Theoretical background
Important concepts
The law of energy conservation, extensive and intensive quantities, thermodynamic state functions, heat, work, internal energy, enthalpy, constant volume heat capacity, constant pressure heat capacity, specific heat capacity, molar heat capacity, reaction enthalpy, Hess’s law, anisothermal calorimeter, adiabatic calorimeter, constant pressure calorimeter, reaction extent.
Calorimetry
The aim of calorimetry is the measurement of the heat of physical or chemical processes. Based on the measured heat we can determine reaction heat, heat of dissolution, heat of hydratation, heat capacity. The equipment in which we can measure the heat is called calorimeter.
Basic types of calorimeters
Based on the heat exchange between the system investigated and the surroundings and the measured quantity connected to the heat we separate four basic types of calorimeters:
-
the isothermal calorimeter the anisothermal calorimeter
the adiabatic calorimeter
the heat flux calorimeter.
The isothermal calorimeter
In the isothermal calorimeters the temperature is constant during the experiment.
The anisothermal calorimeter
In the anisothermal calorimeters there is some heat exchange between the system and the surroundings, but we try to minimize it. The measured quantity is the temperature which changes during the experiment.
A constant volume (bomb) calorimeter is closed when it operates; therefore it is applicable to determine internal energy change. The internal pressure of bomb calorimeter in most of the experiments (combustion reactions) increases, but there is no pV work done by the system.
A constant pressure (open) calorimeter is open when it operates, therefore it is applicable to determine enthalpy change.
We use in this lab a constant pressure anisothermal calorimeter to determine salt hydratation enthalpy.
The adiabatic calorimeter
The extreme case of the anisothermal calorimeter when there is no heat exchange is the adiabatic calorimeter.
The heat flux calorimeter
In the heat flux calorimeters there is some heat exchange between the system and an isothermal heat reservoir, and we measure its amount. The temperature of the system only temporary changes during the experiment.
Experimental task: Measurement of salt hydratation enthalpy in an anisothermal calorimeter
Objective
The determination of the reaction enthalpy of this process:
CH
3
COONa(s) + 3 H
2
O → CH
3
COONa·3 H
2
O (s)
P0
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We will determine this value by measuring the enthalpies of solution for anhydrous sodium acetate and for sodium acetate trihydrate. Application of Hess’s Law will give us the ∆ r
H for the hydration reaction.
CH
3
COONa(s)    2  → CH
3
COO – (aq) + Na + (aq)
CH
3
COONa·3 H
2
O (s)     2  → CH
3
COO – (aq) + Na + (aq) + 3 H
2
O
P1
P2
_________________________________________________________________________
The solution of the anhydrous salt, process P1 produces ∆ r
H
1
solution for the anhydrous salt, and the solution of the trihydrate, process P2 involves ∆ r
H
2
solution for the sodium acetate trihydrate.
Application of Hess’s Law means the subtraction of processes P1 – P2,
CH
3
COONa(s) - CH
3
COONa·3 H
2
O (s) = - 3 H
2
O rearranging we get
CH
3
COONa(s) + 3 H
2
O → CH
3
COONa·3 H
2
O (s) which process is identical to P0, the process for which enthalpy is to determine. Therefore the measured reaction enthalpy difference for P1 and P2 is given as
∆ r
H hidr
Theoretical background
Enthalpy is a function of temperature, pressure and amount of material: H ( T,p,n ). As we treat an isolated system, we omit the dependence on n the partial derivatives are given dH =


∂
∂
H
T

 p dT +


∂ H
∂ p


T dp 2
At constant pressure, d p = 0 dH
= ∆ r
H
1
=


∂ H
∂ T
− ∆ r

 p dT
H
2
1
3 where


∂ H
∂ T

 p
= C total p
is the heat capacity at constant pressure. The enthalpy change for processes, e.g. heat of combustion, heat of boiling or fusion etc., can be determined by taking the integral of function in Equation 3 between states 1 and 2,
∆ H =
2
1 d H 4 which is easy to integrate, if C total p
is not a function of T in the interval T
1
and T
2
:
∆ H = C total p
2
dT = C total p
∆ T
1
Under constant pressure conditions the heat is equal to the enthalpy change: q = ∆ H
5
6
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Theoretically, the heat capacity can be given
C p total =
C i p i
7 as the sum of the heat capacities of all parts of the calorimeter. In calorimetry, it is customary to separate the heat capacity of calorimeter liquid (e.g. water) from the heat capacity of other heat absorbing components:
C total p
= C water p
+
C j p j ≠ water
8
The heat capacity of water can be expressed by c water p
, the specific heat (4.185 J g -1 K -1 ) and m water
, the mass of water.
C total p
= c water p m water
+ C other p
9
The reaction mixture is often a dilute aqueous solution, so the specific heat of the solution can be taken equal to that of water.
Calibration
In practice, C total p
is typically determined by experiment (this procedure is called calibration). A precisely measurable amount of heat can be generated by electric heater, this heat causes a temperature increase of the calorimeter. From the thermally insulated vessel only a very small amount of heat can leak, therefore the temperature difference measured is proportional to the heat capacity of calorimeter. The small heat loss can be taken into account by graphical method from the temperature vs. time function (in details see later in Figure 3) recorded during the heat transfer process. The heat capacity can be calculated easily:
C total p
= q electric
∆ T
10
The temperature difference in the calibration, ∆ T
1
is the difference between the temperature before and after the electric heating ( T
1
and T
2
):
∆ T
1
= T
2
− T
1
11
The heat produced by the electric heater is equal to work done by the current flowing through the resistance for time, t : q electric
=
U
2
R t 12 where U is the voltage applied (given in Volts), R is the resistance of the heater (given in Ohms). If we use t in seconds the unit of q will be J.
When heat is generated or released in the system the temperature of the calorimeter will increase since there is practically no heat loss to the surroundings. The heat releasing process is called exothermic , and a negative sign is assigned to the heat of the process based on the system based sign convention. This leads to the following expression: q = − C total p
⋅ ∆ T 13
Please note that this is not in contradiction with the section above about the electric heat, because the sign of q electric
is positive in the point of view of the calorimeter (we use this way), but it is negative in the point of view of the electric heater.
Determination of the heat of dissolution
Carrying out the solution process some sodium acetate salt we observe ∆ T
2
, which is the difference between the temperature before and after the dissolution ( T
3
and T
4
):
∆ T
2
= T
4
− T
3
14
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The sign of this difference is positive for exothermic process, but it is negative when endothermic process takes place in the calorimeter.
The reaction enthalpy ( ∆ r
H ) is an intensive variable, which can be calculated from the extensive enthalpy change ( ∆ H ):
∆ r
H =
∆ H
∆ ξ
15
The extent of reaction, ∆ξ for the i th component:
∆ ξ = n i
− n
0 , i
ν i
The reaction extent is independent of reacting components and given in moles.
In our case the dissolution process goes to a completion, therefore ∆ ξ = n salt
and
16
∆ H
∆ r
H =
17 n salt
The enthalpy of dissolution slightly depends on the final concentration of the solution. This may lead error in the determined enthalpy of hydration. We can decrease this error if keep the final concentration of the solution the same for all experiments.
Experimental procedure
Students will carry out the experiments in two groups, one group with anhydrous sodium acetate, the other with sodium acetate trihydrate. The procedure of the two experiments are very similar. Each experiment contains two parts: calibration and dissolvation of one salt. The temperature distribution in the calorimeter liquid should be even, which is maintained by mixing it with a magnetic stir-bar. The temperature in sampled regularly by a computer data acquisition system.
Assembling the apparatus
You will assemble a constant pressure adiabatic calorimeter like that of in Figure 2.
Figure 2 A constant pressure (open) calorimeter with heat insulating walls.
1. Dry the sample tube and fit a cork to the bottom of the tube. Hold the tube with closed end downward, and immerse it into molten paraffin. Therefore the tube is isolated from getting calorimeter liquid into it.
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2. Using graduated cylinder, measure out some 400 ml of distilled water and pour it into the dry Dewar vessel. Use the same graduated cylinder for both experiments. Place into the Dewar vessel: the electric heater, the stir-bar and the thermometer. Start mixing the liquid. Do not interrupt mixing during the experiment. From time to time take a glance on the stirrer.
Note: Always hold the heater in vertical position; do not turn it upside down. Therefore you avoid oil leaking from it.
3.a In the first group place sample tube on the balance and tare the balance, than measure into the sample tube 4 –
5 g of anhydrous sodium acetate by four digit precision. Record the mass of anhydrous sodium acetate.
3.b In the second group place sample tube on the balance and tare the balance, than measure into sample tube from sodium acetate trihydrate exactly 1.659 times the mass of anhydrous sodium acetate by four digit precision. Record the mass of sodium acetate trihydrate. (1.659 is the ratio of the molar masses: 136.09 g mol
–1
/ 82.03 g mol
–1
=
1.659)
4.
Place the sample tube in the calorimeter. Please do not put the glass rod in the sample tube!
Determination of the heat capacity of the calorimeter and the heat released/absorbed by the salt dissolution process
5. Start the data acquisition. The computer system automatically collects the temperature regularly.
6. Stage 1 (observation): Observe temperatures for 5 minutes. These values will be used for the determination of the initial temperature.
7. Stage 2 (heating): Turn on the heater for the time given by your instructor. Record the output voltage of power supply, electric resistance of your heater and the precise time interval of heating.
8. Stage 3 (observation): Let the computer collect the temperature values for 5 minutes after the values become almost constant. These values will be used for the determination of the final temperature of the calibration and the initial temperature of the salt dissolution.
9. Stage 4 (salt dissolvation): Push the cork by a glass rod and help dissolving all the salt by mixing vigorously the solution with glass rod for half a minute.
10. Stage 5 (observation): Let the computer collect the temperature values for 5 minutes after the values become almost constant. These values will be used for the determination of the final temperature of the salt dissolution.
The measure data of the two groups will be used mutually.
Steps of calculation
1. Plot two T vs. t functions like Figure 3 on an ORIGIN graph. One for anhydrous sodium acetate and another one for sodium acetate trihydrate. From the three approximately horizontal sections of the graph determine T
1
, T
2
, T
3
, T
4
. In most of the cases T
2
, and T
3
will be identical. Calculate the adequate ∆ T
1
and ∆ T
2
values. If the initial temperature and the final temperatures are not constant in time fit line to these parts of the curves. Set perpendicular to the horizontal axis at the middle of the temperature change (half-wave). The difference of the intercepts of this line with the fitted initial and final lines gives the temperature differences.
2. Calculate the electric work and C total p
separately for each experiment. Use Equations 12 and 10.
3. Test the goodness of the first part of your experiment. Use Equation 9. for the calculation of C other
, which should be positive, but not too large.
If C other p
= C total p
− c water p m water
≤ 0 consult your instructor what to do!
If C other p
is positive use this value in the calculations of the corresponding experiment.
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Figure 3 Tracking the temperature of calorimeter in time.
4. Determine the enthalpy changes using equation 5 for both salt dissolution. Using these values calculate the enthalpies of dissolution ( ∆ r
H
1
and ∆ r
H
2
) using equation 17. Handle the sign of the ∆ T and ∆ r
H values carefully!
5. Finally, calculate ∆ r
H hidr
in kJ mol
-1
units applying equation 1.
Sample questions and answers for the entrance quiz.
These questions are devoted for practicing and preparing to labs at home. Please note that these are samples only and the question of the entrance quiz are not restricted to these ones!
MLT Q and A
Q1. What are the extensive and intensive properties?
A1. An intensive property (also called a bulk property) of a system that does not depend on the size of the system or the amount of material in the system.
By contrast, an extensive property of a system does depend on the system size or the amount of material in the system.
Q2. How would you apply Hess’s law to hydration reaction of sodium acetate?
A2. The reaction enthalpy of hydration reaction,
CH
3
COONa(s) + 3 H
2
O → CH
3
COONa·3 H
2
O (s) cannot be determined by calorimetry. However, the enthalpy of two component solution processes can be measured in a calorimeter. Taking the difference of these two solution processes
CH
3
COONa(s)     2  → CH
3
COO – (aq) + Na + (aq) ∆ r
H
1
CH
3
COONa·3 H
2
O (s)     2  → CH
3
COO
–
(aq) + Na
+
(aq) + 3 H
2
O ∆ r
H
2 we obtain the hydration process itself,
CH
3
COONa(s) - CH
3
COONa·3 H
2
O (s) → - 3 H
2
O which rearranges
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CH
3
COONa(s) + 3 H
2
O → CH
3
COONa·3 H
2
O (s) ∆ r
H
3 and for reaction enthalpies we get: ∆ r
H
3
= ∆ r
H
1
− ∆ r
H
2
. We used up the state function property of enthalpy.
Q3. Why do we use stirbar and double walled insulator tube in calorimeter?
A3. To maintain the condition of even distribution of temperature and concentration throughout the vessel. Insulator walls prevent heat transfer to laboratory.
Q4. What is the difference between enthalpy and reaction enthalpy?
A4. Enthalpy is a state function but an extensive variable, while reaction enthalpy is also a state function but an intensive variable which is independent of the extension of the system.
Q5. Why do we use electric heater for the determination of heat capacity of calorimeter?
A5. We produce a certain amount of heat which is absorbed by the calorimeter liquid. The extent of heat can precisely adjusted by changing parameters R , t or U , phrased in equation
U
2 q surr
= C p
⋅ ∆ T
1
= t
.
R
Q6. What is the reason for determining heat capacity of heat absorbing parts?
A6. All the parts of the calorimeter (glass ending of thermometer, internal wall of Dewar-flask etc.) except the calorimeter liquid belong to this group, and each of the different materials has its own specific heat capacity. They will absorb significant amount of heat when heat is evolved in the calorimeter. Without taking the heat absorbing parts into account, the calculated enthalpy would contain substantial error.
Q6. How long an electric heater have to be operated, when the temperature of calorimeter should be increased by 2.2 °C?
The resistance of the heater R = 24 Ω , its operating voltage U = 18 V. The calorimeter contains 600 g of water, the sum of heat capacities of heat absorbing parts is 100 J K -1 . The specific heat capacity of water: 4,18 J g -1 K -1 .
A6. Calculate first the heat capacity of calorimeter, C k
.
C k
= C v
+ C m
= 600 g ⋅ 4 , 18 Jg
The heat supplied for the 2,2 o C increase
− 1
K
− 1 + 100 JK
− 1 = 2608 JK
− 1 q = C k
∆ T = 2608 JK
− 1
The work done by electric heater:
⋅ 2 .
2 ° C = 5737 , 6 J q = w =
U
2
R
⋅ t
t =
R ⋅ w
U
2
=
24 Ω ⋅ 5737 , 6 J
18 V
2
= 425 s
Q7. What are the main steps of one experiment in an anisothermal calorimeter?
A7. 1. Prepare the sampling tube, measure the given amount of salt in.
2. Assemble the calorimeter.
3. Start the data acquisition.
4. Observe temperatures for 5 minutes.
5. Calibrate by heating.
6. Observe temperatures for 5 minutes again.
7. Dissolve the salt.
8. Observe temperatures for 5 minutes again.
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