Kohlrausch Law

Kohlrausch’s law states that the limiting molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its constituent ions. This law is important because it allows us to calculate the limiting molar conductivity of an electrolyte without having to measure it directly. It also provides insight into the nature of ionic conductivity in solutions.

For example, if we know the limiting molar conductivities of sodium and chloride ions, we can calculate the limiting molar conductivity of sodium chloride. This information can then be used to calculate the conductivity of a sodium chloride solution at any concentration.

Kohlrausch’s law is a fundamental principle of electrochemistry and is used extensively in the study of ionic solutions. It is also used in the development of batteries and other electrochemical devices.

What is Kohlrausch’s Law?

Kohlrausch’s Law

Kohlrausch’s law, also known as the law of independent migration of ions, states that the molar conductivity of an electrolyte solution is the sum of the contributions of its individual ions. This means that the conductivity of a solution is determined by the concentration and mobility of each type of ion present, and not by the overall concentration of the solution.

The law is named after Friedrich Kohlrausch, a German physicist who first proposed it in 1875. Kohlrausch’s law can be expressed mathematically as follows:

$$\Lambda = \lambda_+ c_+ + \lambda_- c_-$$

where:

• (\Lambda) is the molar conductivity of the solution (in S cm^2 mol^-1)
• (\lambda_+) and (\lambda_-) are the molar conductivities of the positive and negative ions, respectively (in S cm^2 mol^-1)
• (c_+) and (c_-) are the concentrations of the positive and negative ions, respectively (in mol L^-1)

Kohlrausch’s law can be used to calculate the molar conductivity of a solution if the molar conductivities of the individual ions are known. It can also be used to determine the concentration of an ion in a solution if the molar conductivity of the solution and the molar conductivities of the other ions present are known.

Examples

The following table shows the molar conductivities of some common ions at 25°C:

Using Kohlrausch’s law, we can calculate the molar conductivity of a solution of NaCl. The concentration of NaCl in the solution is 0.1 mol L^-1.

$$\Lambda = \lambda_+ c_+ + \lambda_- c_-$$

$$\Lambda = (50.1 \text{ S cm}^2 \text{ mol}^{-1})(0.1 \text{ mol L}^{-1}) + (76.3 \text{ S cm}^2 \text{ mol}^{-1})(0.1 \text{ mol L}^{-1})$$

$$\Lambda = 12.6 \text{ S cm}^2 \text{ mol}^{-1}$$

The molar conductivity of the NaCl solution is 12.6 S cm^2 mol^-1.

We can also use Kohlrausch’s law to determine the concentration of an ion in a solution. For example, we can determine the concentration of Cl- in a solution of HCl. The molar conductivity of the HCl solution is 426.2 S cm^2 mol^-1. The molar conductivity of H+ is 349.8 S cm^2 mol^-1.

$$\Lambda = \lambda_+ c_+ + \lambda_- c_-$$

$$426.2 \text{ S cm}^2 \text{ mol}^{-1} = (349.8 \text{ S cm}^2 \text{ mol}^{-1})c_+ + (76.3 \text{ S cm}^2 \text{ mol}^{-1})c_-$$

$$c_- = \frac{426.2 \text{ S cm}^2 \text{ mol}^{-1} - 349.8 \text{ S cm}^2 \text{ mol}^{-1}}{76.3 \text{ S cm}^2 \text{ mol}^{-1}}$$

$$c_- = 1.0 \text{ mol L}^{-1}$$

The concentration of Cl- in the HCl solution is 1.0 mol L^-1.

Kohlrausch’s law is a powerful tool for understanding the behavior of electrolytes in solution. It can be used to calculate the molar conductivity of a solution, to determine the concentration of an ion in a solution, and to study the interactions between ions in solution.

Uses of Kohlrausch’s law

Kohlrausch’s law states that the molar conductivity of a strong electrolyte at infinite dilution is equal to the sum of the molar conductivities of its constituent ions. This law can be used to:

• Determine the molar conductivity of an electrolyte at infinite dilution. This can be done by measuring the molar conductivity of the electrolyte at a series of concentrations and then extrapolating the data to infinite dilution.
• Calculate the ionic strength of a solution. The ionic strength of a solution is a measure of the concentration of ions in the solution. It can be calculated using the following formula:

I = 1/2 * Σc_iz_i^2

where:

• I is the ionic strength (in mol/L)
• c_i is the concentration of ion i (in mol/L)
• z_i is the charge of ion i

Kohlrausch’s law can be used to calculate the ionic strength of a solution by measuring the molar conductivity of the solution and then using the following formula:

I = (λ_m/λ_m^0)^2

where:

• I is the ionic strength (in mol/L)

• λ_m is the molar conductivity of the solution (in S/cm)

• λ_m^0 is the molar conductivity of the solution at infinite dilution (in S/cm)

• Predict the conductivity of a solution. The conductivity of a solution is a measure of its ability to conduct electricity. It can be calculated using the following formula:

κ = λ_m * c

where:

• κ is the conductivity of the solution (in S/cm)
• λ_m is the molar conductivity of the solution (in S/cm)
• c is the concentration of the solution (in mol/L)

Kohlrausch’s law can be used to predict the conductivity of a solution by calculating the molar conductivity of the solution at infinite dilution and then using the above formula.

Examples:

• The molar conductivity of NaCl at infinite dilution is 126.4 S/cm. This means that a 1 mol/L solution of NaCl will have a conductivity of 126.4 S/cm.
• The ionic strength of a 0.1 mol/L solution of NaCl is 0.01 mol/L. This means that the solution contains 0.01 mol of ions per liter.
• The conductivity of a 0.01 mol/L solution of NaCl is 0.1264 S/cm. This means that the solution can conduct electricity with a resistance of 12.64 ohms.

Kohlrausch’s Law and Conductometric Titrations

Kohlrausch’s Law:

Kohlrausch’s law states that the limiting molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its constituent ions. This law is important in understanding the behavior of electrolytes in solution and is used in conductometric titrations.

The limiting molar conductivity of an electrolyte is the molar conductivity of the electrolyte at infinite dilution. At infinite dilution, the ions are completely dissociated and there is no interaction between them. The limiting molar conductivity is a characteristic property of an electrolyte and depends on the nature of the ions and the temperature of the solution.

The limiting molar conductivity of an electrolyte can be determined by measuring the conductivity of the electrolyte at different concentrations and extrapolating the data to infinite dilution. The following equation is used to calculate the limiting molar conductivity:

$$\Lambda_m^0 = \lim_{c \to 0} \frac{\kappa}{c}$$

where:

• (\Lambda_m^0) is the limiting molar conductivity in S cm2 mol-1
• (\kappa) is the conductivity of the electrolyte in S cm-1
• (c) is the concentration of the electrolyte in mol L-1

Conductometric Titrations:

Conductometric titrations are a type of titration in which the endpoint is determined by measuring the conductivity of the solution. Conductometric titrations are used to determine the concentration of an unknown solution by reacting it with a solution of known concentration.

The conductivity of a solution depends on the concentration of ions in the solution. When two solutions are mixed, the conductivity of the resulting solution will change. This change in conductivity can be used to determine the endpoint of the titration.

The endpoint of a conductometric titration is the point at which the conductivity of the solution changes the most rapidly. This point corresponds to the point at which the moles of titrant added are equal to the moles of analyte present.

Conductometric titrations are a versatile technique that can be used to determine the concentration of a wide variety of analytes. They are particularly useful for titrating solutions that are colored or turbid, as the conductivity of the solution is not affected by these factors.

Examples of Conductometric Titrations:

• Determination of the concentration of a hydrochloric acid solution by titrating it with a sodium hydroxide solution.
• Determination of the concentration of a silver nitrate solution by titrating it with a potassium chloride solution.
• Determination of the concentration of a copper sulfate solution by titrating it with a sodium sulfide solution.

Conductometric titrations are a valuable tool for analytical chemists. They are a simple, accurate, and versatile technique that can be used to determine the concentration of a wide variety of analytes.

Electrolysis in Molten State

Electrolysis in the molten state is a process that uses electricity to separate a compound into its constituent elements. This process is typically used to produce metals from their ores, and it is also used to produce other materials, such as chlorine and sodium hydroxide.

In electrolysis, a molten compound is placed in a cell that contains two electrodes. The electrodes are connected to a power source, and when the power is turned on, the electrons from the negative electrode (the cathode) flow through the molten compound to the positive electrode (the anode). This flow of electrons causes the compound to decompose, and the elements that make up the compound are released at the electrodes.

For example, when sodium chloride is electrolyzed, the sodium ions in the compound are attracted to the cathode, and they are reduced to sodium metal. The chloride ions in the compound are attracted to the anode, and they are oxidized to chlorine gas.

The following is a more detailed explanation of the electrolysis process:

1. The molten compound is placed in a cell that contains two electrodes. The electrodes are made of a conductive material, such as graphite or platinum.
2. The electrodes are connected to a power source. The power source provides a direct current (DC) electrical current.
3. When the power is turned on, the electrons from the negative electrode (the cathode) flow through the molten compound to the positive electrode (the anode).
4. This flow of electrons causes the compound to decompose. The elements that make up the compound are released at the electrodes.
5. The products of electrolysis can be collected at the electrodes. For example, in the electrolysis of sodium chloride, the sodium metal is collected at the cathode, and the chlorine gas is collected at the anode.

Electrolysis is a versatile process that can be used to produce a variety of materials. It is an important industrial process, and it is also used in a variety of laboratory applications.

Here are some additional examples of electrolysis in the molten state:

• Production of aluminum: Aluminum is produced by the electrolysis of molten aluminum oxide.
• Production of magnesium: Magnesium is produced by the electrolysis of molten magnesium chloride.
• Production of calcium: Calcium is produced by the electrolysis of molten calcium chloride.
• Production of sodium hydroxide: Sodium hydroxide is produced by the electrolysis of molten sodium chloride.
• Production of chlorine: Chlorine is produced by the electrolysis of molten sodium chloride.

Electrolysis is a powerful tool that can be used to produce a variety of materials. It is an important industrial process, and it is also used in a variety of laboratory applications.

Frequently Asked Questions – FAQs

Who discovered the law of independent migration of ions?

Who discovered the law of independent migration of ions?

The law of independent migration of ions was discovered by Friedrich Kohlrausch in 1875. Kohlrausch was a German physicist who studied the electrical conductivity of solutions. He found that the conductivity of a solution is proportional to the concentration of ions in the solution and that the mobility of an ion is independent of the concentration of other ions in the solution.

Examples of the law of independent migration of ions

The law of independent migration of ions can be seen in a number of different experiments. One example is the electrolysis of water. When water is electrolyzed, the water molecules are split into hydrogen and oxygen ions. The hydrogen ions migrate to the cathode, while the oxygen ions migrate to the anode. The rate at which the ions migrate is proportional to the concentration of ions in the solution.

Another example of the law of independent migration of ions is the separation of ions by chromatography. Chromatography is a technique that is used to separate different substances in a mixture. In chromatography, the mixture is passed through a column that is packed with a stationary phase. The different substances in the mixture interact with the stationary phase to different degrees, and this causes them to separate. The rate at which the substances separate is proportional to the concentration of ions in the mixture.

Applications of the law of independent migration of ions

The law of independent migration of ions has a number of important applications. One application is the use of ion exchange chromatography to separate different ions in a mixture. Ion exchange chromatography is a technique that is used in a variety of different fields, including chemistry, biology, and environmental science.

Another application of the law of independent migration of ions is the use of electroplating to coat metals with a thin layer of another metal. Electroplating is a process that is used in a variety of different industries, including the automotive industry, the jewelry industry, and the electronics industry.

What is kohlrausch law and its applications?

Kohlrausch’s law, also known as the law of independent migration of ions, states that the molar conductivity of an electrolyte solution is the sum of the contributions of its individual ions. This means that the conductivity of a solution is determined by the concentration and mobility of each type of ion present.

The law can be expressed mathematically as follows:

$$\Lambda = \sum_i \lambda_i c_i$$

where:

• (\Lambda) is the molar conductivity of the solution (in S cm^2 mol^-1)
• (\lambda_i) is the molar conductivity of the ith ion (in S cm^2 mol^-1)
• (c_i) is the concentration of the ith ion (in mol L^-1)

Kohlrausch’s law can be used to calculate the molar conductivity of a solution if the molar conductivities of its individual ions are known. It can also be used to determine the concentration of an ion in a solution if the molar conductivity of the solution and the molar conductivities of the other ions present are known.

Applications of Kohlrausch’s law

Kohlrausch’s law has a number of applications in electrochemistry, including:

• Determination of ionic mobilities: Kohlrausch’s law can be used to determine the mobilities of individual ions by measuring the molar conductivity of a solution and the concentrations of the ions present.
• Calculation of ionic strengths: The ionic strength of a solution is a measure of the concentration of ions in the solution. It can be calculated using Kohlrausch’s law by summing the products of the concentrations of the ions present and their molar conductivities.
• Prediction of the conductivity of solutions: Kohlrausch’s law can be used to predict the conductivity of a solution if the molar conductivities of its individual ions are known. This can be useful for designing electrochemical cells and other devices that use electrolytes.

Examples of Kohlrausch’s law

The following table shows the molar conductivities of some common ions at 25°C:

Using Kohlrausch’s law, we can calculate the molar conductivity of a solution of NaCl at 25°C. The concentration of NaCl in the solution is 0.1 mol L^-1.

$$\Lambda = \lambda_{Na+} c_{Na+} + \lambda_{Cl-} c_{Cl-}$$

$$\Lambda = (50.1 \text{ S cm}^2 \text{ mol}^{-1})(0.1 \text{ mol L}^{-1}) + (76.3 \text{ S cm}^2 \text{ mol}^{-1})(0.1 \text{ mol L}^{-1})$$

$$\Lambda = 12.6 \text{ S cm}^2 \text{ mol}^{-1}$$

The molar conductivity of the NaCl solution is 12.6 S cm^2 mol^-1. This value is equal to the sum of the molar conductivities of the Na+ and Cl- ions.

Kohlrausch’s law is a powerful tool for understanding the behavior of electrolytes in solution. It has a number of applications in electrochemistry, including the determination of ionic mobilities, the calculation of ionic strengths, and the prediction of the conductivity of solutions.

What is Kohlrausch law of independent migration?

Kohlrausch’s law of independent migration states that the molar conductivity of an electrolyte solution is the sum of the contributions of the individual ions present in the solution. This law is based on the assumption that the ions in a solution are independent of each other and that their movement is not affected by the presence of other ions.

The law can be expressed mathematically as follows:

$$\Lambda = \lambda_+ + \lambda_-$$

where:

• (\Lambda) is the molar conductivity of the electrolyte solution
• (\lambda_+) is the molar conductivity of the cation
• (\lambda_-) is the molar conductivity of the anion

The law can be used to calculate the molar conductivity of an electrolyte solution if the molar conductivities of the individual ions are known. For example, the molar conductivity of a 0.1 M solution of NaCl can be calculated as follows:

$$\Lambda = \lambda_{Na^+} + \lambda_{Cl^-} = 50.1 \text{ S cm}^2 \text{mol}^{-1} + 76.3 \text{ S cm}^2 \text{mol}^{-1} = 126.4 \text{ S cm}^2 \text{mol}^{-1}$$

Kohlrausch’s law is a useful tool for understanding the behavior of electrolytes in solution. It can be used to predict the molar conductivity of an electrolyte solution, to determine the relative mobilities of different ions, and to study the effects of temperature and concentration on the conductivity of electrolyte solutions.

Examples of Kohlrausch’s law

The following are some examples of how Kohlrausch’s law can be used to understand the behavior of electrolytes in solution:

• The molar conductivity of an electrolyte solution increases with increasing temperature. This is because the ions in a solution move more quickly at higher temperatures, which increases their mobility and hence their contribution to the molar conductivity.
• The molar conductivity of an electrolyte solution decreases with increasing concentration. This is because the ions in a solution become more crowded at higher concentrations, which hinders their movement and hence their contribution to the molar conductivity.
• The molar conductivity of an electrolyte solution is different for different electrolytes. This is because the molar conductivity of an electrolyte solution depends on the mobilities of the individual ions present in the solution. For example, the molar conductivity of a solution of NaCl is higher than the molar conductivity of a solution of KCl because the Na+ ion is more mobile than the K+ ion.

Kohlrausch’s law is a powerful tool for understanding the behavior of electrolytes in solution. It can be used to predict the molar conductivity of an electrolyte solution, to determine the relative mobilities of different ions, and to study the effects of temperature and concentration on the conductivity of electrolyte solutions.

Why do we need Kohlrausch law?

Kohlrausch’s law states that the limiting molar conductivity of an electrolyte is equal to the sum of the limiting molar conductivities of its constituent ions. This law is important because it allows us to calculate the limiting molar conductivity of an electrolyte without having to measure it directly.

Example:

Consider the electrolyte NaCl. The limiting molar conductivity of NaCl is 126.4 S cm2 mol-1. The limiting molar conductivity of Na+ is 50.1 S cm2 mol-1, and the limiting molar conductivity of Cl- is 76.3 S cm2 mol-1. According to Kohlrausch’s law, the limiting molar conductivity of NaCl should be equal to the sum of the limiting molar conductivities of Na+ and Cl-, which is 126.4 S cm2 mol-1. This is indeed the case.

Kohlrausch’s law is also important because it allows us to understand the relationship between the limiting molar conductivity of an electrolyte and its concentration. At low concentrations, the limiting molar conductivity of an electrolyte is approximately equal to the sum of the limiting molar conductivities of its constituent ions. However, as the concentration of the electrolyte increases, the limiting molar conductivity decreases. This is because the ions in the electrolyte begin to interact with each other, which hinders their movement.

Kohlrausch’s law is a fundamental principle of electrochemistry. It is used to calculate the limiting molar conductivity of electrolytes, to understand the relationship between the limiting molar conductivity of an electrolyte and its concentration, and to design electrochemical cells.

What is infinite dilution in electrochemistry?

Infinite Dilution in Electrochemistry

In electrochemistry, infinite dilution refers to a hypothetical situation in which the concentration of a solute in a solution is so low that it has no effect on the properties of the solvent. This is in contrast to finite dilution, in which the concentration of the solute is high enough to have a noticeable effect on the solvent.

The concept of infinite dilution is important in electrochemistry because it allows scientists to study the properties of ions in solution without having to worry about the interactions between the ions and the solvent molecules. This is important because the interactions between ions and solvent molecules can have a significant effect on the properties of the ions, such as their mobility and reactivity.

Examples of Infinite Dilution

There are a number of examples of infinite dilution in electrochemistry. One example is the study of the properties of ions in water. Water is a polar solvent, meaning that it has a positive end and a negative end. This polarity allows water molecules to interact with ions, which are charged particles. The interactions between water molecules and ions can affect the mobility and reactivity of the ions.

Another example of infinite dilution is the study of the properties of ions in non-polar solvents. Non-polar solvents, such as hexane, do not have a positive end or a negative end. This means that they do not interact with ions. This allows scientists to study the properties of ions in non-polar solvents without having to worry about the interactions between the ions and the solvent molecules.

Applications of Infinite Dilution

The concept of infinite dilution is used in a number of applications in electrochemistry. One application is the development of electrochemical sensors. Electrochemical sensors are devices that use the properties of ions in solution to detect the presence of specific substances. The concept of infinite dilution is used to design electrochemical sensors that are sensitive to very low concentrations of specific substances.

Another application of infinite dilution is the development of batteries. Batteries are devices that store electrical energy in chemical form. The concept of infinite dilution is used to design batteries that have a long shelf life and can deliver a high power output.

Conclusion

Infinite dilution is a hypothetical situation in which the concentration of a solute in a solution is so low that it has no effect on the properties of the solvent. This concept is important in electrochemistry because it allows scientists to study the properties of ions in solution without having to worry about the interactions between the ions and the solvent molecules. The concept of infinite dilution is used in a number of applications in electrochemistry, such as the development of electrochemical sensors and batteries.