Enthalpy of Reaction
The objective of this experiment is to determine the enthalpy of reaction of
an acid with base. The method employed is a general one.
PRINCIPLES
The amount of heat that is absorbed or liberated in a physical or chemical change
can be measured in a well-insulated vessel called a calorimeter. You will use a simple
calorimeter, Fig. l, that is suitable for measuring heat changes in solution. Calorimetry is
based on the principle that the observed temperature change which results from a
chemical reaction can be simulated with an electrical heater. The electrical measurements
of current (I), heater resistance (R), and duration (t) of heating make it possible to
calculate the amount of heat equivalent to that produced by the chemical change; the
formula I2Rt is used, as derived in the following section. The use of weighed quantities
of reactants makes it possible to calculate the enthalpy change per mole.
In this experiment you will obtain the enthalpy change for the reaction:
HA(aq) + OH-(aq) → A-(aq) + H2O(l)
(I)
Since you will be working with solid acids, the desired quantity will be obtained by
measuring the enthalpy of net reaction for the solid acid with the reaction:
HA(s) + OH-(aq) → A-(aq) + H2O(l)
(II)
and the enthalpy of solution with the reaction:
HA(s) → HA(aq)
(III)
In measuring ∆H(II) and ∆H(III), the solid acid is added to NaOH solution and
water, respectively. The required ∆H(I) is obtained by combining the two measured
quantities:
∆H(I) = ∆H(II) - ∆H(III)
In addition, you will attempt to establish a relationship between the enthalpy
change, ∆H(I), and a structural or chemical property of the acid. Measurement is one
component of experimental science, but interpretation of the results is just as important.
Electrical Energy
1
Electrical current, measured in amperes, is the time rate of flow of electrical
charge (coulombs); by definition,
amperes 
coulombs
sec onds
The common relationships between electrical potential in volts (V), current in amperes
(I), and resistance in ohms (R) is known as Ohm’s Law,
V = IR
Electrical energy is given by
 coulombs 
Energy  volts amperes sec onds   volts 
sec onds 
 sec onds 
E = V I t volt coulombs
By definition:
l joule = l volt coulomb
By combining these laws and definitions, we get
Electrical energy = I2 Rt joules
Figure 1. Calorimeter and power supply.
The Calorimeter
2
The calorimeter operation is outlined below with reference to Fig. 1. The 400-ml
beaker is surrounded by Styrofoam insulation to minimize heat loss or gain through the
walls. The transparent Lucite cover (C) serves as a support for the electrical immersion
heater (H). It also has three holes: two large and one small. The stainless-steel
temperature probe (T) in inserted into the small hole. One large hole provides an opening
for the purpose of adding solid reagents, and the other permits the insertion of a
thermistor temperature probe which is no longer used. The solution is stirred by a
Teflon-covered magnet (M) which is rotated by a motor-driven magnet (M').
The temperature is measured by means of a platinum resistor, which is located at
the end of the thermometer probe. The device depends on the nearly linear dependence of
the probe’s resistance with temperature. It will determine temperature changes to a
precision of 0.001°C and, with calibration, absolute temperature to 0.05°C.
Figure 1 shows a greatly simplified circuit that indicates how the electrical heating
is measured and controlled.
The double-pole switch (S) controls two things
simultaneously: the timer (W), and the constant current source, represented by the battery
(B) and the resistance (Z), that supplies the current that flows through the heater (H). The
current (I) which flows through the heater is read from the ammeter (A). The resistance
of Z is chosen so as to give a current of about 1 ampere through the circuit. The heater
resistance has already been measured on another instrument and its value in ohms will be
shown on a label on the Lucite cover (C). The timer will give you, to the nearest 0.1 sec,
the length of time that the current passes through the heater. You will take temperature
measurements at 30-sec intervals before, during, and after the electrical heating process,
and for this you will use a small electronic timer externally mounted to the power supply.
Treatment of the Data
3
Experimentally, it is almost impossible to duplicate exactly the temperature change
from a chemical reaction by electrical heating. Instead, it is customary to calibrate the
calorimeter; that is, find the number of joules of electrical energy required to raise the
temperature of the reaction mixture and calorimeter by 1.000°C. This calibration is made
by dividing the total electrical energy input (Ec) by the temperature rise (∆Tc) resulting
from the input, to give the calibration factor Ec/Tc, joules per degree. Then, to obtain the
energy resulting from the chemical change, all you have to do is multiply this calibration
factor by the observed temperature change (∆Tx) for the reaction.
 E 
Energy of the Chemical Change =  c Tx 
 Tc 
Because the calorimeter is not perfectly insulated, it slowly loses or gains heat
depending on whether it is warmer or cooler than its surroundings. A second source of
small temperature changes is the mechanical work performed by the stirrer. Hence, a
constant stirring rate in each run is essential. An accurate determination of the
temperature changes for both the reaction and the heater requires that some allowance be
made for this slow rate of cooling or heating that occurs in the calorimeter when it is not
in use. Therefore, before mixing the reactants (or turning on the heater) a continuous
record is made for several minutes of the very slow rate of temperature change while the
calorimeter liquid is being stirred; then, after mixing the reactants (or turning off the
heater) another record is kept for several minutes of the very slow rate of temperature
change of the reaction mixture.
A plot of typical data for a complete heat of solution and calibration experiment is
shown in Fig. 2. The linear sections of the plot before and after the major temperature
changes are extrapolated forward and backward in time. One vertical line is drawn at a
time corresponding to 15 sec after the addition of the salt, and another at the midpoint of
the time interval between turning the heater on and 30 sec after turning the heater off.
∆Tx is then taken as the vertical distance between the points at which the first vertical line
intersects the lines extrapolated before and after adding the salt; ∆Tc is taken as the
vertical distance between the points at which the second vertical line intersects the lines
extrapolated before and after using the heater. Since ∆Tx and ∆Tc should be estimated to
the nearest 0.001°C, the graph must be carefully plotted on a generously large scale.
4
2.200
salt added
2.100
2.000
heater off
1.900
Temperature
1.800
Tc
(vertical line
is drawn at
midpoint
between
turning heater
on and 30
seconds after
turning it off)
1.700
1.600
Tx
(vertical
line is
drawn 15
seconds
after salt
addition)
1.500
1.400
1.300
1.200
heater on
1.100
1.000
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Time, min
Figure 2. Plot of sample data for a heat-of-solution
and calibration experiment. In this case
a salt with endothermic enthalpy of
solution is dissolved in water.
Note that in order to obtain the data for the graph just described it is necessary to
record the temperature as a function of actual time as measured on the external timer. In
addition, in order to calculate the electrical energy dissipated in the calibration of the
calorimeter, the length of time during which the current flows must be obtained
independently from the calorimeter timer.
5
EXPERIMENTAL PROCEDURE
1.
Getting Started
(a)
Select a partner with whom you want to work on the lab.
(b)
Obtain one solid acid per pair from the desiccator and transfer it to your
desiccator. Record the identity of the acid in your notebooks.
(c)
Decide which partner will be finding the enthalpy of solution (dissolving
the solid acid in water) and which will be finding the net enthalpy
(dissolving the solid acid in 0.2 M NaOH).
2.
Weighing the Solid Acid and Solvent
(a)
Put a weighing boat on the analytical balance and tare the balance to zero.
(b)
The table below gives the approximate values of how much solid acid is
needed in each run. The amounts have been adjusted to yield temperature
changes (mostly) between 0.5°C and 1.0°C. In the resulting concentration
range, the dependence of the molar enthalpy on concentration is very small
and can be ignored. Add the appropriate amount of acid to the weighing
and accurately record the mass in your notebook. Put the weighing boat
containing the sample into a second desiccator for transport to your
calorimeter. In weighing out the sample, break up any lumps.
Moles of Solid Acid to Use in Each Run
Enthalpy of Solution Enthalpy of Net Reaction
(Acid & Water)
(Acid & Base)
NaHCO3
0.036 mol
0.036 mol
KHSO4
0.029 mol
0.015 mol
HIO3
0.028 mol
0.017 mol
Na2HPO4
0.028 mol
0.014 mol
KH2PO4
0.037 mol
0.007 mol
(c)
(d)
Put a dry 400-ml beaker containing a magnetic stirring bar on the top
loading balance in the laboratory and tare the balance to zero.
Add approximately 250 ml distilled water or base to the beaker using your
250-ml volumetric flask. With a dropper adjust the weight of the water or
base to 250.0 g.
6
3.
Preparing the Apparatus for Measurements
(a)
Prior to each run, measure the room air temperature using the mercury
thermometer in the room. You can also use the digital thermometer but
the probe must be dry. Expect fluctuations in this result due to the air
currents. A value to ± 0.2°C is sufficient.
(b)
Place the Lucite cover with the thermometer probe in place over the cavity
of the Styrofoam block on the magnetic stirrer. Remove the cover, place
the beaker into the cavity, and put the Lucite cover on the beaker. Turn on
the magnetic stirrer so as to give vigorous but not turbulent stirring. The
stirring rate must be constant during a single run. Check that the back
(c)
(d)
two-pronged plug for the heater is plugged into the DC power supply. The
orientation of the plug in the socket is not important. Why?
Turn on the power supply with power switch located on the lower left
hand corner of the supply. The power on pilot light must light.
Preparation of the solvent. You need to adjust the starting temperature of
the solvent as discussed below. If the temperature of the solvent is not in
the desired range, turn the switch of the heating circuit ON and heat the
water until the temperature does lie in this range. Then turn the heating
circuit OFF, and press the reset button beside the timer display.
(i)
(ii)
Case of measurement of the enthalpy of net reaction: Prechilled
base is provided; heat it up so that its temperature is about 0.50.7°C below the room temperature reading.
Case of measurement of the enthalpy of solution: Except in the
case of Na2HPO4, heat the water so that its temperature is about
0.3-0.5°C above the room temperature reading. In the case of
Na2HPO4, heat the water so that it is 0.5-0.7°C below the room
temperature reading.
4.
Establishing the Initial Temperature
Commence a 15-20 minute series of temperature measurements taken in
unbroken succession (through step 7 below) at 30-sec intervals; use the external
timer for determining the 30-sec intervals when the digital thermometer is read.
5.
Introducing the Salt Sample
When it is clear from the measurements of about the first 3-5 minutes that
the temperature is changing only slowly and in a regular manner, prepare for the
7
addition of the solid acid as follows. Immediately following one of the 30-sec
temperature observations:
(a)
(b)
(c)
(d)
Remove the weighed acid sample from the desiccator.
Insert the dry powder funnel into the larger hole at the front of the Lucite
cover. Do not insert the funnel prior to this in order to avoid the possibility
of moistening the funnel with spray generated by stirring.
Poise the solid acid over the funnel with one hand and hold the brush in
the other hand.
At the time normally scheduled for making the next 30-sec temperature
observation, pour the solid acid into the tunnel brushing any remaining
acid from the boat and funnel into the beaker. Do not try to read the
(e)
temperature of the solution at the instant you add the sample; merely
record which of the 30-sec points was used for addition to the sample
Check to make sure that the magnetic stirrer is spinning. If it is not, turn
down the speed control until it begins spinning again and then readjust the
speed to give vigorous stirring.
6.
Re-establishing a Steady-State Temperature
Again read the temperature at 30-sec intervals, even though the first
reading after adding the salt is not a very stable one. The rate of solution varies
considerably from sample to sample. Once the sample as dissolved as evidenced
by a small rate of temperature change, record the temperature at 30-sec intervals
for an additional 3-5 minutes.
7.
Calibration of the Calorimeter
When the temperature baseline has been established, take a thermometer
reading at a regular 30-sec interval and simultaneously turn on the heater. (Before
you turn on the heater, make sure that the timer has been reset to zero.). Let
the current flow until the solution temperature had been raised by about 0.6-0.7°,
then turn the heater OFF. During the heating period continue to take temperature
measurements at the scheduled 30-sec intervals but realize that they can be only
approximate, since the temperature will be changing rather rapidly. Also during
the heating period while the current is flowing, tap the ammeter gently and record
the ammeter reading to the nearest 0.00l amp.
After turning off the heater, continue to record the temperature at 30-sec
8
intervals for a period of 3-5 minutes after the temperature stops rising. Record, to
the nearest 0.l sec, the reading on the timer. Record the resistance of the heater
used in your calorimeter; it is given on a label on the Lucite cover.
8.
Repeating the Determination
(a) Remove the Lucite cover, rinse the heater and thermometer probe, and
gently dry them with a tissue. Put the cover over the cavity. Empty the
beaker, being careful not to lose the stirring bar. Remove your beaker
from the Styrofoam block. Rinse the beaker and stirring bar, and wipe dry
with a Kimwipe.
(b)
(c)
Repeat the experiment twice more, starting each time with a dry beaker.
When you are finished turn off the power supply and the digital
thermometer. Thoroughly rinse the temperature sensor, heating element,
and beaker before you leave.
CALCULATIONS
Part I. Personal Measurements
A.
Plot, on a piece of millimeter graph paper provided with the lab manual, your
measurements of temperature vs. time for the solution or net reaction of the acid.
Use a separate piece of graph paper for each repetition of the experiment.
B.
For the process that you studied, i.e. the solid acid dissolving or water or reacting
with base, calculate the enthalpy change per mole of solute for each run, the mean
value, the standard deviation, and the relative 95% confidence interval of the
mean expressed as parts per hundred (%). Since you used the same amount of
solvent in each run, the calibration factors, EC/∆TC, should be nearly constant.
C.
By subtracting the mean enthalpy change of solution from the mean net enthalpy
change for the reaction with base, you and your partner should be able to
determine the solution-phase enthalpy of reaction for your acid mixed with base
(∆H(I) = ∆H(II) - ∆H(III)).
D.
Include the graphs of your runs with your report.
9
Part II. Derivation of Your QSAR
The lab instructor will quickly grade the report submitted by each member of the
group and provide via Email the pooled results to all members of the group as well of
data for compounds not examined by the group. Use the full set of data including the
data found in the lab manual to derive a QSAR. Complete the second page of the lab
report and submit the full report in class on the Wednesday following acquisition of the
data.
The final task is the interpretation of your data and the data collected by the other
groups of students. By examining the variation in the enthalpy change and the variation
in other physical properties, you may discover a relation, i.e. a correlation, that will
increase your understanding of the properties of acids and bases. Lord Kelvin argued that
legitimate science must be quantitative and we shall follow his dictum in our discovery of
a relationship.
Our tool will be the method of least squares that was introduced at the start of the
semester. If ∆H depends on a physical property X, then a least squares fit of ∆H, the
dependent variable, to X, the independent, will be good. R2, the square of the correlation
coefficient, will be our criterion for identifying a statistically significant relationship. A
table of R2 as a function of confidence level (95% is normally used) and degrees of
freedom (# data points - # parameters) is provided.
Table of Critical Values of R2
Degrees of
Freedom
90% Confidence
Level
95% Confidence
Level
1
0.976
0.994
2
0.810
0.903
3
0.648
0.771
4
0.531
0.658
5
0.448
0.569
6
0.386
0.500
7
0.339
0.446
8
9
10
0.301
0.271
0.247
0.399
0.362
0.332
10
Consider the case of 5 data points and 2 parameters, e.g. a slope and an intercept. We
have 5 – 2 = 3 degrees of freedom and at the 95% confidence level, R2 must equal or
exceed 0.771 or the proposed model must be rejected as unsupported by the data. Hence,
if R2 were 0.875, we would accept the hypothesis that ∆H depends on property X; with R2
0f .650, we would reject the model. However, although R2 would be unacceptable with 3
degrees of freedom, it would be more than acceptable with 6! In numbers, there is
strength! We note that the community of chemists that uses modeling and statistical
methods in the design of new and more effective drugs insists that a data set contain at
least 5 compounds. This approach, which is very productive, was developed at Pomona
College by Professor Emeritus Corwin Hansch. The equation resulting from his powerful
approach is called a QSAR for quantitative structure activity relationship.
Hence we are asking you to develop a QSAR involving the enthalpy of reaction,
∆H(I). To this end, we have provided a tabulation of properties of the acids that you have
studied. Many of those properties were calculated with Spartan, a modeling program that
you will use this semester. You may wish to consider other properties and are invited to
do so. We have supplemented the data with data for other acids so that your data set is
large enough. Armed with this information, we invite you to develop your own QSAR
for ∆H(I). You will identify a statistically significant relationship, i.e. which variables are
correlated, but will also derive an equation, the mathematical relationship between the
correlated variables. Be sure to include this equation with your report. Also submit all
Excel output with your report sheet.
11
Selected Properties of Acids
Acid
∆H(reaction)
pKa
qH
qO
qM
rOH
OH
EPE
cm-1
3833
kcal
-58.9
kJ/mol
-62.54
4.27
0.408
-0.665
0.724
Ǻ
0.991
-50.49
8.32
0.449
-0.726
0.518
0.974
3841
-54.8
HCO3-
10.33
0.408
-0.853
1.232
0.965
3469
-51.9
HSO4-
1.97
0.456
-0.812
1.875
0.967
3863
-20.9
HIO3
0.77
0.535
-0.720
1.233
0.974
3803
80.5
12.35
7.20
0.368
0.430
-0.897
-0.862
1.743
1.743
0.970
0.966
3784
3892
-144.5
-32.4
HC2O4
-
HSeO3-
2-
HPO4
H2PO4-
∆H is the enthalpy change for the removal of one proton
qH is the partial charge on the acidic H atom
qO is the partial charge on the O atom attached to the acidic hydrogen
qM is the partial charge on the atom to which the OH group is attached
rOH is the O-H bond length in Ǻngstrom
OH is the vibrational frequency of the O-H bond stretch in cm-1
EPE is the energy of interaction at the site of the acidic proton with a test charge in kcal
12
NAME________________________________
Lab Section_____________
Calorimeter Number__________________
Acid_______________________
Date Report Submitted______________________
ENTHALPY OF REACTION
1. Personal Measurements: Your solvent: base or water (Circle one)
Sample 1
Sample 2
Sample 3
Weight of acid (g)
__________
__________
_________
Weight of solvent (g)
__________
__________
_________
Solution concentration
(mol/kg of solvent)
__________
__________
_________
∆Tx caused by addition of acid
(from graph)
__________
__________
_________
∆Tc caused by electrical heating
(from graph)
__________
__________
_________
Ammeter reading (amp)
__________
__________
_________
t, time during which current
passed (sec)
__________
__________
_________
R, electrical resistance of
heater (ohms)
__________
__________
_________
Ec, electrical energy input
__________
__________
_________
Calibration factor (Ec/∆Tc)
__________
__________
_________
Enthalpy Change (J/g)
__________
__________
_________
Enthalpy Change (kJ/mol)
__________
__________
_________
Average enthalpy change (kJ/mol) ____________
Standard deviation ____________
Relative 95% confidence interval of the mean, % ____________
13
2. Shared Data
Your Acid
__________
Mean Enthalpy Change of Solution (H/mole for equation III)
__________
Mean Enthalpy Change for Solid + Base (H/mole for equation II) __________
Enthalpy Change of Reaction (H/mole for equation I)
__________
Other Partners’ Results:
Acid
∆H(equation I)
__________
__________
__________
__________
__________
__________
3. What relationship, if any, did you establish between ∆H(reaction)
and the physical properties given? Provide your QSAR and the
statistics supporting it. What does your QSAR tell you about the
properties of acids?
4. Show sample calculations on the back side of this page.
Attach a graph for each run.
14