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Heats of Reaction: Hess’s Law
PRE-LAB ASSIGNMENTS:
To be assigned by your lab instructor.
STUDENT LEARNING OUTCOMES:


Learn how to calculate the enthalpy change for a reaction from temperature data and
specific heats.
Learn how to use Hess’s Law to calculate the enthalpy change for a reaction.
EXPERIMENTAL GOALS:
The goal of this lab is to experimentally determine the enthalpy changes for two reactions, and
use this data to determine the enthalpy change for a third reaction, which can then be compared
to the expected enthalpy change using the given thermodynamic data.
INTRODUCTION:
Under conditions of constant pressure, the amount of heat gained or lost in a chemical or
physical change is the enthalpy change for the process, often denoted as H. The enthalpy
change for a chemical reaction is also known as the heat of reaction, Hrxn. Enthalpy is a state
function, which means it is path independent. In other words, the path which leads from the
initial conditions to the final conditions is irrelevant to the calculation of the overall enthalpy
change.
The path independence of Hrxn is best demonstrated by Hess’s Law: if a reaction can be
expressed as the sum of a series of steps, then the enthalpy change for the overall reaction is the
sum of the H values for the individual steps. This can be generally shown as
A  B  C; H 1  - 100 kJ
C  D; H 2   30 kJ
A  B  D; H 3  H 1  H 2  - 70 kJ
With Hess’s Law, it is possible to determine the reaction enthalpy without actually measuring
that reaction’s enthalpy change. This is only possible if other reaction enthalpies are known that
sum to the desired products from the desired reactants. This ability is important because
experimentally, some reactions are difficult or nearly impossible to measure directly.
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In this experiment the enthalpy changes for two chemical reactions will be measured, and
the results will be used to calculate the enthalpy change for a third chemical reaction using
Hess’s Law. The reactions for which H will be measured are:
I.
H+(aq) + OH-(aq)  H2O(l)
II.
Mg(s) + 2H+(aq)  Mg2+(aq) + H2(g)
From these measurements, H will be calculated for reaction III:
III.
Mg(s) + 2H2O(l)  Mg2+(aq) + 2OH-(aq) + H2(g)
Since reactions I and II are exothermic, the measured value for their H’s will be
negative. Each heat of reaction is obtained by assuming that all of the heat liberated by the
reaction (Hrxn) goes toward heating up the solution containing the reacting chemicals (H1) and
the container (H2):
reactants
products
heat liberated, Hrxn
heat absorbed by solution, H1
solution
heat absorbed by container, H2
container
Since the solution and container are absorbing heat, both H1 and H2 are positive, and are given
by the formulas
H1 = csoln m ΔT
H2 = Ccontainer ΔT
where csoln is the specific heat of the solution, Ccontainer is the heat capacity of the container, m is
the mass of the solution, and ΔT is the change in temperature (ΔT = Tfinal – Tinitial). The heat of
the reaction, Hrxn, is calculated from the equation
Hrxn = -(H1 + H2)
When the chemicals are mixed, the temperature of the solution and container will rise,
then start to fall when the reaction is complete. While the temperature is rising, some of the heat
will be lost to the surroundings, and will not be available to warm the solution. To correct for
this, a graph is made of the temperature vs. time; when this graph is extrapolated back to zero
time (time of mixing), the correct (maximum) final temperature, Tf, can be obtained, which is the
value that is used to calculate ΔT. (See Figure 1.)
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Tf
Temperature, °C
32°
30°
28°
26°
24°
0
1
2
3
4
Time, min
Figure 1. Graph of time vs. temperature used to determine Tf.
split stopper
clamp
thermometer
stirrer
lid
2 nested Styrofoam cups
Figure 2. Calorimeter setup.
5
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PROCEDURE:
I. H+ + OH-  H2O
a. Weigh an empty, dry coffee cup calorimeter made by nesting two Styrofoam cups together.
(3) Using a graduated cylinder, measure 48.0 mL of 2.0 M HCl and add it to the calorimeter.
b. Measure 50.0 mL of 2.0 M NaOH and place it in a 150 mL beaker. Allow this solution to sit
for about five minutes.
c. Using a thermometer, determine the temperature of the HCl solution in the calorimeter to the
nearest 0.1 oC. Clean and dry the thermometer to measure the temperature of the NaOH
solution. These solutions should have the same or very close to the same temperature. Take
the average of these two temperatures as your initial temperature, Ti (1).
d. Now assemble the calorimeter. Insert the thermometer into the split stopper; slide the
stopper toward the top of the thermometer. Slide the thermometer into the center hole of the
calorimeter lid. Place the ring stand clamp on the stopper, and adjust the clamp on the ring
stand to where it will hold the thermometer bulb about 1 cm from the bottom of the cup.
Insert the stirrer in the second hole of the lid with the loop encircling the bulb of the
thermometer. (See Figure 2.)
e. Be ready to start timing and recording temperatures as soon as you mix the acid and base.
Rapidly add the NaOH solution to the HCl solution in the calorimeter, being careful not to
splash any on the upper sides of the calorimeter. Note the time of adding, close the lid, begin
stirring, and read the thermometer to the nearest 0.1°C every 10 seconds for the first 90
seconds, and then every 30 seconds until a total of 5 minutes has elapsed.
f. When the above procedure is completed, weigh the calorimeter and its contents (2), empty
the solution into the sink, and rinse and dry the calorimeter and thermometer to prepare for
the second reaction.
II. Mg + 2H+  Mg2+ + H2
a. Re-weigh the empty, dry calorimeter (16).
b. Measure 50.0 mL of 2.0 M HCl into the calorimeter. Measure and record the temperature of
the HCl. This will be Ti (14).
c. Accurately weigh about 0.5 g of Mg turnings onto a piece of weighing paper (18).
d. Assemble the calorimeter and thermometer as in part I, and add the Mg to the HCl. Stir and
record the temperatures as in part I.
e. When the reaction is completed, weigh the calorimeter and contents, (15) calculate the
weight of the contents (17), empty the solution into the sink, and rinse and dry the
calorimeter and thermometer.
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III. Calculations.
a. H+ + OH-  H2O
1. Plot the temperature of the reaction mixture versus time after mixing. The graph should
be expanded as much as possible: the lowest temperature you recorded during the run
should be near the bottom of the graph paper, and the highest temperature should be
somewhere near the middle of the graph paper. (Do not graph the initial temperature!
This will compress the scale of the graph too much.) Using a straight edge, draw a
straight line that falls closest to the most points on the later part of the curve. (See Figure
1.) Extend the straight line to cross the y-axis at time t = 0, the time of mixing (6). From
this intercept (Tf), and the initial temperature (Ti), calculate ΔT (7).
2. Calculate ΔH1, the heat absorbed by the solution (H1 = csoln m ΔT). Since the solution is
relatively dilute, we can use the specific heat of water, 4.18 J g-1 °C-1, as csoln (8)
3. Calculate ΔH2, the heat absorbed by the container (H2 = Ccontainer ΔT).
capacity of the container, Ccontainer, is 8.36 J °C-1 (9).
The heat
4. Calculate ΔHrxn [Hrxn = -(H1 + H2)].
5. Calculate the number of moles of H+ (HCl) reacted (12).
6. Divide ΔHrxn by the number of moles of HCl to obtain ΔHI (13).
b. Mg + 2H+  Mg2+ + H2
1. Plot the temperature of the reaction mixture versus time after mixing. Using a straight
edge, draw a straight line that falls closest to the most points on the later part of the curve.
Extend the straight line to cross the y-axis at time t = 0, the time of mixing (20). From
this intercept (Tf), and the initial temperature (Ti), calculate ΔT (21).
2. Calculate ΔH1, the heat absorbed by the solution (H1 = csoln m ΔT). Since the solution is
relatively dilute, we can use the specific heat of water, 4.18 J g-1 °C-1, as csoln (8)
3. Calculate ΔH2, the heat absorbed by the container (H2 = Ccontainer ΔT). The heat
capacity of the container, Ccontainer, is 8.36 J °C-1 (9).
4. Calculate ΔHrxn [Hrxn = -(H1 + H2)].
5. Calculate the number of moles of Mg (25).
6. Divide ΔHrxn by the number of moles of Mg to obtain ΔHII (13).
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c. Mg + 2H2O  Mg2+ + 2OH- + H2
1. Using Hess’s Law and your values for ΔHI and ΔHII for reactions I and II, calculate ΔHIII
for reaction III:
III.
Mg(s) + 2H2O(l)  Mg2+(aq) + 2OH-(aq) + H2(g)
2. Using the heats of formation (Hf°) below, calculate the “true” value of ΔHIII. (28)
Hf° (heat of formation, kJ/mol)
Mg
0
H2O -285.8
Mg2+: -467.0
OH-: -230.0
H2:
0
3. Calculate the % error between your value and the true value:
% error 
(your valu e - true value)
 100
true value
(29)
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LAB REPORT: Heats of Reaction — Hess’s Law
Name ________________________________
Date _________
Partner ________________________________
Section _________
Report Grade ______
I. H+ + OH+  H2O
1.
Temperature of HCl (Ti)
__________
2.
Weight of calorimeter + solution
__________
3.
Weight of empty, dry calorimeter
__________
4.
Weight of solution
__________
5.
Temperatures of reaction mixture at:
0 s (Ti)
10 s
20 s
30 s
40 s
50 s
60 s
70 s
80 s
90 s
2.0 min 2.5 min 3.0 min 3.5 min 4.0 min 4.5 min 5.0 min
6.
Tf (extrapolated from graph)
__________
7.
ΔT
__________
8.
ΔH1 (show calculations)
__________
9.
ΔH2 (show calculations)
__________
10. ΔHrxn (show calculations)
__________
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11. Volume of 2.0 M HCl solution in liters
__________
12. Moles of H+ in HCl solution
__________
13. ΔHI (= ΔHrxn / moles H+)
__________
II. Mg + 2H+  Mg2+ + H2
14. Temperature of HCl (Ti)
__________
15. Weight of calorimeter + solution
__________
16. Weight of empty, dry calorimeter
__________
17. Weight of solution
__________
18. Weight of Mg
__________
19. Temperatures of reaction mixture at:
0 s (Ti)
10 s
20 s
30 s
40 s
50 s
60 s
70 s
80 s
90 s
2.0 min 2.5 min 3.0 min 3.5 min 4.0 min 4.5 min 5.0 min
20. Tf (extrapolated from graph)
__________
21. ΔT
__________
22. ΔH1 (show calculations)
__________
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23. ΔH2 (show calculations)
__________
24. ΔHrxn (show calculations)
__________
25. Moles of Mg (from #18)
__________
26. ΔHII (= ΔHrxn / moles Mg)
__________
III. Mg + 2H2O  Mg2+ + 2OH- + H2
27. ΔHIII for Mg + 2H2O  Mg2+ + 2OH- + H2
(calculated from ΔHI and ΔHII using Hess’s law) (show calculations)
__________
28. ΔHIII for Mg + 2H2O  Mg2+ + 2OH- + H2
(calculated from heats of formation) (show calculations)
__________
29. % error 
(your valu e - true value)
 100
true value
__________
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Name ________________________________
162
Name ________________________________