Experiment 12 – Calorimetry
02/14/2007
Experiment 12
Calorimetry
WS 2006/2007
Authors:
Lorenz Germann, Lukas Bischoff
Team members:
Lorenz Germann, Lukas Bischoff, Adrian Jenni,
Dimitri Kokkinis
Date:
29.11.2006
Assistant:
Ashley Harvey
E-mail:
[email protected]
[email protected]
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Experiment 12 – Calorimetry
02/14/2007
1. Abstract
Different calorimetrical measurements were executed. First the solution enthalpy of potassium nitrate was determined. The calculated value (12.854
kJ*mol-1) was three times too small in comparison to the standard value
(32.014 kJ*mol-1). Most likely the KNO3 did not dissolve completely or the
experiment was stopped too early. Like this only the solution enthalpy for a
part of the reaction was calculated.
In a second experiment the specific heat capacity (cp) of raw and cooked potatoes were determined. For the raw potatoes the results correspond well with
the theory. The results for the cooked potatoes were quite surprising. More
experiments should be executed.
Lastly an unknown metal should have been identified by calculating its atomic
mass out of its cp. This result wasn’t quite clear. The only reasonable
possibility was aluminium. The metal’s density was calculated to be sure. It
was aluminium indeed.
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Experiment 12 – Calorimetry
02/14/2007
2. Introduction
2.1. Goal
The aim of the experiment was to determine the heat of solution of potassium
nitrate, the atomic weight of an unknown metal through its heat capacity, and
the difference in heat capacity between cooked and raw potatoes as the
structure of their starch molecules was changed.
2.2. Theory [1]
2.2.1. Thermodynamics
First rule:
Energy doesn’t get lost: U = Q+W
(1)
The internal energy of an insulated system is constant. It is the sum of the
work W and the heat energy Q. It is measured in Joule [J].
Second rule: Heat capacity
C= dQ/dT
(2)
The internal energy of a system increases by heating. The temperature difference dT is proportional to the added heat energy Q.
Third rule: Enthalpy
H = U + pV (3)
Enthalpy H is the sum of the internal energy with the multiplication of pressure
and volume.
The enthalpy designates a quantity of energy, which a thermodynamic system
possesses and which can transfer between it and its environment.
When the pressure of a system is constant, the enthalpy can be written as
H = Q
The enthalpy H is lower than 0 for endothermic reactions (heat is put in the
substance) and higher than 0 for exothermic reactions (substance transfers
heat to environment). Its unit is the Joule.
2.2.2. Calorimeter
A calorimeter is a container, thermally insulated from the environment using a
material such as styrofoam. In its
cover there is a small hole for a
Thermometer
thermometer. The thermometer is
the only measuring instrument
needed for this experiment.
Cover Styrofoam
The insulation is to prevent the
calorimeter from losing thermal
Insulation
Styrofoam
energy through the walls. This way
the calorimeter can be described as
250ml beaker
an independent, insulated container
that is usable for thermodynamic
1000ml beaker
experiments. Inside the calorimeter,
3/31. Structure of calorimeter
Fig.
Experiment 12 – Calorimetry
02/14/2007
heat energy can be exchanged between materials, but there ideally is no loss
of energy.
2.2.3. Correction factor
Before getting started with the experiment there must be found a correction
factor that compares the calculated result with the measurement. This correction factor is determined by melting a piece of ice in a predefined mass of
water in the calorimeter and the first rule of thermodynamics:
H(ice)
m(Eis) m
+ c p (Water) (t'e t A ) = mwater c p (water) (t'e t a )
1
18g mol
(4)
tA = 0°C (Temperature of the ice)
t’e = calculated final temperature
ta = Start temperature water
te = final temperature water
J
cp (water) = 4.1868 g°C
J
m H(ice) = 6010 mol
Correciton factor f:
f =
Ttheoretical t'e t a
=
Tmeasured
te ta
(5)
2.2.4. The rule of Dulong-Petit
The specific heat of a metal depends on its atomic weight.
The rule of Dulong-Petit says that increasing the temperature of the molar
mass of many metals 1°C needs 24J of energy.
24J /°C mol = C p(metal ) M metal
(6)
2.2.5. Consistence of potatoes
The heat capacity of potatoes cannot specifically be identified because of the
vast amount of various sorts. An average potato consists of 77% water, 15%
starch, 2% protein, 1,5% organic acids, 1% minerals and 2.5% amino acids,
polysaccharides (without starch), sugar, lipids, polyphenols and alkaloids. Its
average energy per 100 g is 376.2 kJ. Starch, a polysaccharide is not homogeneous. It consists of 73 - 86% of Amylose and 14 – 27% of Amylopektin.
The molecules of Amylopektin and the molecules of Amylose form mixed
crystallites, which are bound together by hydrogen bonds. In cool water the
starch is not soluble; they extend at maximum 28 vol%. Above a certain
temperature (58-66°C) the starch suspension in the water solution dissolves.
This increases the viscosity and the conductivity and heat capacity.
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Experiment 12 – Calorimetry
02/14/2007
3. Materials and methods
3.1. Materials
Besides the standard equipment of a laboratory there was used a self made
calorimeter (see 2.2.2.), potatoes, a microwave and an onion chopper.
3.2. Methods
3.2.1. Calibrate the calorimeter and determine the correction factor
First of all, the empty calorimeter was weighed. To determine the correction
factor 150.018g of water was put into the calorimeter. The temperature (ta)
was measured. Then an ice cube was dried with a paper towel to take away
the water on its surface and put into the water. After the calorimeter was immediately closed, the system’s temperature was continuously observed and
the minimal temperature was noted. Also the calorimeter was weighed to determine the weight of the ice cube.
3.2.2. Solution enthalpy of potassium nitrate
150.011g of water was put in the empty calorimeter and the temperature ta
was measured.
Afterwards 15.032g of potassium nitrate (KNO3) was crushed with a mortar
and pestle. The potassium nitrate now was given into the calorimeter and the
calorimeter was closed. Constantly the calorimeter was agitated to dissolve
the KNO3. The temperature was measured.
After continuous observation, the temperature stood still on a certain value
(te). Using the following formula, the concentration of the potassium nitrate
was calculated and with the given chart of the handout, the specific heat
capacity of KNO3 was determined:
s H ° = m( Lsg ) c p ( KNO3 ) (t a t e ) f
3.2.3. Specific heat capacity of potatoes
Raw potatoes
Some potatoes were peeled and chopped with the onion chopper. Afterwards
30g were put into the tared calorimeter. Then approximately 100ml water was
put into a 250ml beaker and heated for 20 seconds in the microwave oven
(highest level). After the temperature was measured the water was given into
the calorimeter. While constantly stirring one waited until the temperature was
constant. The temperature tEnd was noted. Afterwards the calorimeter was
weighed. After cleaning and drying the calorimeter the test was repeated with
heating different heating times (30, 60 and 90 seconds).
In the end, the specific heat capacity of the potato was calculated.
c p (potato ) =
m(water ) c p (water ) (tend twater , hot ) f
m(potato ) (tend t potato )
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(7)
Experiment 12 – Calorimetry
02/14/2007
Cooked potatoes
Finely chopped potatoes were cooked with maximum power in the microwave
oven for one minute. After they cooled down, one proceeded in the same way
as described for the raw potatoes. Differently to the method above, the water
was heated only for 30, 60 and 90 seconds.
3.2.4. Specific heat capacity of an unknown metal
Two metal cubes were weighed. The calorimeter was filled with 120g of water.
The temperature (ta) was measured. The two metal cubes were heated in
boiling water in a beaker for 10’. After the water bath’s temperature (= metal’s
temperature, tmetal) was measured, the cubes were thrown in the calorimeter
as quickly as possible. After the calorimeter was closed immediately, one
waited until the temperature was stable (tEnd). With these results, the specific
heat capacity of the metal could be calculated:
c p (metal ) =
m(water ) c p (water ) (tend t water ) f
m(metal ) (tend tmetal )
(8)
This experiment was executed three times.
To determine the metal, the cp was inserted in the Dulong-Petit formula.
24 J / °C mol = C p ( Metal ) Molmass( Metal )
(9)
In order to have a second identification method the volume (V) of the two
metal cubes was measured, so that the density () can be determined.
=
m
V
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Experiment 12 – Calorimetry
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4. Results
4.1. Correction factor
Table 1. Calculation of correction factor f
tA’ [1]
cp (water) [1]
mH(ice) [1]
ta
te
m (water)
m (ice)
t’e
f
0°C
4.1868 J*g-1*°C-1
6010 J* mol-1
20.4°C
15.9°C
150.018g
9.502g
14.435°C
1.326
As we see in table 1 the calculated correction factor 1.326 is too high. It
should lie between 1.05 and 1.2 [1].
4.2. Solution enthalpy of potassium nitrate
Table 2. Calculation of solution enthalpy
m (solution)
ta
te
cp (KNO3) from table [1]
f
sH° for 15.032g
sH° for 1 mol
165.043g
20.4°C
18.1°C
3.75 J*g-1*°C-1
1.326
1911.362 J
12.854 kJ*mol-1
The solution enthalpy (sH°) for 1 mol (12.854 kJ*mol-1) depends on the concentration of the solution. It can be calculated as the difference between the
standard enthalpy of solution of a KNO3-solution and the standard enthalpy of
formation of solid KNO3 (-494.514 kJ mol-1).
The proportion in the used solution is 0.148 mol(KNO3)/8.334 mol(H2O) =
1/56.3. A solution with the proportion 1/50 has a standard building enthalpy of
-462.887 kJ*mol-1 one with 1/75 -461.916 kJ*mol-1. For the used solution this
value is approximately -462.5 kJ*mol-1. So sH° should theoretically be:
-462.5 kJ*mol-1- (-494.514 kJ*mol-1) = 32.014 kJ*mol-1
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Experiment 12 – Calorimetry
02/14/2007
4.3. Specific heat capacity of potatoes
Table 3. Specific heat capacity of raw potatoes
time in microwave oven [s]
temperature water [°C]
temperature potato [°C]
temperature end [°C]
mass water [g]
mass potatoes [g]
cp (raw potatoes) [Jg-1°C-1]
cp(water) [Jg-1°C-1] 2
20
53
18.5
41.4
101.97
29.39
7.358
4.1868
30
60
19
46.4
103.48
30.55
7.039
4.1868
60
94
19.7
68.3
105.02
29.95
7.763
4.1868
90
100
21
69.2
102.27
30.82
8.878
4.1868
As we see in table 3 potatoes tend to have a higher specific heat capacity the
hotter the water was.
Table 4. Specific heat capacity of cooked potatoes
time in microwave oven [s]
temperature water [°C]
temperature potato [°C]
temperature end [°C]
mass water [g]
mass potatoes [g]
30
51.2
19.7
46.1
105.8
30.87
60
89.1
21.9
68.1
96.29
31.1
90
100
21.5
74.5
108.9
31.65
cp (cooked potatoes) [Jg-1°C-1]
2.772
5.892
6.931
4.1868
4.1868
4.1868
cp(water) [Jg-1°C-1] 2
Table 4 shows that the cooked potatoes have a lower specific heat capacity
than the raw ones. They also tend to have higher cp values in hotter water.
There is a significant rising of the cp from 30 to 60 seconds long heated water.
Figure 2: Heat Capacity of the potato
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Experiment 12 – Calorimetry
02/14/2007
4.4. Specific heat capacity of an unknown metal
Table 5. Calculation of metal’s specific heat capacity and molar mass
temperature
Water [°C]
mass calorimeter
[g]
mass metal [g]
mass water [g]
temperature
metal [g]
end temperature
[°C]
cp metal [Jg-1°C-1]
molar mass
[gmol-1]
20.4
21.0
21.4
384.18
384.18
384.18
43.4602
120.005
95.0
43.4602
120.060
93.7
43.4602
120.012
92.3
25.3
25.7
26.4
0.812
29.531
0.799
30.022
0.877
27.360
The average calculated molar mass plus standard difference is:
x + SD = 28.971 ± 1.4
So the best matching element is silicon (28.09 gmol-1). But silicon is not a
metal. Considering all the faults in executing the experiment and measuring,
even values that are not included in the standard difference are possible. So it
could be aluminium (26.98 gmol-1) as well. The density of the used metal was
calculated as 2.716 g*cm-3. The density of silicon is 2.33 g*cm-3, of aluminium
it’s 2.7 g*cm-3 [3]. Now the metal can definitively be identified as aluminium.
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Experiment 12 – Calorimetry
02/14/2007
5. Discussion
5.1 Solution enthalpy of potassium nitrate
KNO3 dissolves to K+ and NO3-. It is possible that there are further reactions to
consider that might affect the result of the solution enthalpy. While K+ stays in
the solution as itself, the NO3- is the conjugated base to the strong acid HNO3.
It can be concluded that NO3- also stays as itself in the solution without
reaction. So there are no chemical processes that influence the result.
To break a chemical bond, energy is needed. Having the calorimeter as
closed system, the energy for the bond break has to be taken out of the
internal energy of the water (see the first rule of thermodynamics: the internal
energy of a system is constant), which results in a deeper te for water. Using
the formulas for the specific heat capacity, a calorimeter can be used to get
approximate specific bond energy. With the used calorimeter in this
experiment the result would be quite imprecise.
The calculated solution enthalpy of the used solution (12.854 kJ*mol-1) is approximately three times too low (value calculated out of standard data: 32.014
kJ*mol-1 [1]). It is highly probable that the KNO3 did not dissolve completely.
Like this, less energy was taken from the system (water) as it would take to
dissolve KNO3 entirely. So the measured end temperature (te) of 18.1°C is too
high and the value for cp is too small. By testing different values for te it was
found that the correct te should be something like 14.7°C. With this value the
cp becomes 31.856 kJ*mol-1 which nearly equals the value calculated out of
standard data (32.014 kJ*mol-1).
To get a better result one should make sure that the KNO3 dissolves completely. It’s not enough to just swing the calorimeter. The solution in the calorimeter should be mixed by using a magnet stirrer. Further one should wait
longer until the end temperature is noted.
5.2. Specific heat capacity of potatoes
5.2.1. Raw potatoes
The results correspond well with the theory. In water above 60°C the cp is
higher. At about 60°C the starch is starting to dissolve in the water. This
causes a higher heat capacity.
5.2.2. Cooked potatoes
Generally the cp of cooked potatoes is lower than the one for raw potatoes.
According to Fig B1 of the Journal of Materials Education [4], it can be seen
that heat capacity of the potato increases until it is fully cooked. Then, the
heat capacity abruptly falls on a significant deeper level and increases again
with alternated temperature, still at a deep level. This is exactly the same as
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Experiment 12 – Calorimetry
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observed in this experiment (fig 2). The bend in the curve of the cp at the
state of the cooked potato might be affected by the broken hydrogen bonds.
5.3. Identify a metal by its specific heat capacity
The determination of the metals atomic mass by its cp did not lead to a clear
result. The only possible metal is aluminium. But its atomic mass (26.98 gmol1
) is not included in the interval of the calculated atomic mass 28.971± 1.4.
Only by determining the metals density (2.716 g*cm-3) it was definitively identified as aluminium (2.7 g*cm-3).
The cp of the metal is quite deep with an average value of 0.829 Jg-1°C-1
compared to the cp of water (4.1868 Jg-1°C-1). This means that the metal
looses its temperature quickly. An explanation for the problems of identifying
the metal is, that the metal lost too much of energy while putting it from the
hot water bath to the calorimeter: Before putting it in the calorimter, the metal
was allowed to drip down the hot water so that no hot water comes in the
calorimeter and falsifies the results. In this period (1-2s) the metal might have
lost too much energy.
The experiment could be enhanced more exactly using a metal with a higher
specific heat capacity.
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Experiment 12 – Calorimetry
02/14/2007
6. References
[1] Handout Versuch 12 Kalorimetrie, D-MATL, ETH Zurich, WS 06/07
[2] http://de.wikipedia.org/wiki/Silizium
Visited 01/29/2007
[3] http://de.wikipedia.org/wiki/Aluminium
Visited 01/26/2007
[4] Journal of Materials Education 14 (1&2), sent as e-mail-attachement by
Ashley Harvey
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