System/Product
Atlas
Model/Module
Atlas Calorimeter
Subject Type
Measuring the Specific Heat Capacity (Cp) for components and
mixtures
Subject Version
1.0
Author
Yann Lecouturier
Date
21st December 2011
Technical Note:
Measuring the Specific Heat Capacity (Cp) for components and
mixtures with the Atlas Calorimeter
1 Introduction
There are a number ways of measuring Cp which may be more or less appropriate
depending on cost/availability of materials, reactivity etc.
This document describes two methods which are simple to do using the Atlas Calorimeter.
•
Method 1: Measuring Cp using one single PCC experiment– Direct method
•
Method 2: Measuring Cp using two PCC experiments at 2 different temperatures –
Indirect method
Before explaining the details of both methods of measurement, it is important to clarify
what we are measuring and calculating.
1.1 Specific Heat Capacity:
The objective of this technical note is to measure Cp, the Specific Heat Capacity. Therefore
the following terms should be clarified:
•
Heat Capacity or Thermal Capacity is the measurable physical quantity that
characterizes the amount of heat required to change a substance's temperature by a
given amount. In the International System of Units (SI), heat capacity is expressed in
units of Joule(s) (J) per Kelvin (K).
•
Specific Heat Capacity (J/g/K): It is the Heat Capacity per gram of the component
studied. (Called Cp in this document)
Technical note-Measuring Cp for components and mixtures.doc Measuring Cp for components and mixturesPage 1 of 6
•
Molar Heat Capacity (J/mol/K): It is the Heat Capacity per mole of the component
studied.
Specific Heat Capacity and Molar Heat Capacity are commonly used in scientific papers.
NOTE: The Calorimetry analysis section in the Atlas Reporting Software requires Specific
Heat Capacity for calculations. I will therefore describe two methods to calculate the Specific
Heat Capacity referred to as Cp in the rest of this document.
1.2 Equations and enthalpies involved in the calculation of Cp.
Q is the overall Enthalpy of the whole process. This is what is seen and measured by the
Atlas Calorimeter. This is not the Enthalpy of Reaction. The Enthalpy of Reaction ( ∆HR ) has
to be calculated from the Overall Enthalpy Q.
The Overall Enthalpy measured is the addition of several aspect of the reaction. They can be
defined as three different enthalpies:
•
Enthalpy of Reaction ( ∆HR ): This is thermal energy released/absorbed by a chemical
reaction. This is linked with the molecular/chemical transformation.
•
Enthalpy of Addition ( ∆Hadd ): This is simply due to the difference of temperature
between the two solutions (components) mixed together. The software calculates
the Enthalpy of Addition using Cp values entered in the software. The majority of
chemist use Cp given in the literature but Cp can be measured as described in this
document. The Cp is calculated using the following equation:
∆Hadd = Cp ⋅ M X ⋅ (Tf − Ti )
Mx (g)is the mass of component x added. Ti (°K) is the initial temperature of X and Tf
is final temperature of the system after addition.
•
Enthalpy of Solvation ( ∆HX ): Also called enthalpy of dissolution. This the energy
released/absorbed due to the physical effect of mixing a component into another
one. In other words, this is the energy involved in the process of forming a solution,
i.e. dissolving a solute in a solvent. This is linked with hydrogen bonding, interaction
dipole-dipole, anionic interaction etc. This is equal to ZERO when the same
component is added to itself as there is no dissolution happening.
So the Overall Enthalpy Q can be expressed as the addition of the three enthalpies
described above.
Q = ∆HR + ∆Hadd + ∆HX
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2 Experimental Methods
2.1 Method 1: Measuring Cp using one single PCC experiment –
Direct method
The simplest method is a single experiment where we mimic the calorimetry of reaction. In
this case we add a component X to a large volume of the same component X at a single
temperature (TR).
We just need to run a standard Power Compensation Calorimetry experiment on Atlas
Software.
1. In the reactor: Large amount of Compound X
2. Running standard PCC at a given temperature TR
3. Addition of small amount Mx of compound X (X being at ambient
temperature)
4. Getting the Overall Enthalpy Q value using Atlas Reporting software.
This PCC experiment will give us the Overall Enthalpy Q after the baseline correction in Atlas
reporting software. The calculation of the Enthalpy of Reaction are irrelevant here. We are
only interested in the Overall Enthalpy value Q.
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We are adding the component X to itself so:
Enthalpy of Reaction ( ∆HR ) = 0
and
Enthalpy of Solvation ( ∆HX ) = 0
Therefore Q is simplified as follow:
Q = ∆Hadd = Cp ⋅ M X ⋅ (Tf − Ti )
Tf in this case is the temperature of “reaction” or the temperature chosen for the
calorimetry experiment TR. In principle the compound added will be at ambient temperature
so Ti = Tamb .
So,
Q = Cp ⋅ M X ⋅ (TR − Tamb ) . We can then isolate Cp:
Cp =
Q
M X ⋅ (TR − Tamb )
It is important to note that Cp here is the average value of Cp over the temperature interval.
This temperature interval cannot be too small, otherwise the Enthalpy of Addition detected
would be too small to give an accurate result. However, this interval cannot be too large
either, otherwise an average Cp over a large temperature would be irrelevant.
You can use this method to estimate Cp for mixtures. Simply replace X with the mixture of
interest
•
Advantage of method 1: It is a simple and quick method to use.
•
Disadvantage of method 1: It may require large amounts of the component X. It
requires Tamb to be accurately measured.
2.2 Method 2: Measuring Cp using two PCC experiments at 2
different temperatures – Indirect method
We just need to run 2 standard Power Compensation Calorimetry experiment on Atlas
Software.
1. In the reactor: Large amount of H2O or another suitable solvent (it cannot
react with the compound X added !)
2. Running standard PCC at a given temperature T1
3. Addition of small amount MXof compound X
4. Getting the Overall Enthalpy QT1 value using Atlas Reporting software.
Technical note-Measuring Cp for components and mixtures.doc Measuring Cp for components and mixturesPage 4 of 6
5. Running a similar PCC at a different temperature T2, addition of the same
quantity MX of compound X and getting QT2.
These PCC experiments will give us the Overall Enthalpy QT1 and QT2 after the correction of
the baseline in Atlas reporting software. The calculation of Enthalpy of Reaction are
irrelevant here. We are only interested in the Overall Enthalpy value QT1 and QT2.
We are adding the component X to h2O (or any suitable solvent not reacting with X itself),
so:
Enthalpy of Reaction ( ∆HR ) = 0,
Therefore Q is simplified as follow: Q = ∆Hadd + ∆HX = Cp ⋅ M X ⋅ (Tf − Ti ) + ∆HX
Tf in this case is the temperature chosen for the calorimetry experiment: T1 or T2. The
component added will be at ambient temperature so Ti = Tamb . So, we can write the
following 2 equation for both experiment at T1 or T2.
Q(T ) = M X ⋅ Cp ⋅ (T1 − Tamb ) + ∆H x
1
Q(T ) = M X ⋅ Cp ⋅ (T 2 − Tamb ) + ∆H x
2
ΔHx is the heat of solvation of X in a large excess of water (or other suitable solvent). It is
independent of temperature of the experiment and so constant in these two experiments as
long as the amount of compound X added is the same: MX in both cases.
If we isolate ΔHx in both equation above we get:
∆HX = Q( T ) − M X ⋅ Cp ⋅ (T1 − Tamb )
1
∆HX = Q(T ) − M X ⋅ Cp ⋅ (T2 − Tamb )
2
ΔHx being the same in both experiments we can write the following, rearrange and finally
isolate Cp as follow:
Q(T ) − M X ⋅ Cp ⋅ (T1 − Tamb ) = Q( T ) − M X ⋅ Cp ⋅ (T2 − Tamb )
1
2
⇔ M X ⋅ Cp ⋅ (T1 − Tamb ) − M X ⋅ Cp ⋅ (T2 − Tamb ) = Q( T ) − Q( T )
1
2
⇔
Cp =
Q( T ) − Q( T )
1
2
M X ⋅ (T1 − T2 )
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As for method 1, it is important to note that Cp here is the average value of Cp over the
temperature interval between T1 and T2. This temperature interval cannot be too small,
otherwise the Enthalpy of Addition detected would be too small to give an accurate result.
However, this interval cannot be too large either, otherwise an average Cp over a large
temperature would be irrelevant.
You can use this method to estimate Cp for mixtures. Simply replace X with the mixture of
interest.
•
Advantage of method 2: It only requires a small amount of component X and Tamb
does not need to be known.
•
Disadvantage of method 2: It is not as quick as method 1.
2.3 Important note to apply these methods successfully with the
Atlas Software.
Calorimetry of reaction is usually done to assess the risk associated with exothermic
reactions. Therefore, the Enthalpy of Reaction measured should be negative as we are
talking about exothermic reactions. However, the Atlas Reporting software gives positive
values of Enthalpies of Exothermic Reaction for ease of use.
This means the following for the Overall Enthalpies values measured in Method 1 and 2:
•
Any positive Q value given by the Calorimetry software is in fact negative and
therefore an Exothermic process. It should be used a negative values in Cp
calculations.
•
Any negative Q value given by the Calorimetry software is in fact postive and
therefore an Endothermic process.
Method 1: It is likely that the TR chosen will be higher than Tamb. For example: TR = 30°C and
Tamb = 20°C:
In this case, because we are adding an amount of X at a colder temperature than the large
amount of X in the reactor, the overall process will be endotermic, therefore Q used in
calculation of Cp should be positive.
The Atlas reporting software will show a negative Overall Enthalpy value.
Method 2: The process can be Endothermic or Exothermic. This depends on T1 and T2
chosen and the amount of energy released/absorbed by the dissolution ΔHx.
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