Isopiestic Method-Thermodynamic Method to Determine the Activity Coefficients of Components of a Solution

Abstract

The isopiestic method is a thermodynamic technique used to measure the activity coefficients of components in a solution. In the context of ionic liquids, which are salts in liquid state below 100°C, the isopiestic method can be applied to study their behavior and properties in various solutions. In the isopiestic method, two solutions with different concentrations of a solute are prepared, and the vapor pressure of the solutions is measured at the same temperature. By comparing the vapor pressures, the activity coefficients of the solute in the solutions can be determined. When it comes to ionic liquids, this method can be used to explore their interactions with other substances, such as different solvents or salts. Understanding these interactions is crucial for various applications of ionic liquids, including their use as green solvents, electrolytes in batteries, and in other chemical processes.

1. Introduction

The isotopic method in ionic liquids involves using isotopically labeled compounds to trace and understand various processes within the liquid. This can include studying diffusion, structure, and interactions. Isotopic labeling allows researchers to track specific atoms or molecules and gain insights into the behavior and mechanisms of ionic liquids at a molecular level. It is a powerful technique for elucidating the properties and dynamics of these unique liquid systems.

Achieving the thermodynamic equilibrium point between two solutions is the primary requirement for this approach. The solutions’ initial compositions alter and eventually find equilibrium when they come into contact with one another during the vapor phase and exchange solvents. The solvents’ chemical potential, activity, and hence their vapor pressure are all equivalent when the solutions are in equilibrium. An example of an isopistic device is shown in Figure 1.

Figure 1.

Schematic of isopistic device.

The heat of evaporation from the solvent in the solutions’ evaporation and distillation causes the solutions’ temperatures to differ from one another during the solvent exchange process. The entire system is housed in a thermostat environment in order to avoid this circumstance and isotherm of the solutions. We weigh every solution both before and after equilibrium. The method’s correctness is contingent upon the precision of the analytical measurements and the reporting of the reference solution’s vapor pressure data. At the point when the temperature and strain of all stages become equivalent, thermodynamic harmony is laid out among them and the action of the dissolvable is equivalent in all stages on the grounds that the substance capability of the dissolvable in every one of the arrangements in a shut framework has a similar worth:

$$a_1^{\alpha }=a_2^{\beta }$$E1

The accompanying relationship exists between dissolvable movement and osmotic coefficient:

$$Ln{a}_1=-v_s.m_s.M_1.{\varnothing }_s$$E2

where M₁ is the molecular mass of the dissolvable (kg/mol), m_s is the molality of the non-unstable solute (mol/kg), ∅_s is the osmotic coefficient of the arrangement, and sν is the amount of the stoichiometric coefficients [1, 2, 3].

As indicated by relations (1) and (2), we will have:

$$\begin{array}{l}{v}_{\alpha }.{\varnothing }_{\alpha }.m_{\alpha }=v_{\beta }.{\varnothing }_{\beta }.m_{\beta }\\ {\varnothing }_{\beta }=\left(v_{\alpha }.m_{\alpha }/v_{\beta }.m_{\beta }\right).{\varnothing }_{\alpha }\Rightarrow {\varnothing }_{\beta }=R{\varnothing }_{\alpha }\end{array}$$E3

When the values of R and Ln${\gamma }_{\pm A}$ are available, the value of Ln${\gamma }_{\pm B}$can be calculated as follows:

$$Ln{\gamma }_{\pm B}=Ln{\gamma }_{\pm A}+\underset{0}{\overset{m_A}{\int }}dLn\frac{m_A}{m_B}+\underset{0}{\overset{m_A}{\int }}\left(R-1\right)dLn{\gamma }_A{m}_A$$E4

2. The application of ionic liquids in other electrochemical methods

Ionic liquids, besides isopiestic method, are also utilized in other electrochemical methods such as electrode composition, current composition, electrolyte composition, and more. The unique characteristic of ionic liquids includes their high ionic conductivity and wide electrochemical windows, indicating their high capability for electrochemical operations. This capability allows us to adjust the properties of ionic liquids according to various needs.

One common electrochemical application of ionic liquids is in electrolysis processes, where they can serve as electrolytes due to their high ionic conductivity. Additionally, ionic liquids are used in electrochemical sensors and biosensors due to their ability to solubilize a wide range of analytes and their compatibility with various electrode materials. Furthermore, ionic liquids are employed in electrodeposition and electrosynthesis reactions, where they can act as solvents, electrolytes, or both. Their wide electrochemical stability window allows for the deposition of metals and the synthesis of various organic compounds under mild conditions. Overall, the unique properties of ionic liquids make them valuable components in various electrochemical methods beyond the isopiestic method.

3. The concentration range of ionic liquids used in the isopiestic method for determining activity coefficients

In the isopiestic method, solutions with low concentrations are typically used to determine the activity coefficients of solutes. This is because:

1. At low concentrations, the assumptions of ideal behavior for solutions are usually valid, leading to more accurate thermodynamic calculations.

2. Measurement of vapor pressures of solutions and water vapor (as a reference) is easily performed and provides higher accuracy at low concentrations.

Therefore, in the isopiestic method, solutions with low concentrations, particularly in the range of 0.01–0.1 molar, are commonly employed [4].

4. What are ionic liquids and what are their uses in chemistry?

Ionic liquids can be employed in the isopiestic method to measure their activity coefficients in various solutions. For example, researchers might investigate the behavior of an ionic liquid in water or in a mixed solvent system using the isopiestic method.

Let us consider an ionic liquid like 1-butyl-3-methylimidazolium chloride ([BMIM]Cl). Figure 2 shows the structure of [BMIM]Cl. To determine its activity coefficients, researchers could create solutions of [BMIM]Cl in different concentrations and use the isopiestic method to measure the vapor pressures of these solutions. By maintaining the same water activity in these solutions and comparing their vapor pressures, scientists can calculate the activity coefficients of [BMIM]Cl in the respective solutions [5].

Figure 2.

Composition structure 1-butyl-3-methylimidazolium chloride.

This information is valuable for understanding how [BMIM]Cl behaves in different environments and can be crucial for various applications, such as in electrolyte systems, catalysis, or solvent-related processes. Physical and chemical properties of [BMIM]Cl are given in Table 1.

CAS Nr	Sum formula	Molecular weight	Melting point	Density	Solubility
[79917–90-1]	C8H15ClN	174.67	65°C	1.08 Kg/m^3	DMSO (Slightly), Methanol (Sparingly)

Table 1.

Physical and chemical properties of [BMIM]Cl.

5. What are ionic liquids and what are their uses in chemistry?

Ionic liquids are salts that are in a liquid state at relatively low temperatures, often below the boiling point of water. Unlike traditional salts, which have high melting points, ionic liquids are composed entirely of ions (charged particles) and exhibit unique properties due to their ionic nature. Typically, they consist of large organic cations paired with various anions. The combination of different cations and anions allows for a wide range of ionic liquids with diverse properties.

5.1 Some of ionic liquids used in chemistry

1. Solvents: Ionic liquids are excellent solvents for a wide range of compounds, including gases, metals, and organic molecules. They can dissolve a variety of substances that are insoluble in traditional organic solvents, making them valuable in chemical synthesis and catalysis [6].

2. Green Chemistry: Ionic liquids are often considered more environmentally friendly than traditional organic solvents. They are non-volatile and can be recycled, reducing environmental pollution. Their use in green chemistry initiatives has gained attention for sustainable chemical processes.

3. Catalysis: Ionic liquids can serve as catalysts or co-catalysts in various chemical reactions. They can stabilize reactive intermediates and enhance reaction rates, making them useful in both academic research and industrial applications.

4. Electrolytes: Ionic liquids are used in batteries and supercapacitors as electrolytes. Their high ionic conductivity and stability under a wide range of conditions make them attractive for energy storage devices. Some examples of ionic liquids used in batteries are given in Table 2.

5. Extraction and Separation: Ionic liquids are employed in extraction and separation processes due to their selectivity for specific compounds. They can extract valuable chemicals from natural sources or separate different components of a mixture efficiently.

6. Catalyst Immobilization: Ionic liquids can serve as a medium for immobilizing catalysts. Immobilized catalysts are easier to handle, recover, and reuse, making the overall catalytic process more efficient and sustainable.

7. Gas Absorption: Some ionic liquids have the ability to absorb gases like carbon dioxide and sulfur dioxide. This property is essential in gas purification and separation processes, especially in environmental and industrial applications. Figure 3 shows the processes of gas purification and separation by ionic liquids.

8. Lubricants: Ionic liquids can be used as lubricants, especially in situations where traditional lubricants fail, such as at extreme temperatures or in vacuum environments.

9. Nanotechnology: Ionic liquids are utilized as suitable solvents for the synthesis of nanoparticles and nanomaterials. Some examples of nanoparticle synthesis using ionic liquids are given in Table 3. The steps of nanoparticle synthesis are shown in Figure 4.

([C5H12NO][N(SO2F)2])

([C8H17NO][N(CF3SO2)2]

([C6H11N2][N(CN)2])

Table 2.

Some examples of ionic liquids used in batteries.

Figure 3.

Processes of gas purification and separation by ionic liquids.

Gold Nanoparticles

Silver Nanoparticles

Magnetic Nanoparticles

Metal Oxide Nanoparticles

Carbon Nanomaterials

Table 3.

Some examples of nanoparticle synthesis.

Figure 4.

The steps of nanoparticle synthesis.

6. Obtaining the activity coefficient for ionic solutions using the isopiestic method?

The isopiestic method is a technique used to measure the activity coefficients of solutes in solutions. In the context of ionic liquids, which are salts that are in a liquid state at relatively low temperatures, the isopiestic method can be employed to determine their activity coefficients [7].

Here is how it works:

1. Preparation of Solutions: Prepare two solutions with different concentrations of the ionic liquid. These solutions should have the same water activity, which means they have the same ratio of vapor pressures.

2. Equilibration: Allow the solutions to equilibrate in a closed system until the water activity in both solutions is the same. This is usually achieved by keeping the solutions in a controlled environment until no further changes in water activity are observed.

3. Measurement: Measure the vapor pressures of both solutions once equilibrium is reached. The vapor pressure is related to the activity coefficients of the components in the solutions.

4. Calculation: By comparing the vapor pressures and knowing the solution concentrations, you can calculate the activity coefficients of the ionic liquid in each solution.

5. Analysis: Analyze the data to obtain the activity coefficients at different concentrations of the ionic liquid. This information is valuable for understanding the behavior of ionic liquids in various applications, such as in electrolytes, solvents, or green chemistry processes.

7. How activity coefficients of ionic liquids can help us determine their usefulness for various applications such as solvents, catalysis, electrolytes, extraction and separation, catalyst immobilization, gas adsorption, and lubricants?

The activity coefficients of ionic liquids, including their physical and chemical properties such as density, viscosity, ion exchange, gas solubility, and solubility, can play a crucial role in determining their usefulness for various applications. For instance, for solubility applications, the high and tunable activity coefficients of ionic liquids can be used as alternative solvents to traditional solvents like water or organic oils. Their high activity coefficients and tunability are among the advantages of this application.

Moreover, for catalysis, the activity coefficients of ionic liquids can be utilized to stabilize catalysts and enhance their activity in chemical reactions. Given the diverse properties of ionic liquids and the variety in their activity coefficients, these substances can be used for various applications including extraction, separation, gas absorption, and lubricants, and activity coefficients can play an important role in these areas [8].

8. Conclusion

The isopiestic method in ionic liquids involves using isotopically labeled compounds to trace and understand various processes within the liquid. This can include studying diffusion, structure, and interactions. Isotopic labeling allows researchers to track specific atoms or molecules and gain insights into the behavior and mechanisms of ionic liquids at a molecular level. It is a powerful technique for elucidating the properties and dynamics of these unique liquid systems. The concentration range of ionic liquids used in the isopiestic method for determining activity coefficients typically falls within the lower concentration range. This range is generally around 0.01–0.1 molar or even lower, as within this range, the ideal behavior assumptions of the solutions can be better satisfied.

Acknowledgments

I am grateful to “IntechOpen”, the world’s leading publisher of Open Access books.

I would also like to express my gratitude to “Prof. Pradip K. Bhowmik”, the academic editor, and “Dorian Salatic”, the publishing process manager who helped me in completing this chapter of the book Ionic liquids.

Appendices and nomenclature

1. The Gibbs energy of the above system(M₁X₁–M₂X₂–H₂O) consists of two terms, viz.

$$G=G^{DH}+G^{Hy}$$

1. where G^DH is the Debye Hockel contribution and G^Hy is the pseudo-ideal mixture description of the resulting species resulting from the mole fraction of component X.

For the ternary aqueous solution of electrolyte A + electrolyte B under isopistic equilibrium, a linear empirical relationship was proposed using Zdanowski [9].

$$\frac{m_A}{m_A^{°}}+\frac{m_B}{m_B^{°}}=1\left(a_W=constant\right)$$