qsystem + qsurroundings = qreaction + qcalorimeter = n⋅ΔH + C⋅ΔT = 0 (3)

This equation can be rearranged to determine either C or ΔH as shown in equations (4) and (5). C = − n⋅ΔH/ΔT (4)
ΔH = − C⋅ΔT/n (5)

For exothermic reactions, ΔH < 0 and ΔT > 0.
The main experimental problem in any calorimetric measurement is obtaining an accurate value of ΔT. The initial temperature, Ti, of the reactants can be determined directly using a thermometer. However, it is difficult to obtain a precise value for the final temperature, Tf (the instantaneous temperature when the reactants are mixed together and react), because (1) reactions do not occur instantaneously, and (2) calorimeters are not perfectly insulating, but actually allow some heat energy to slowly enter or escape from the calorimeter over time. This occurs both during the reaction and after its completion. If an exothermic reaction occurs in a hypothetical calorimeter that is perfectly insulated, all of the heat produced by the reaction will remain in the calorimeter, resulting in a constant final temperature. This would yield the same ΔT whether or not the reaction is instantaneous.

Now consider a hypothetical exothermic reaction that occurs instantaneously, but in a realistic calorimeter that is not perfectly insulated. In this case, the temperature of the calorimeter would diminish over time due to the gradual escape of heat energy to the surroundings. The “final” temperature to be used in determining ΔT in this case is actually the maximum temperature reached immediately after reaction occurs, since this temperature change is due exclusively to the heat produced in the reaction, and no escaping of heat to the surroundings has occurred yet. For real calorimeter experiments, reactions neither occur instantaneously nor are calorimeters perfectly insulated. Thus, during an exothermic reaction the temperature of the calorimeter increases initially, but never has a chance to reach the correct maximum “final” temperature since heat is escaping to the surroundings even while the reaction is proceeding toward completion.

A correction for this heat exchange is made by an extrapolation process using the temperature vs. time curve (see Figure 1). First, a plot of the temperature readings as a function of time for the reaction is generated. By extrapolating only the linear portion of the curve (e.g., the points including and after the maximum temperature) back to zero time (the time when the reactants were mixed in the calorimeter), Tf is obtained. The Tf value determined in this manner will be the temperature that the calorimeter and the solvent would have reached, had the reaction occurred instantaneously and with no heat exchange to the room. This value should be used for the calculation of change in temperature, ΔT. Consult with your TA for specific instructions for extrapolation using Microsoft Excel.

A. Determination of the Enthalpy of Combustion of Mg Using Hess’s Law The calorimeter will be used to determine the enthalpy of combustion of magnesium by application of Hess’s law. Consider the following reactions:

(a) H2(g) + ½ O2 (g) → H2O (l) ΔHa = − 285.84 kJ/mole
(b) Mg(s) + 2 H+ (aq) → Mg2+ (aq) + H2 (g) ΔHb
(c) Mg2+ (aq) + H2O (l) → MgO (s) + 2 H+ (aq) ΔHc

By adding equations (a), (b), and (c) we obtain

(d) Mg (s) + ½ O2 (g) → MgO (s) ΔHrxn = ΔHa + ΔHb + ΔHc

which represents the combustion of Mg(s).

Reaction (a) represents the formation of liquid water from its constituent elements. The enthalpy change for this reaction, symbolized ΔHa above, is the standard heat of formation of liquid water (or ΔHf (H2O)) and is a known quantity. ΔHb and ΔHc will be determined experimentally by measuring the temperature rise when known masses of magnesium metal and magnesium oxide, respectively, are added to hydrochloric acid. Reaction (c) as written is an endothermic reaction. Since it is easier to perform the reverse (exothermic) reaction, the data you collect will be of opposite sign to that needed for the Hess’s law calculation for reaction (d). When data from your analysis is correctly combined with that for the known reaction (a), the enthalpy of combustion of magnesium metal can be obtained.

PROCEDURE:
Note: Handle the Styrofoam cups gently. They will be used by other lab sections!

A. Determination of the Enthalpy of Combustion of Magnesium
Reaction of Magnesium Metal and Hydrochloric Acid
1. Using the graduated cylinder, add 50.0 mL of 1.0 M HCl to the empty calorimeter. Wait for a few minutes to allow the set-up to reach thermal equilibrium. 2. While waiting, determine the mass of a sample of magnesium ribbon (about 0.15 g) on the analytical balance, and then wrap it with a piece of copper wire. The copper will not react in the solution; its purpose is to prevent the magnesium from floating to the surface during the reaction. Do not wrap the magnesium too tightly or it will not react quickly enough with the HCl solution. Do not wrap the magnesium too loosely since it may escape the copper “cage” and float. 3. Using LoggerPro, start a run of 500 seconds with the temperature probe in the 1.0 M HCl in the calorimeter (with lid). 4. The magnesium/copper bundle is added to the HCl solution. Replace the lid with the thermometer in place, and begin swirling to mix. Be sure to support the temperature probe.

Continue swirling and collecting data and record about 300 seconds or until the temperature starts decreasing. This will provide the linear part of the curve, and are the most important points for the extrapolation procedure. 5. When data collection is completed, rinse the calorimeter and thermometer with distilled water and dry as completely as possible. Place the piece of copper in the container labeled “copper waste.” B. Reaction of Magnesium Oxide and Hydrochloric Acid

1. Place 50.0 mL of 1.0 M HCl into a clean graduated cylinder. 2. On a top-loading balance, transfer approximately 0.7 to 0.8 g of MgO to a clean weighing boat (no need to record this mass). Next, determine the mass of the MgO and the weighing boat on the analytical balance and record the data. Transfer the MgO to the dry calorimeter. 3. On the analytical balance, record the mass of the “empty” weighing boat after the transfer and calculate the mass of MgO actually transferred to the calorimeter. 4. Record the initial temperature (Ti) of the 1.0 M HCl solution in the graduated cylinder. 5. Note the time (time = zero) and add the 50.0 mL of 1.0 M HCl to the calorimeter containing the MgO. 7-8 points after the temperature maximum.

In this reaction all the MgO should react since HCl is used in excess. However, if the solid MgO is allowed to sit on the bottom or sides of the cup it will not dissolve and hence it will not react. Make sure the solution is mixed constantly but gently. (NOTE: Before discarding this solution, check to see that all of the MgO has reacted. If solid MgO remains, the results from this portion of the experiment are not accurate. If any solid is present, this portion of the experiment must be repeated.) 6. When data collection is completed, rinse the calorimeter and thermometer with distilled water and dry as completely as possible.