# Experiment 7 Hess' Law ```Experiment 7: Enthalpy of Formation of Magnesium Oxide
Objective: In this experiment, a simple calorimeter will be constructed and calibrated,
and Hess' law of constant heat summation will be used to determine the enthalpy of
formation of magnesium oxide, MgO.
When magnesium is burned in oxygen, a large quantity of heat is released which results
in a large, negative ∆H&deg;rxn value:
(1)
Mg(s) + 1/2 O2(g) → MgO(s) ; ∆H&deg;rxn = large negative number of joules, J
The change in enthalpy of this reaction is quite difficult to measure directly by
experiment. However, the heat of reaction can be obtained indirectly by measuring the
enthalpies of other reactions and using Hess' law.
Review of ∆E and ∆H.
Virtually all chemical processes involve energy transfer of one type or another, and the
branch of chemistry that explores this transfer is called thermochemistry. The energy
change of a reaction, symbolized by the expression ∆Erxn, is the sum of energy which is
transferred as both heat, q, and work, w:
∆Erxn = q + w
For a reaction that occurs at constant pressure, the term enthalpy is used, which is the
sum of the energy of all the atoms and molecules plus the work of displacing the
environment, that is, the PV work:
H = E + PV
Thus, the enthalpy change for a chemical reaction at constant pressure is defined by the
following equation:
∆Hrxn = ∆Erxn+ P∆V
In the case of an enthalpy change which takes place at 1 atm of pressure, we use the
notation ∆H&deg;rxn.
In accordance with Hess' Law, enthalpy changes for chemical reactions are additive.
If two chemical equations are added together to form a third equation, the enthalpy
change of the third equation, ∆H&deg;rxn(3), is equal to the sum of ∆H&deg;rxn(1) and ∆H&deg;rxn(2).
When applying Hess' law, it is important to establish a convention for the signs, positive
or negative, of the enthalpy changes. An exothermic reaction is one which releases
energy and is assigned a negative value. An endothermic reaction is one which absorbs
energy and is assigned a positive value. The additive property of ∆H&deg;rxn values will be
applied in this experiment in order to determine the enthalpy change associated with the
burning of magnesium metal in air.
For the combustion of magnesium, reaction (1) [previous page], one possible set of
reactions is:
(2)
Mg(s) + 2 H+(aq) → Mg2+(aq) + H2(g)
∆H&deg;rxn(2) = negative number
(3)
MgO(s) + 2 H+(aq) → Mg2+(aq) + H2O (l)
∆H&deg;rxn(3) = negative number
(4)
1/2 O2 (g) + H2(g) → H2O (l)
∆H&deg;rxn(4) = negative number
Reaction (1) is equal to reaction (2) minus reaction (3) plus reaction (4):
∆H&deg;rxn(1) = ∆H&deg;rxn(2) – ∆H&deg;rxn(3) + ∆H&deg;rxn(4)
The enthalpy of formation of liquid H2O has been measured and is given by:
∆H&deg;rxn(4) = ∆H&deg;f (H2O) = –285840 Joules/mole = –285.84 kJ/mol
The enthalpies of reactions (2) and (3) are measurable quantities. Heat is released by the
addition of excess strong acid to Mg, thus the quantity ∆H&deg;rxn(2) will be a negative
number. Similarly, the addition of excess strong acid MgO will release heat, and
∆H&deg;rxn(3) will also be negative.
Measuring the Heat Capacity of a Calorimeter
A calorimeter is a reaction vessel that is well insulated in order to prevent heat transfer
between the reaction and its surroundings. As heat is evolved by the reaction inside the
calorimeter, the temperature of the contents increases, and it is this temperature change
which is measured and related to the enthalpy of the reaction. Thus, all heat effects that
are observed in the calorimeter should be the result only of the ∆H&deg; value
of the reaction or process occurring in the calorimeter.
The relationship between the amount of heat absorbed or released by a system, q, and the
resulting change in temperature, ∆T = Tfinal – Tinitial, may be expressed in terms of the heat
that is absorbed or released by the water and the heat that is absorbed or released by the
calorimeter. The reactions you are observing today are both exothermic, so the system is
losing heat and the water and calorimeter are gaining heat.
q (gained by water) = swater x mwater x ∆Twater and q (gained by calorimeter) = Ccal x ∆Tcal
At constant pressure ∆H = qp. Therefore the
∆Hsystem = - (swater x mwater x ∆Twater + Ccal x ∆Tcal)
This is just like what you did last week.
A calorimeter must be calibrated to determine its heat capacity, that is, the amount of heat
required to raise the temperature of the calorimeter itself by one degree Celsius or Kelvin.
The same Ccal from last week will be used this week.
To measure the ΔHorxn values for reactions (2) and (3) a small amount of each solid will
be added to 100.0mL of HCl. The heat released by the reaction goes into the calorimeter.
The ΔHorxn is then calculated by ∆Ho = - (swater x mwater x ∆Twater + Ccal x ∆Tcal). The unit
for this ΔHo will of course be in Joules (J). The ΔHo needs to be expressed as a per mole
quantity however. Since the amount of solid will limit (limiting reagent) in all cases, the
calculated ΔHo needs to be divided by the number of moles of the solid reacted.
ΔHorxn/mole = = - (swater x mwater x ∆Twater + Ccal x ∆Tcal)/moles of reactant (Mg or MgO
solid)
Measuring ΔT
Instead of a thermometer, a temperature probe interfaced to a computer will be used to
acquire the temperature readings in this experiment. Because no calorimeter is free from
heat leaks, it is possible that you will see some heat loss to the surroundings reflected in
your data. Figure 1 below shows a temperature vs. time plot for a calorimetric experiment
in which the reaction was exothermic. After the initial sharp rise in temperature when the
reaction is begun (at time of mixing, t = 0 seconds), the temperature begins to decrease
due to heat loss from the calorimeter. As the temperature equilibrium becomes complete,
the loss becomes steady and the temperature decrease is linear.
Extrapolation of this linear portion of the curve back to t = 0 seconds gives an accurate
value for the maximum temperature attained, Tf, if equilibrium were to take place
instantaneously with no thermometer lag.
Procedure
The Temperature will be monitored using the Logger Pro program. Open the program on
the Mac and, if the Temperature probe is properly connected, you will see a screen
labeled Temperature vs. time. The program is now ready for data acquisition.
When you want to acquire data you click on the start button (green arrow). When you are
finished collecting a data set, click stop (red square).
For reaction (1) you should use 100.0 mL of 1 M HCl and 0.07 g of Mg
For reaction (2) you should use 100.0 mL of 1 M HCl and .25 g of MgO
Record the exact masses of each solid reagent. Run each experiment 3 times.
Data
You will need to construct your own data tables for this lab. You are going to perform
the heat of reaction with Mg three times and the heat of reaction with MgO three times.
Carefully consider all of the data you will need for all three trials when you prepare your
data tables.
Print a copy of your graphs of temperature vs time for each trial to include in your lab
writeup.
Analysis and Calculations:
Use the data you collected to calculate the enthalpy change/mol (ΔHorxn/mole) for Mg or
MgO for each individual trial.
ΔHorxn/mole = - (swater x mwater x ∆Twater + Ccal x ∆Tcal)/moles of reactant (Mg or MgO
solid)
Don’t average the change in temperature (ΔTcal.) and don’t average the mass.
Do 6 separate calculations. Three for Mg and three for MgO.
2. Determine an average value of ΔHorxn/mole for Mg and MgO from your three trials for
each.
3. Using the answer from question 2 along with the enthalpy of formation for water
(given earlier in the lab) use Hess’s law to calculate the enthalpy of formation for
magnesium oxide (see equations 1-4 on pages 1 and 2).
4. Compare your value of the enthalpy of formation of magnesium oxide to the value in
your text. Determine a value for percent error.