LEC
02.09
Determination of the melting enthalpy of a pure substance
Related concepts
Heat capacity, melting point, latent heat, calorimetry, Gibbs’
phase rule, enthalpy of sublimation, enthalpy of vaporization.
Principle
When a solid melts, energy is required for the destruction of the
crystal lattice. A substance whose melting point lies slightly
below room temperature is first cooled until it solidifies and then
melted in a calorimeter. The melting enthalpy is calculated from
the decrease in temperature due to the melting process which is
measured in the calorimeter.
Tasks
1. Take a temperature-time-diagram for the melting process of
dioxan
2. Calculate the melting enthalpy and entropy of 1,4-dioxan.
Equipment
Cobra3 Basic-Unit
Power supply 12 V/2 A
Data cable, RS232
Temperature measuring module Pt 100
Software Cobra 3 Temperature
Temperature probe Pt 100
Calorimeter, transparent
Heating coil with sockets
Work and power meter
Universal power supply
Connection cable, l = 500 mm, black
12150.00
12151.99
14602.00
12102.00
14503.61
11759.01
04402.00
04450.00
13715.93
13500.93
07361.05
1
1
1
1
1
1
1
1
1
1
4
Magnetic heating stirrer
Magnetic stirrer bar, l = 30 mm, oval
Separator for magnetic bars
Support rod, l = 500 mm, M10 thread
Right angle clamp
Universal clamp
Laboratory balance
with data output, 800/1600/3200 g
Test tube, 30/200 mm, Duran, PN 29
Rubber stopper 26/32
Dewar vessel, 500 ml
Pasteur pipettes
Rubber bulbs
Wash bottle, 500 ml
1,4-Dioxan, 1000 ml
Water, distilled, 5 l
PC, Windows® 95 or higher
35720.93
35680.04
35680.03
02022.20
37697.00
37715.00
1
1
1
1
2
2
48803.93
36294.00
39258.00
33006.00
36590.00
39275.03
33931.00
31266.70
31246.81
1
2
2
1
1
1
1
1
1
Set-up and procedure
Set up the experiment as shown in Fig. 1 but for the time being
do not connect the heating coil with the work and power meter.
Connect the temperature probe to T1 of the measuring module.
Call up the ‘Measure’ programme in Windows and enter
<Temperature> as measuring instrument. Set the measuring
parameters as shown in Fig. 2. Under <Diagram 1> select
Temperature T0a, the appropriate range for the temperature and
the X bounds and ‚auto range‘. After having made these settings, press <Continue> to reach the field for the recording of
measured values. Arrange the displays as you want them.
Fig. 1. Experimental set-up.
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P3020911
1
LEC
02.09
Determination of the melting enthalpy of a pure substance
Weigh out 44.05 g (0.5 mol) of 1,4-dioxan in a test tube (weighing accuracy 0.01 g) and close it with a stopper. Fill the Dewar
vessel with 300 g of ice and 100 ml of cold water. Place the test
tube in this water-ice mixture for about 1 hour until the dioxan is
frozen. In the meantime, fill the calorimeter with 850 g of distilled
water (weighing accuracy 0.1 g). Place it on the magnetic stirrer,
put in the oval magnetic stirrer bar and switch on the stirrer
(Caution: Do not switch on the heating unit by mistake!). Insert
the heating coil and the temperature probe into the lid of the
calorimeter and fix them in position.
When temperature equilibrium has been reached (after approximately 10 min) start the measurement by pushing <Start measurement>. Wait 3 to 4 minutes, then take the test tube out of
the Dewar vessel, quickly dry it, and insert it through the hole in
the lid into the water. The water level in the calorimeter should be
about 1 cm higher than the level of the dioxan in the test tube.
When the dioxan has completely melted and a thermal equilibrium has been established, continue to measure the temperature
for about another 5 minutes. Subsequently perform electrical
calibration to determine the total heat capacity of the calorimeter. Supply 10 V AC to the work and power meter for the electric
heating. Push the <Reset> button and then put the free ends of
the heating coil connection cables into the output jacks. The
system is now continuously heated and the supplied quantity of
energy is measured. As soon as the temperature in the calorimeter has reached the initial temperature, switch off the heating and
read the exact quantity of electrical energy supplied. After a further three minutes, stop recording the temperature.
Fig. 3 shows the graph as it is presented by the programme
when the measurement is stopped. If you use <survey> from the
toolbar you can read the temperature difference data.
Perform an analogous experiment with an empty test tube in
order to determine the heat capacity of the test tube.
Fig. 2:
Theory and evaluation
Phase changes of substances are linked with energy changes.
The phase transition from the solid into the liquid state is termed
melting. Under isobaric conditions the phase transition of a pure
substance occurs at constant temperature. The phase transitions temperatures (melting point, boiling point) can therefore be
used as substance constants for characterising substances.
If energy is applied to solid (frozen) dioxan, its temperature rises
until the phase transition temperature (melting temperature) is
reached. During the melting process, solid and liquid dioxan
coexist. However, as long as both phases are present, adding
heat does not result in a further temperature increase (latent
heat), as this energy is required for phase transformation. Only
when the melting process is completed does the temperature of
the system again increase.
The melting process normally occurs under isobaric conditions.
The heat of fusion QF is equal to the melting enthalpy ∆FH in this
case.
QF = ∆FH
(1)
Referred to the amount of substance n, this results in
∆FH ∆Fh
n
(1a)
This is the amount of energy which is required to overcome the
lattice forces. The same quantity of energy which must be added
during the melting process is released as heat of solidification
during the freezing process (liquid-solid phase transformation).
∆FH = -∆crystH
(2)
Measurement parameters
Fig. 2:
2
p = const.
P3020911
Temperature-time diagram for the melting process of
dioxan
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEC
02.09
Determination of the melting enthalpy of a pure substance
Analogous energy changes occur during the vaporization or
condensation processes. According to Hess’s law, the sublimation enthalpy ∆sublH must be additively composed of the melting enthalpy ∆FH and the enthalpy of vaporization ∆VH.
∆sublH = ∆FH + ∆VH
Q can be determined from the experimentally measured values
as follows:
Q = Qexp - Qempty
(3)
The pressure dependency of the phase transition temperature is
described by the Clapeyron-Clausius equation.
T1Vs Vl 2
dT
dp
∆FH
Qexp = - CK . ∆Texp
(8.1)
Wel = CK · ∆Tcal = Qcal
(8.2)
Qexp Wel ·
(4)
(8)
∆Texp
(8.3)
∆Tcal
where
Vs
Vl
Volume of solid substance
Volume of liquid substance
For reversible processes, the phase transition entropy is calculated according to the second law of thermodynamics. The following relation results for the melting entropy ∆FS:
∆FH
∆FS TF
(5)
∆Texp
∆Tcal
CK
Wel
Temperature difference during the melting of dioxan
Temperature difference during calibration
Heat capacity of the calorimeter
Electrical work during calibration
Qempty is the quantity of heat which must be applied to heat the
empty test tube under the same experimental conditions:
Qempty Wel, empty Wel ·
If n moles of a substance at a temperature Tl, which is below the
melting point of the substance, is heated to a temperature Th,
which is above the melting point, the following amount of heat is
required under isobaric conditions:
where
Q = ∆h = n Cp(s)(TF – Tl) + n ∆FH + n Cp(l)(Th – TF)
∆Texp, empty
Cp(s)
Cp(l)
TF
Tl
Th
n
(6)
∆Tcal, empty
Molar heat capacity of the solid substance
Molar heat capacity of the liquid
Melting point
Arbitrary temperature below the melting point
Abitrary temperature above the melting point
Quantity of dioxan
Wel, empty
Using these variables, the enthalpy of fusion is:
∆FH Q
Cp1s2 1TF Tl 2 Cp1l2 1Th TF 2
n
(7)
When the enthalpy of fusion is determined in the manner
described in this experiment, the temperature-dependent terms
in equation (7) can be neglected, as the temperature changes
are relatively small and the calibration of the system is performed
under identical conditions as those under which the measurement is performed. As a consequence, the following is obtained
for the enthalpy of fusion:
∆FH Q
n
∆Texp, empty
∆Tcal, empty
(9)
Temperature difference during heating the empty
test tube
Temperature difference during calibration with the
empty test tube
Electrical work during calibration with the empty
test tube
Data and results
Values from the literature:
= 147.6 J · mol-1 · K-1
Cp(s) (dioxan)
= 152.7 J · mol-1 · K-1
Cp(l) (dioxan)
M (dioxan)
= 88.11 g J · mol-1
TF (dioxan)
= 11.8 °C = 284.9 K
= 12.8 kJ · mol-1
∆FH (dioxan)
∆FS (dioxan)
= 45.1 J · mol-1 · K-1
The following values were determined experimentally :
= 13.6 kJ · mol-1
∆FH (dioxan)
∆FS (dioxan)
= 47.7 J · mol-1 · K-1
(7.1)
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
P3020911
3
LEC
02.09
4
P3020911
Determination of the melting enthalpy of a pure substance
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen