Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
TEC
Related concepts
Differential molar mixing enthalpy, real and ideal behaviour, integral molar mixing enthalpy, fundamental
principles of thermodynamics, calorimetry.
Principle
When two miscible liquids are mixed, a positive or negative heat effect occurs, which is caused by the interactions between the molecules. This heat effect is dependent on the mixing ratio. The integral mixing
enthalpy and the differential molar mixing enthalpy can be determined by calorimetric measurements of
the heat of reaction.
Equipment
2
1
1
1
1
1
1
1
1
3
3
1
1
1
4
1
1
1
Cobra4 USB Link
Cobra4 Sensor Unit Temperature
Cobra4 Sensor Unit Energy
Software measure Cobra4
Precision Balance, Sartorius
QUINTIX5102-1S, 5100 g / 0.01 g
Magnetic stirrer MR Hei-Standard
Magnetic stirrer bar, l = 30 mm, oval
Separator for magnetic bars
Support rod, l = 500 mm, M10 thread
Right angle clamp
Universal clamp
Power supply universal
Calorimeter, transparent
Heating coil with sockets
Connection cable, l = 500 mm, black
External circulation set for thermostat
Alpha A
Immersion thermostat Alpha A
Bath for thermostat, 6 l, Makrolon
12610-00
12640-00
12656-00
14550-61
49285-99
35751-93
35680-04
35680-03
02022-20
37697-00
37715-00
13500-93
04402-00
04450-00
07361-05
08493-02
08493-93
08487-02
1
1
3
4
1
2
5
1
1
6
1
1
Pasteur pipettes
Rubber bulbs
Rubber tubing, di = 6 mm
Hose clips, d = 8…16 mm
Retort stand, h = 500 mm
Erlenmeyer flask, 250 ml,
narrow neck, PN 29
Erlenmeyer flask, 100 ml,
narrow neck, PN 19
Funnel, do = 80 mm
Powder funnel, do = 65 mm
Acetone, chem. pure, 250 ml
Wash bottle, 500 ml
Water distilled, 5 l
36590-00
39275-03
39282-00
40996-02
37692-00
36424-00
36418-00
34459-00
34472-00
30004-25
33931-00
31246-81
Additional equipment
1 PC with USB interface,
Windows XP or higher
Fig. 1: Experimental set-up.
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TEC
Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
Safety instructions
When handling chemicals, you should wear suitable protective gloves, safety goggles, and suitable
clothing. Please refer to the appendix for detailed safety instructions.
Tasks
1. Measure the integral mixing enthalpy of 7 different water acetone mixtures.
2. Plot the molar integral mixing enthalpy versus the quantity of substance (mole fraction) and determine the molar mixing enthalpy.
3. Discuss the results on the basis of the interactions in the mixture.
Set-up and procedure
Weigh out the individual components of these mixtures with an accuracy of 0.1 g in accordance with
the values given in Table 1.
Table 1: Preparation of the seven test mixtures.
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Substance quantity
Calorimeter
Erlenmeyer flask
Mixture number
X = 0.1
475 g Water
169 g Acetone
1
X = 0.2
Mixture 1
213 g Acetone
2
X = 0.9
557 g Acetone
19 g Water
7
X = 0.8
Mixture 7
24 g Water
6
X = 0.6
Mixture 6
72 g Water
5
X = 0.5
Mixture 5
59 g Water
4
X = 0.4
Mixture 4
86 g Water
3
Set up the experiment as shown in Fig. 1.
Combine the Cobra4 Sensor Unit Energy and the Cobra4 Sensor Unit Temperature with the Cobra4
USB Links.
Connect the power supply and the heating coil with the Cobra4 Sensor Unit Energy as shown in
Fig. 2.
Fig. 2: Connection between the Cobra4 Sensor Unit Energy and
the power supply (“in”) and the heating coil (“out”).
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2
Start the PC and connect the Cobra4 USB Links with the computer via USB cables.
Call up the “Measure” programme and boot the experiment “Determination of the mixing enthalpy of
binary fluid mixtures with Cobra4” (experiment > open experiment). The measurement parameters
for this experiment are loaded now.
Now the sensors are automatically recognized and some ID numbers (01 and 02) are allocated to
them, which is indicated in the display of the Cobra4 USB Links.
For the first measurement, fill 475 g water into the calorimeter.
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P3020661
Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
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TEC
Insert the oval magnetic stirrer bar in the calorimeter and switch the magnetic stirrer on
(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.
Weigh 169 g of acetone in a 250 ml Erlenmeyer flask.
Wait until temperature equilibrium has been established.
Cut a rubber stopper with hole lengthwise, put the temperature probe through the hole and close the
Erlenmeyer flask before hanging it into the temperature-controlled bath.
Adjust the immersion thermostat to the temperature of the water in the calorimeter and wait until the
temperature difference between the acetone in the bath and the calorimeter does not exceed 0.02 K.
Insert the temperature probe back into the lid of the calorimeter.
Start the measurement with .
Wait a few minutes, then pour the acetone into the water in the calorimeter.
After a new temperature equilibrium has been reached, perform electrical calibration for the determination of the total heat capacity of the calorimeter.
Do this by supplying 10 V AC to the heating coil.
The system is now continuously heated and the supplied quantity of energy is measured.
When the temperature increase in the calorimeter induced by the electrical heater is approximately
equal in size to the temperature change resulting from mixing the two liquids, switch off the heating
and read the exact quantity of electrical energy supplied.
Continue to measure for another three minutes, then stop the measurement by pressing .
Send all data to “measure” and save the measurement (File > Save meausrement as…).
Fig. 3 shows the graph as it is now presented by the programme.
Fig. 3: Temperature-time diagram of the mixing of two miscible fluids and determining the heat capacity of the system.
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Use
for determining the temperature difference for the mixing process (see Fig. 3)
In a second experiment, add an additional portion of acetone (213 g) to the mixture in the calorimeter (see Table 1).
Perform the experiment completely analogously to the first measurement and pay attention that the
temperature of the mixture in the calorimeter and of the acetone is the same.
In a further series of experiments, successively add the 5 portions of water listed in Table 1 to the
557 g of acetone in the calorimeter.
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-
-
Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
Carry out this series in the same manner as in the first set of measurements, after carefully cleaning
and drying the calorimeter.
It is important that the calorimeter is recalibrated after each addition, as the heat capacity of the system is different after each temperature change.
Theory and evaluation
The change in enthalpy observed when two liquids are mixed is the sum of the changes in enthalpy
which occur during the mixing process. The mixing enthalpy ΔM 𝐻 is influenced by the interactions of the
molecules involved, which in turn are a function of the mixing ratio. The mixing enthalpy is zero if there
are no interactions between the molecules (so-called ideal mixtures). The interactions between two liquids can cause endothermic effects (decreasing supramolecular assemblies) or exothermic effects (formation of supramolecular assemblies of different molecules). The quantity of heat exchanged by mixing
𝑛A moles of the component A with 𝑛B moles of component B is termed the integral mixing enthalpy ΔM 𝐻I .
If a substance is successively added to another one until a certain mixing ratio is reached, the integral
mixing enthalpy is obtained by adding the individual enthalpy values:
∆M ℎI = ∑ ∆M ℎ𝐽I
(1)
𝐽
with
∆M ℎ𝐽I = 𝑄exp = 𝑄cal
∆𝑇exp
∆𝑇exp
= 𝑊el
∆𝑇cal
∆𝑇cal
(2)
The molar integral mixing enthalpy (referred to 1 mol of the mixture) is calculated as follows:
∆M 𝐻 I =
∆M ℎ I
𝑛A + 𝑛B
(3)
The mixing ratio is normally characterised by the molecular abundance (mole fraction).
𝑛A
𝑥A =
𝑛A + 𝑛B
(4.1)
𝑛B
𝑛A + 𝑛B
(4.2)
𝑥A + 𝑥B = 1
(4.3)
𝑥B =
for binary mixtures.
The dependence of the integral mixing enthalpy on the number of moles of the two components at constant pressure and constant temperature is defined by:
d(∆M ℎI ) = (
𝛿∆M ℎI
𝛿∆M ℎI
) d𝑛A + (
) d𝑛B
𝛿𝑛A 𝑛
𝛿𝑛B 𝑛
B
(5)
A
or
d(∆M ℎI ) = ∆M 𝐻A d𝑛A + ∆M 𝐻B d𝑛B
(6)
with
∆𝑀 𝐻𝑗 = (
ΔM 𝐻𝑗
4
𝛿∆M ℎI
)
𝛿𝑛𝑗 𝑇,𝑝,𝑛
(7)
Differential molar mixing enthalpy of the component 𝑗
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P3020661
Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
TEC
Integration at constant composition results in:
∆M ℎI = ∆M 𝐻A 𝑛A + ∆M 𝐻B 𝑛B
(8)
Division of (5) by (𝑛A + 𝑛B ) results in:
∆M 𝐻I = ∆M 𝐻A 𝑥A + ∆M 𝐻B 𝑥B
(9)
Fig. 4 shows the graph of ΔM 𝐻I versus the mixing ratio expressed as the molecular abundance of acetone 𝑥acetone .
Fig. 4: Temperature-time curve of the mixing enthalpy of mixture 1.
Using the equations (10) and (11),
𝛿∆M 𝐻I
) 𝑥B + ∆M 𝐻I
𝛿𝑥A
(10)
𝛿∆M 𝐻I
) 𝑥A + ∆M 𝐻I
𝛿𝑥B
(11)
∆M 𝐻A = (
∆M 𝐻B = (
the differential molar mixing enthalpy of water and acetone for the different compositions of the solutions
can be calculated. You can enter the results each for water and acetone into a data table (measurement > enter data manually) and put them together in one diagram as shown in Fig. 5.
Fig. 5: Differential molar mixing enthalpies of water and acetone as a function of the composition.
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TEC
Determination of the mixing enthalpy of binary
fluid mixtures with Cobra4
Disposal
The organic substances have to be collected in a correspondingly labelled container and passed to safe
waste disposal.
Appendix
Hazard symbol, signal word
Hazard statements
Precautionary statements
H225: Highly flammable
liquid and vapour
H319: Causes serious
eye irritation
H336: May cause drowsiness or dizziness
EUH 066: Repeated exposure may cause skin
dryness or cracking
P210: Keep away from
heat/sparks/open flames/hot
surfaces – No smoking
P233: Keep container tightly
closed
P305+351+338:
IF IN EYES: Rinse cautiously
with water for several
minutes. Remove contact
lenses if present and easy to
do – continue rinsing
Acetone
Danger
6
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