Explorations in Thermodynamics:
Calorimetry, Enthalpy & Heats of Reaction
Dena K. Leggett, Ph.D. and Jon H. Hardesty, Ph.D.
Collin County Community College
Dept. of Chemistry
1. Introduction:
One of the earliest scientific observations made by humans must have been the
warmth provided by fire, and since that time the extraordinary utility of heat as a tool has
contributed to many of the most profound technological advances in humanity’s history.
The science of heat flow, or more generally energy flow, is called thermodynamics. Many
of the fundamental foundations of thermodynamics have been discussed in our lectures
on gas laws and the kinetic molecular theory of gases where we learned that heat and
kinetic energy (the energy of motion) of gaseous atoms/molecules are equivalent. Now
we are ready to turn our attention to more subtle aspects of thermodynamics relating to
thermal energy being extracted from or stored within a wider array of chemical
compounds than gases.
In this set of experiments we will focus our attention upon one particular area of
thermodynamics, namely calorimetry, a technique used to measure heat flow into and
out of matter. The basic idea of the technique is quite simple. The matter we are
interested in studying is placed into a container called a calorimeter that segregates the
thermal process we are interested in studying from the rest of the universe. As changes
occur to that matter, we can follow the movement of heat from one portion of the matter
to another by observing temperature changes. The container we use as a calorimeter
should thermally insulate the matter we’re interested in studying, it should prevent matter
from entering or exiting once our measurement has begun, and it should allow for easy
measurement of temperature changes. A reasonable calorimeter can be constructed from
a pair of nested (i.e. one stacked inside the other) Styrofoam cups with a loose fitting
“cap” on top to limit heat/material transfers into and out of the device (see Figure 1).
2. Specific Heat Capacity:
Experimentally, measuring
heat flows is somewhat difficult.
We do not have a “heat meter”
that we can use to directly
measure the amount of heat
released/absorbed by matter
when a thermodynamic process
occurs. Thermometers, however,
can be used to measure changes
in temperature that can be
utilized as indirect measures of
heat flow. In order to precisely correlate measured temperature changes to the flow of
particular amounts of thermal energy, a proportionality constant that relates these two
quantities called the heat capacity of a material is used. It indicates the amount of heat
required to raise the temperature of a sample of that material by 1˚C. Heat capacity is an
extensive property of matter, meaning that it varies with sample size. To account for this
fact, experimentally measured heat capacities are routinely corrected to account for a
measurement on a 1 g sample, giving rise to a slight variation called the specific heat
capacity (c) that indicates the amount of heat required to raise the temperature of 1 g of
the substance by 1˚C. Mathematically, the proportionality can be expressed as shown in
equation 2.1:
qreleased/ absorbed
m c
T
(Eqn 2.1)
where c is the specific heat capacity (in J/(g ˚C)), q is the quantity of thermal energy
released/absorbed (in J), m is the mass of the sample (in g), and T is the change in
temperature (in ˚C), which is taken as Tfinal-Tinitial for the sample.
Since specific heat capacities are positive constants for a given material, heat flow
is directly proportional to changes in temperature. Thus if the change in temperature
( T) is positive, then q is also positive indicating the absorption of heat by the sample (an
endothermic process). Alternatively, if T is negative then q is also negative indicating
the loss of heat by the sample (an exothermic process). The fascinating feature of
specific heat capacities is that they adopt a wide array of values depending upon material
as shown in the Table 1.
Table 1-Specific Heat Capacities of Common Substances
Material
Specific Heat Capacity
(J/g ˚C) at 25˚Ci
Aluminum
Graphite
Gold
Wood
Cement
Granite
H2O(l)
0.900
0.711
0.129
1.76
0.88
0.79
4.184
3. Determining a Calorimeter Constant:
When a measurement is made in a calorimeter, we must account for the fact that
the calorimeter itself can release heat into or absorb heat out of the process we are
investigating while our measurement is being recorded. The calorimeter is in thermal
contact with the matter we are interested in studying (the system of interest), so heat can
be transferred between the system and the calorimeter (a portion of the surroundings).
While we may not be particularly interested in studying the heat flow into or out of the
calorimeter, it is essential that we account for it to prevent errors in the measurement of
the heat flow pertaining to the system of interest. Since our calorimeter (the nested
Styrofoam cups) is a fixed mass, we can rearrange the expression for the specific heat
capacity of the calorimeter and take the product of the specific heat capacity of the
calorimeter (ccal) and the mass of the calorimeter as a new constant called the calorimeter
constant (Ccalorimeter) as shown below:
qcal
mcal c cal
qcal
Ccal
(where Ccal
Tcal
Tcal
(Eqn 3.1)
Calorimeter Constant
mcal c cal )
To measure the magnitude of the calorimeter constant we will carry out a measurement in
which “hot” water is mixed with “cold” water in the calorimeter. Common experience
tells us that the temperature of the water after mixing should lie between the initial “hot”
and “cold” values. The First Law of Thermodynamics tells us that the sum of all of the
thermal energy present in the calorimeter and in the two samples of water must stay
constant throughout our measurement. (Remember, energy cannot be created or
destroyed.) However, it will redistribute itself among all three components (the “hot”
water, the “cold” water, and the calorimeter). Mathematically, the First Law for this
mixing process can be written as:
0 qhot
qcold qcal (Eqn 3.2)
We know from our everyday experience that heat will exit the hot water and enter the
cold water and the calorimeter, so we can rearrange Eqn. 3.2 to give:
qhot
qcold qcal (Eqn3.3)
Notice that this expression can be interpreted as an exothermic process from the
perspective of the hot water (–q, heat lost) and an endothermic process from the
perspective of the cold water and the calorimeter (+q’s, heat gained). Since we know the
heat capacity of liquid water (4.184 J/g ˚C), and we can easily measure the masses of the
hot water and the cold water that we pour into the calorimeter as well as the initial and
final temperatures for each component, we can make the following substitutions into Eqn
3.3:
qhot
mhot c hot
qcold
mcold c cold
qcal
Ccal
Tcal
Thot
Tcold
(from Eqn 3.1)
(We assume that Tcal = Tcold because the cold water is in contact with the calorimeter at
all times during the experiment, allowing these two components to maintain thermal
equilibrium throughout the experiment.) The resulting mathematical equation (that you
should derive) contains only one unknown, the calorimeter constant, Ccal. The value we
determine for this constant is true for your calorimeter, and it will be incorporated into
the next two portions of the experiment.
4. Determining the Specific Heat Capacity of a Metal:
The specific heat capacity of a metal can be readily measured using a very similar
technique. A sample of “hot” metal of known mass and temperature can be placed into a
calorimeter containing a sample of “cold” water of known mass and temperature.
Practical experience tells us that heat should exit the metal sample and enter the cold
water and the calorimeter, resulting in an increase in the temperature of the water above
its initial value. Assuming that no additional thermal energy will be generated or
destroyed once the “hot” metal is added to the “cold” water we can utilize the First Law
to write the following equation:
0 qmetal qwater qcal (Eqn4.1)
Rearranging this expression to solve for qmetal results in equation 4.2:
qmetal qwater qcal (Eqn4.2)
Equation 4.2 can be interpreted in terms of an exothermic process from the perspective of
the metal (-q, heat lost by the metal) and an endothermic process from the perspective of
the water and the calorimeter (+q, heat gained by the cold water and the calorimeter). We
can write heat flow expressions for each component in Eqn 4.2 as shown below:
qmetal
mmetal c metal
Tmetal
qwater
mwater c water
Twater
qcal
Ccal
Tcal
These expressions can be substituted into Eqn 4.2 to arrive at an equation (that you
should derive) that allows us to calculate the specific heat capacity of the metal (cmetal).
Once this expression is obtained, we can turn our attention to the following facts. The
masses of the water (mwater) and the metal (mmetal) can be easily measured along with the
changes in temperatures of the water ( Twater ) and the metal ( Tmetal). We also know the
specific heat of water (cwater), the calorimeter constant, (Ccal), and we can assume Twater =
Tcal (because the water and the calorimeter remain in contact with one another
throughout the experiment). Plugging all of these known values into the expression
results in an equation containing only one unknown, cmetal.
5. Determining the Heat of Reaction ( Hrxn) for an Acid/Base Neutralization
Reaction:
Most chemical reactions occur with a net absorption or liberation of energy in the form of
heat. These heat flows largely originate from two primary sources:
A. In the case of matter undergoing changes in composition in the gas phase where
reactants and products do not interact with solvent particles (such as H2(g) +
Cl2(g)
2HCl(g)) these heat flows result from changes in the potential
energies of the electrons as reactant particles are converted into product
particles. When the electrons are less stable in the products than they are in the
reactants, energy is absorbed by the reacting particles and transferred into the
surrounding environment as heat (Figure 2a). If this condition occurs the
reaction is said to be an endothermic reaction. Alternatively, when electrons
are more stable in the products than they are in the reactants, energy is released
from the reacting particles in the form of heat extracted from the surrounding
environment (Figure 2b). If this condition occurs the reaction is said to be an
exothermic reaction. Effectively, the heat flow that is observed in these
reactions equates to the changes in the relative stabilities of the electrons within
the atoms/molecules/ions as reactants are converted to products.
Products
Products
Reactants
a
qfinal> qinitial
+qreaction
Reactants
qfinal< qinitial
-qreaction
b
Figure 2. Potential Energy Diagrams for Endothermic (I) and Exothermic (II)
Reactions
B. In the case of matter undergoing changes in composition in solution where
reactants and products do interact with solvent particles (such as the reaction
HCl(aq) + NaOH(aq)
H2O(l) + NaCl(aq)) these heat flows result from a
combination of a) changes in the potential energies of the electrons in reactant
particles versus product particles as described above, and b) changes in the
strengths of the interactions between solvent particles and reactant particles
versus the strengths of the interactions between solvent particles and product
particles as the reaction proceeds from start to finish. Since most reactions that
we study in the laboratory are carried out in solution, the values that are typically
measured and tabulated incorporate these combined effects unless otherwise
indicated.
To properly measure the heat flows into/out of a chemical reaction in solution using
a calorimeter, it is essential that the system be carefully defined as only the chemical
reaction of interest. In this context, the system is precisely defined as the point of
location of bond breakage and/or bond formation in the reactant atoms/molecules/ions
along with those few solvent molecules directly interacting with the reactant particles.
The surroundings are taken as the calorimeter and the bulk solution that in practice means
those solvent molecules not directly interacting with the reactant particles. The
overwhelming majority of solvent molecules in a reasonably dilute solution fall into this
bulk solution category, and as a result it must be remembered that when a thermometer
is placed into the solution to measure the temperature of the solution, it is
measuring the temperature of this bulk solvent (i.e. the surroundings).
In this portion of the experiment we will mix a measured volume of 1.00 M
aqueous NaOH solution with an equivalent measured volume of 1.00 M aqueous HCl
solution to provide a stoichiometric ratio of reactants for the neutralization reaction
shown below.
HCl(aq) + NaOH(aq)
H2O(l) + NaCl(aq)
Thermodynamically, we can follow the same line of reasoning adopted in the prior two
sections. According to the First Law of Thermodynamics, energy cannot be created or
destroyed as the reaction occurs within the calorimeter, it can only be transferred from
one component to another. Thus, we can write the following expression:
0 qrxn qsolution qcal (Eqn5.1)
where qrxn is the heat released/absorbed by the reaction (system), qsolution is the heat
absorbed/released by the bulk solution and qcal is the heat absorbed/released by the
calorimeter. Since we are attempting to measure the heat released or absorbed by the
reaction, we can solve for qrxn to generate equation 5.2.
qrxn
qsolution
qcal
(Eqn 5.2)
At this point, we can take advantage of our understanding of the specific heat capacity of
the solution and the previously measured calorimeter constant to write the following
expressions.
qsolution msolution c solution Tsolution
qcal
Ccal
Tcal
(from Eqn 3.1)
In order to use the expression for the heat absorbed/released by the solution, we need to
make an important assumption. In a dilute solution, the overwhelming majority of all the
particles in solution are solvent molecules; therefore, it is reasonable to assume that the
specific heat capacity of the solution will be very close to the specific heat capacity of the
solvent, and in fact, we will set csolution = cwater to simplify our problem. Moreover, since
the solution and the calorimeter are in contact with one another throughout the
measurement period, we can take Tsolution = Tcal. Finally, the mass of the solution can
be approximated as the sum of the masses of the HCl and NaOH solutions combined in
the calorimeter. When these approximations are made our expressions for qsolution and qcal
become:
qsolution msolution c water Tsolution
qcal
Ccal
Tsolution
When these two expressions are substituted into Eqn 5.2 we arrive at an equation (that
you should derive) that will allow us to calculate the amount of heat released or absorbed
by the acid/base neutralization reaction.
When a reaction is carried out in an open container, under a constant pressure
(such as atmospheric pressure) this observable heat flow (qrxn) is equal to the change in
Enthalpy for a Reaction ( Hrxn) (also called the heat of reaction). Enthalpy (H) is a
defined thermodynamic function that possesses certain specific properties that are
valuable for understanding the theory of thermodynamics and for making experimental
measurements. Since the amount of heat released or absorbed from a specific chemical
reaction is dependent upon the size of the chemical reaction carried out (i.e. the number
of moles of limiting reagent used) it is customary to correct the observed heat flow for the
reaction size by dividing qrxn by the number of moles of limiting reagent. It is this value
that is typically reported as Hrxn.
PROCEDURES:
1. DETERMINATION OF THE CALORIMETER CONSTANTii
 Assemble your calorimeter as close to the picture in Figure 1 as equipment allows.
Make sure the thermometer/temperature probe is not touching the bottom of the
calorimeter.
 Determine the mass of the assembled calorimeter.
 Measure approximately 50 mL of water and deliver into the calorimeter. Determine
the mass of the calorimeter and the water.
 Allow the “cold” water and the calorimeter to thermally equilibrate for 15 minutes.
While this is occurring, accurately measure approximately 50 mL of water and
deliver into a dry 250 mL beaker.
 Heat the water in the 250 mL beaker to approximately 40˚C. Allow the temperature
to stabilize.
 Accurately measure the temperature of the “cold” water in the calorimeter and the
temperature of the “hot” water in the beaker immediately before pouring into the
calorimeter.
 Add the hot water to the calorimeter and begin recording the temperature every 10
seconds for 3-5 minutes. (A maximum temperature should be clearly observed in this
data.)
 Determine ∆T for the cold water and record. This is assumed to be the same ∆T for
the calorimeter. Determine T for the hot water and record.
2. DETERMINATION OF THE SPECIFIC HEAT CAPACITY OF A
METALiii
 Rinse and dry the calorimeter. Place 75mL of water into the calorimeter, and
complete assembly of the thermometer/stirrer apparatus as near to the picture in
Figure 1 as equipment allows.
 Determine the mass of the water/calorimeter apparatus, and set aside temporarily.
 Obtain the unknown metal and accurately weigh a sample of approximately 50 g.
Record the precise mass of the metal sample.
 Set up a 600mL beaker containing approximately 400mL of water and heat the water
to a boil. Once a boil is achieved record the temperature of the boiling water.
 Transfer the metal sample to a large, clean, dry test tube and heat the test tube in the
boiling water bath for at least 15 minutes to allow the metal to reach the temperature
of the boiling water. (Do not allow water to condense inside the test tube. You may
find it helpful to cap the test tube with a rubber stopper containing one or more holes
to prevent this from happening.)
 Once the 15-minute heating period of the metal is complete, make one final check of
the temperature of the water in the calorimeter and record the temperature. (Do not
place a hot thermometer into the cold water!)
 Pour the metal sample out of the hot test tube into the calorimeter. Cover the
calorimeter, and carefully stir the water for 60 seconds. Using the temperature probe,
record the temperature every 10 seconds during this 60 second interval. Determine
the highest recorded temperature from the graph.
3. NEUTRALIZATION OF HYDROCHLORIC ACID WITH SODIUM
HYDROXIDE1
 Rinse and dry the calorimeter.
 Record the exact concentrations of the HCl and the NaOH solutions.
 Accurately deliver 50 mL of HCl into the calorimeter. Determine the temperature of
the acid.
 Accurately deliver 50 mL of NaOH into a beaker. Determine the temperature of the
base. If it is not equal to the temperature of the acid, you can run cool water on the
outside of the beaker to lower the temperature of the base, or you can warm the
beaker in your hands to heat base until an equivalent temperature is achieved.
 Have a stopwatch ready to record temperature readings in the calorimeter every 10
seconds.
 Add the NaOH solution to the calorimeter and begin recording the temperature of the
reaction mixture. Once a maximum has been reached, record the temperature every
30 seconds for 3 minutes.
 Determine ∆T for the bulk solution and calorimeter (assumed to be equivalent for
both).
 Dispose of the neutralized acid as instructed.
Critical Data to Include in your Lab Report:
Show all calculations:
o Calculate the calorimeter constant and the specific heat capacity of the
calorimeter.
o Calculate the specific heat capacity of the metal sample.
 Determine percent error for the specific heat capacity of the metal.
o Calculate ∆Hrxn per mole of hydrochloric acid neutralized with sodium
hydroxide.
 Determine the percent error for the heat of reaction for the
neutralization reaction. (Use the theoretical heat of reaction calculated
using heats of formation from your lecture textbook as the “true”
value.)
In the measurement of a calorimeter constant, Ccal, a negative value is occasionally
found. What does a negative value for this constant indicate?
If you used 100 mL of HCl solution and 100 mL of NaOH solution in your
measurement, would qrxn be larger, smaller, or equal to the value you measured?
Why? Would Hrxn be larger, smaller, or equal to the value you observed
experimentally? Why?
Cite references in the format specified by your instructor
Endnotes:
i
Silberberg, M.S. Principles of General Chemistry; McGraw-Hill:Boston, 2007; p 187.
Adapted from Bishop, Bishop, and Whitten Standard and Microscale Experiments in
General Chemistry, 5th Ed.; Brooks-Cole, 2003.
iii
Adapted from Hall, J.F. Experimental Chemistry, 6th Ed.; Houghton-Mifflin: New
York, 2003
ii