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eISSN: 2574-9927

Material Science & Engineering International Journal

Short Communication Volume 1 Issue 1

Measurement of the standard free energy change of chemical reactions by the chemical equilibration technique using a thermogravimetric apparatus: a novel approach

Aniket K Dutt,1 Dinabandhu Ghosh2

1Department of Materials Science & Engineering, University of North Texas, USA
2Department of Metallurgical and Materials Engineering, Jadavpur University, India

Correspondence: Aniket K Dutt, Department of Materials Science & Engineering, University of North Texas, Denton, TX 76203, USA

Received: March 03, 2017 | Published: April 21, 2017

Citation: Dutt AK, Ghosh D. Measurement of the standard free energy change of chemical reactions by the chemical equilibration technique using a thermogravimetric apparatus: a novel approach. Material Sci & Eng Int J. 2017;1(1):5-8. DOI: 10.15406/mseij.2017.01.00002

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Abstract

The current work aims at determining the standard free energy change (Δ) as a function of temperature (T), using the chemical equilibration technique. A novel approach was made to find the equilibrium state with the assistance of a Thermogravimetric Analyzer. The Δ for lead carbonate dissociation reaction PbCO3(s) = PbO(s) + CO2 (g) was calculated as an example. The weight of PbCO3started decreasing at specific temperature termed as equilibrium temperature. At this temperature ΔG = 0 and the equilibrium relation between Δand the equilibrium constant K applied. Below this temperature, when there was no change in weight, ΔG> 0, and above this temperature, when the weight kept changing for continued dissociation of PbCO3 (s), ΔG< 0. The obtained ΔG° for PbCO3(s) matched closely with the information found within in the literature.

Keywords: standard free energy, chemical equilibration technique, thermogravimetric analysis, thermodynamic data

Introduction

A thermogravimetric analyzer (TGA) measures the change in the mass of a reacting sample as function of time at any specified temperature or as a function of both temperature and time, which are conventionally used in the kinetic analysis of the reaction under study. Commonly, the change in the mass is converted into the fractional (or, percentage) conversion of the sample. A set of data of fractional conversion vs time helps to graphically detect the correct rate controlling mechanism by referring to the governing equations of differentrate controlling mechanisms such as gas film diffusion, product layer diffusion, and the interfacial reaction. However, it is not much heard of that a thermogravimetric analyzer has ever been used for any thermodynamic measurements. In the last decades, researchers used different approach like thermo barometry, EMF, and calorimetry methods for the determination of thermodynamic data.1-10 Berman1 used thermo barometry techniques to measure the thermodynamic data of minerals.1 Hugh et al8 studied the Gibbs free energies of formation of RuO2, OsO2 and IrO2 using an electrochemical method with calcia-stabilized zirconia (CSZ) solid electrolytes.8

The current work aims at adapting the apparatus to the determination of the standard (Gibbs) free-energy change of a chemical reaction as a function of temperature, in the form ΔG° = A + BT, where A = ΔH° and B = -ΔS°, by using the chemical equilibration technique. An attempt was made to verify this new method by comparing the results obtained by it with the known, published data of the standard free-energy changes for the dissociation of two solid carbonates CaCO3 and PbCO3.Particularly, the reaction PbCO3 (s) = PbO (s) + CO2 (g) was studied in details. It is proposed that if the new method is found to be successful, it can be extended to measuring the standard free-energy change of many other reactions for which the data have not yet been available.

Principle

The principle of determining the standard free energy change (ΔG°) by the chemical equilibration technique in the thermogravimetric analyzer (TGA) is elucidated with the help of an example of the dissociation of lead carbonate expressed as

PbCO3 (s) = PbO (s) +CO2 (g); ΔG° = A + BT (1)

Here, both A and B, which are standard enthalpy change (ΔH°) and negative standard entropy change (-ΔS°), respectively, are treated as unknown, and it is required to evaluate them experimentally so that the measured value of ΔG° can be expressed in the above common form of two-term equation.

The two most important variables in the current method are the temperature (T) and the partial pressure of carbon dioxide (pCO2). These are mutually dependent because of the fact that the thermodynamic equilibrium constant of Reaction (1), K(1), expressed by the ratio (αPbO. aCO2) / (αPbCO3), is solely governed by pCO2, the activities (ai) of the two pure condensed phases (PbCO3 and PbO) being 1 and αCO2being equal to pCO2. In the thermogravimetric apparatus, a chosen pCO2 (1 or less) is maintained by letting pure CO2 (for pCO2 = 1atm) or a mixture of CO2 and Ar(for pCO2< 1atm), Ar (argon) being the diluent, flow over the solid sample (PbCO3) continuously to ensure equilibration between the gas and solid while the furnace is heating and the temperature is slowly rising. Now, there is a unique temperature at which Reaction (1) comes to equilibrium with respect to the applied pCO2, satisfying the thermodynamic condition of ΔG = 0 for equilibrium. Below this temperature, ∆G is greater than 0 (criterion for the impossibility of reaction), and above this temperature, ΔG is less than 0 (criterion for the spontaneity of reaction). The manifestation of the condition ΔG< 0 in the TGA is the occurrence of Reaction (1) leading to the release of CO2 from the sample and the accompanying decrease in the mass of the sample. Thus, starting from the room temperature up to this unique temperature there is no change in the mass of the sample and the mass (weight) vs temperature curve, a TGA output, will remain flat for this particular temperature span. Just above the unique temperature, the mass of the sample will start decreasing and there will be a consequent descent of the curve, which will continue descending with the increasing temperature till the sample lasts. Thus, at this unique temperature (T1, say), Reaction (1) will attain equilibrium (ΔG = 0) under the applied pCO2 (pCO2 (1), say). Alternatively, one can write, ΔG°T1 = -RT1ln KT1 = -RT1ln pCO2 (1), where the value of R, the universal gas constant, is 8.314 J/mol. K. Knowing both pCO2 (1) and T1 experimentally, the value of ΔG° at the temperature T1, ΔG°T1, is obtained. Similarly, by applying several other chosen partial pressures of CO2 (with the help of CO2-Ar mixtures produced at varying proportions) and by repeating the experiment, ΔG° at several other temperatures (T) can be found. These values of ΔG° when plotted against T will give ΔG° in the form of A + BT, where A and B are now known quantities.

Experimental

Commercially available powder PbCO3(s) and CaCO3 (s) were used for this work. To measure the weight change in the powder material with temperature and pressure thermogravimetric analyze (Bysakh, Okay) was used. The powdered sample of PbCO3(s) and CaCO3(s) was placed into the crucible. A heating rate of 10K/min was used for the experiment. A gas mixture of Ar and CO2 was used for experiments. Gas mixture is passed through silica gel moisture trap to get rid of the moisture. For PbCO3, three different values of pCO2 were considered: 0.4 atm, 0.5 atm, and 0.75 atm. These partial pressures were established by mixing CO2 and Ar (pCO2+pAr=1 atm) in the ratio 2:3 (for pCO2 = 0.4 atm), 1:1 (for pCO2 = 0.5 atm), and 3:1 (for pCO2 = 0.75 atm). However, for the experiment with CaCO3, pure CO2 (pCO2 = 1 atm) alone was considered. (Figure 1) shows the schematic of TGA experimental set-up.

Figure 1 Schematic diagram of the experimental set-up: 1. CO2 cylinder; 2. Ar cylinder; 3. Flow meter; 4. Moisture trap; 5. Mixer and gas channeling arrangement; 6. TGA.

Result and discussion

CaCO3

The weight vs temperature plot obtained from the TGA run on the dissociation of CaCO3, the dissociation reaction

CaCO3 (s) = CaO (s) + CO2 (g) (2)

Under 1 atm of CO2, is shown in (Figure 2). Barring some small fluctuations in the curve because of gas flow disturbance, the temperature at which there is a monotonic descent of the curve is clearly noticeable and is found to be 853 °C (1126 K). Now, according to the published data,11 the standard free-energy change for Reaction (2) is

ΔG°=178500 – 159.1 T J (3)

This gives T = 178500/159.1 = 1122 K = 849 °C for ΔGG° = 0, noting that this is a case of standard state equilibrium because not only the two solids (CaCO3 and CaO) but CO2 also is at the standard state (1 atm). This means that according to the published data, the onset of the descent of the curve should have been at 849 °C. The agreement between the TGA result and the published one is thus very close.

Figure 2 Weight versus temperature plot for the dissociation of CaCO3under 1 atm CO2.

PbCO3

The weight vs temperature plots obtained from the TGA run on the dissociation of PbCO3 (Reaction (1)) for the three different values of pCO2, 0.4 atm, 0.5 atm, and 0.75 atm, are shown in (Figures 3a, b, c), respectively. The corresponding temperatures for the onset of the descent of the curve, in a monotonic and noticeable manner, are 280±4°C (553±4 K), 287±3°C (560±3 K), and 300±6°C (573±6 K), respectively. This allows one to find the values of ΔG° at these temperatures by using the relation ΔG° = -RT ln K = -RT ln pCO2 (applied). These values are listed in (Table 1).

Figure 3 Weight versus temperature plot for the dissociation of PbCO3 under (a) 0.4 atmpCO2 (b) 0.5 atmpCO2 and (c) 0.75 atmpCO2.

Exp. No.

Sample

PCO2(Atm)

Equilibrium Temp. °c(K)

Δ(J)

1

PbCO3(s)

0.4

280±4 (553±4)

4212.77±25

2

PbCO3(s)

0.5

287±3 (560±3)

3227.18±14

3

PbCO3(s)

0.75

300±6 (573±6)

1370.49±12

Table 1 Clinical and biochemical variables of individuals with overweight-obesity.

SD: Standard Deviation; BMI: Body Mass Index; WC: Waist Circumference; AC: Abdominal Circumference; HC: Hip Circumference; RER: Respiratory Exchange Ratio; HR: Hear Rate.

In (Figure 4), a plot of ΔG° vs T is made and a good linear fit is found, which yields the following expression for the standard free energy change of Reaction (1):

Δ=82955-142.37 T J (4)

In comparison, the published data11 for Reaction (1) is

Δ= 86700-149 T J (5)

The two results differ by only about 4%, which may be considered quite satisfactory, and the standard free-energy data thus measured by the thermogravimetric analyzer may be considered reliable. This method may be extended to measure the standard free energy changes for the dissociation of CrCO3(s), NiCO3(s), TiCO3(s), and WCO3(s) and for similar other gas-solid reactions (dissociation of oxides, nitrides, etc) for which data are not yet available in the literature.

Figure 4 Plot of standard free energy change (Δ) vs temperature (T) for the reactionPbCO3(s) = PbO (s) + CO2 (g).

Conclusion

The salient features of the current work are as follows:

  1. The thermogravimetric analyzer (TGA) has been traditionally used for kinetic studies. The current work aims at adapting the apparatus to the determination of the standard (Gibbs) free-energy change of a chemical reaction as a function of temperature, by using the chemical equilibration technique.
  2. An attempt was made to verify this new method by comparing the results obtained by it with the known, published data of the standard free-energy changes for the dissociation of two solid carbonates CaCO3 and PbCO3.
  3. The standard free energy change for the reaction PbCO3 (s) = PbO (s) + CO2 (g) was measured by the current method and the result obtained compared well with the published data:
  4. Δ = 82955-142.37 T J (current work)
    Δ= 86700 - 149 T J (published in data book)11.
    The two results differ by only about 4%. Hence, the standard free-energy data thus measured by the thermogravimetric analyzer may be considered reliable.

  5. This method may be extended to measure the standard free energy changes for the dissociation of CrCO3(s), NiCO3(s), TiCO3(s), and WCO3(s) and for similar other gas-solid reactions (dissociation of oxides, nitrides, etc) for which data are not yet available in the literature.

Acknowledgements

None.

Conflict of interest

The author declares no conflict of interest.

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