Electrochemistry - Molar Conductance

Definition of molar conductance.
Factors affecting molar conductance:
- Concentration of electrolyte solution.
- Nature of electrolyte.
Calculation of molar conductance using the equation:
- $\Lambda_m = \frac{1000}{C \times l} \times \kappa$, where:
  - $\Lambda_m$ is the molar conductance (in S cm^2 mol^-1).
  - C is the concentration of electrolyte (in mol L^-1).
  - l is the distance between the electrodes (in cm).
  - $\kappa$ is the cell constant.
Units of molar conductance.
Variation of molar conductance with dilution.
Kohlrausch’s Law.
Strong electrolytes vs weak electrolytes.
Limiting molar conductance.
Applications of molar conductance.

Variation of Molar Conductance with Dilution

Molar conductance generally increases with dilution.
As the concentration of electrolyte decreases, the number of ions available for conduction decreases.
However, the specific conductance of each ion remains constant.
This leads to an increase in molar conductance as dilution increases.

Kohlrausch’s Law

Kohlrausch’s law states that, at infinite dilution, the molar conductance of an electrolyte can be expressed as the sum of the individual molar conductances of its constituent ions, each multiplied by their respective molar concentration.
Mathematically, it can be represented as:
- $\Lambda_{m} = \lambda_{+} \times C_{+} + \lambda_{-} \times C_{-}$,
- where $\Lambda_{m}$ is the molar conductance,
- $\lambda_{+}$ and $\lambda_{-}$ are the molar conductances of cation and anion respectively,
- $C_{+}$ and $C_{-}$ are the molar concentrations of cation and anion respectively.

Strong Electrolytes vs. Weak Electrolytes

Strong electrolytes are substances that completely dissociate into ions when dissolved in water.
Examples of strong electrolytes include strong acids (HCl, HNO3) and strong bases (NaOH, KOH).
Weak electrolytes are substances that only partially dissociate into ions in water.
Examples of weak electrolytes include weak acids (acetic acid, carbonic acid) and weak bases (ammonia).
The molar conductance of strong electrolytes is greater than weak electrolytes due to the higher degree of ionization.

Limiting Molar Conductance

Limiting molar conductance is the molar conductance of an electrolyte at infinite dilution.
It is denoted by $\Lambda_{m}^{0}$.
Limiting molar conductance can be calculated using Kohlrausch’s law.
By extrapolation, the molar conductance is determined when the concentration approaches zero.
Limiting molar conductance is a characteristic property of an electrolyte and depends on its nature.

Applications of Molar Conductance

Molar conductance is used to determine the degree of ionization of an electrolyte.
It helps in identifying the nature of an electrolyte (strong or weak).
Molar conductance measurements are useful in determining the dissociation constants of weak electrolytes.
Molar conductance data is used to calculate the solvation number and the ionic radius of ions.
It is used in the study of electrochemical cells and battery technology.

Example 1

Calculate the molar conductance of a solution containing 0.1 mol L^-1 of NaCl at a distance of 5 cm using a cell constant of 0.01 cm^-1.

Given:
- Concentration of NaCl = 0.1 mol L^-1
- Distance between electrodes (l) = 5 cm
- Cell constant (κ) = 0.01 cm^-1
Using the formula:
- $\Lambda_m = \frac{1000}{C \times l} \times \kappa$
- Substitute the values:
- $\Lambda_m = \frac{1000}{0.1 \times 5} \times 0.01$
- $\Lambda_m = 200 , \text{S cm}^2 \text{mol}^-1$

Example 2

Calculate the molar conductance of a 0.2 mol L^-1 solution of acetic acid (CH3COOH) at a distance of 6 cm, given that the cell constant is 0.02 cm^-1. The molar conductance of acetic acid at infinite dilution is 390 S cm^2 mol^-1.

Given:
- Concentration of acetic acid (CH3COOH) = 0.2 mol L^-1
- Distance between electrodes (l) = 6 cm
- Cell constant (κ) = 0.02 cm^-1
- Limiting molar conductance of acetic acid = 390 S cm^2 mol^-1
Using the formula:
- $\Lambda_m = \frac{1000}{C \times l} \times \kappa$
- Substitute the values:
- $\Lambda_m = \frac{1000}{0.2 \times 6} \times 0.02$
- $\Lambda_m = 166.67 , \text{S cm}^2 \text{mol}^-1$

Summary

Molar conductance is a measure of the ability of an electrolyte to conduct electricity.
It depends on factors such as the concentration of the electrolyte and the nature of the electrolyte.
Molar conductance can be calculated using the formula $\Lambda_m = \frac{1000}{C \times l} \times \kappa$.
Molar conductance increases with dilution and can be determined using Kohlrausch’s law.
It is used in various applications, including determining the degree of ionization and solvation number.

References

Brown, T. L., LeMay Jr, H. E., Bursten, B. E., Murphy, C., Woodward, P., & Stoltzfus, M. (2017). Chemistry: The Central Science (14th ed.).
NCERT (2021). Chemistry Part II Textbook for Class XII.

Questions

What is the significance of molar conductance in electrochemistry?

How does molar conductance vary with dilution?

Differentiate between strong electrolytes and weak electrolytes.

Explain Kohlrausch’s law and its applications.

Calculate the molar conductance of a 0.5 mol L^-1 solution of HCl at a distance of 8 cm, given that the cell constant is 0.03 cm^-1.

Slide 21

Q1: What is the significance of molar conductance in electrochemistry?
- A1: Molar conductance helps in characterizing the conductivity of electrolytes, which is crucial in understanding the behavior of electrochemical cells and reactions. It provides information about the degree of ionization, nature (strong or weak), and concentration of the electrolyte, influencing various electrochemical processes.
Q2: How does molar conductance vary with dilution?
- A2: Molar conductance generally increases with dilution. As the concentration decreases, the number of ions available for conduction decreases, but the specific conductance of each ion remains constant. This results in an increase in the molar conductance.
Q3: What is the difference between strong electrolytes and weak electrolytes?
- A3: Strong electrolytes completely dissociate into ions when dissolved, while weak electrolytes only partially dissociate. Strong electrolytes have high molar conductance values, indicating a high degree of ionization, whereas weak electrolytes have lower molar conductance due to partial ionization.

Slide 22

Q4: Explain Kohlrausch’s law and its applications.
- A4: Kohlrausch’s law states that the molar conductance of an electrolyte at infinite dilution is the sum of the individual molar conductances of its constituent ions, each multiplied by their respective molar concentrations. This law helps in determining the molar conductance of weak electrolytes and can be used to calculate dissociation constants and ion mobilities.
Q5: Calculate the molar conductance of a 0.5 mol L^-1 solution of HCl at a distance of 8 cm, given that the cell constant is 0.03 cm^-1.
- A5: Given:
  - Concentration of HCl = 0.5 mol L^-1
  - Distance between electrodes (l) = 8 cm
  - Cell constant (κ) = 0.03 cm^-1
- Using the formula:
  - $\Lambda_m = \frac{1000}{C \times l} \times \kappa$
  - Substitute the values:
  - $\Lambda_m = \frac{1000}{0.5 \times 8} \times 0.03$
  - $\Lambda_m = 75 , \text{S cm}^2 \text{mol}^-1$

Slide 23

Q6: What is the limiting molar conductance?
- A6: The limiting molar conductance is the molar conductance of an electrolyte at infinite dilution. It represents the maximum possible value of molar conductance for that electrolyte. The limiting molar conductance is a characteristic property of the electrolyte and is useful for comparing the degree of ionization of different electrolytes.
Q7: What are the applications of molar conductance in chemistry?
- A7: Molar conductance finds applications in:
  - Determining the degree of ionization and dissociation constants of weak electrolytes.
  - Calculating the solvation number and ionic radii of ions.
  - Understanding the behavior of electrochemical cells and batteries.
  - Studying the conductivity and properties of electrolyte solutions in various processes.

Slide 24

Q8: What is specific conductance?
- A8: Specific conductance, also called conductivity, is the conductance of an electrolyte solution containing a fixed concentration of an electrolyte. It is the reciprocal of resistivity and can be calculated using the formula:
  - Specific conductance ($\kappa$) = $\frac{1}{\text{resistivity}}$
- Specific conductance is measured in units of Siemens per centimeter (S cm^-1).
Q9: How can we determine the molar conductance of a strong electrolyte using Kohlrausch’s law?
- A9: For a strong electrolyte, which completely dissociates into ions, Kohlrausch’s law can be used by considering the individual molar conductances of the constituent ions. The sum of the molar conductances, multiplied by their respective molar concentrations, gives the overall molar conductance of the strong electrolyte at a particular concentration.

Slide 25

Q10: Explain the relationship between molar conductivity and degree of ionization.
- A10: Molar conductivity is directly proportional to the degree of ionization of an electrolyte. Higher the degree of ionization, greater the number of ions available for conduction, leading to a higher molar conductance. Weak electrolytes, with low ionization, exhibit lower molar conductance compared to strong electrolytes.
Q11: Compare the molar conductance values of a strong electrolyte and a weak electrolyte at the same concentration.
- A11: At the same concentration, the molar conductance of a strong electrolyte is higher than that of a weak electrolyte. This is due to the complete dissociation of the strong electrolyte, resulting in more ions available for conduction, whereas the weak electrolyte partially ionizes, leading to lower molar conductance.

Slide 26

Q12: What is the importance of determining the solvation number of ions using molar conductance?
- A12: The solvation number of ions provides information about the number of solvent molecules surrounding an ion. It helps in understanding the nature of ionic solutes and their interaction with the solvent. Molar conductance measurements aid in determining the solvation number and provide insights into the behavior of electrolyte solutions.
Q13: How does the nature of the solvent affect molar conductance measurements?
- A13: The nature of the solvent influences molar conductance measurements by affecting the degree of solvation and ion mobility. Different solvents have varying abilities to solvate ions, leading to differences in their molar conductance values. Polar solvents generally exhibit higher molar conductance compared to nonpolar solvents due to better solvation of ions.

Slide 27

Q14: Why does molar conductance increase with dilution?
- A14: Molar conductance increases with dilution as the concentration of the electrolyte decreases. With lower concentration, the number of ions available for conduction decreases, but the specific conductance of each ion remains constant. Hence, the molar conductance increases due to the decrease in ionic overcrowding and increased distance between ions.
Q15: What are the units of molar conductance?
- A15: Molar conductance is expressed in Siemens per centimeter squared per mole (S cm^2 mol^-1) or, equivalently, Ohm^-1 cm^2 mol^-1.

Slide 28

Q16: Describe the concept of specific conductance and its measurement.
- A16: Specific conductance, also known as conductivity, is the conductance of an electrolyte solution of fixed concentration. It measures the ease with which the solution conducts electricity. Specific conductance is determined by measuring the resistance of the solution using a conductivity cell and applying Ohm’s law. The cell constant and measured resistance are used to calculate specific conductance.
Q17: Explain the effect of temperature on molar conductance.
- A17: Temperature affects the molar conductance of electrolytes. As the temperature increases, the mobility of ions generally increases, resulting in higher molar conductance. However, for some electrolytes, like strong acids, as the temperature increases, the degree of ionization decreases, leading to a decrease in molar conductance.

Slide 29

Q18: Can molar conductance be used to determine the concentration of an unknown electrolyte solution?
- A18: Yes, molar conductance can be used to determine the concentration of an unknown electrolyte solution if the molar conductance at infinite dilution is known. By measuring the molar conductance of the solution and applying Kohlrausch’s law, the concentration of the unknown electrolyte can be calculated.
Q19: Explain the significance of molar conductance in battery technology.
- A19: Molar conductance plays a crucial role in battery technology by providing information on the conductive properties of battery electrolytes. It helps in designing and optimizing battery systems, determining the ionic conductivity of electrolytes, and understanding the behavior and efficiency of different types of batteries.

Slide 30

Q20: Define the cell constant and its role in molar conductance measurements.
- A20: The cell constant is defined as the ratio between the distance between the electrodes (l) and the area of contact between the electrodes (A). It accounts for the geometry and dimensions of the conductivity cell used for measurements. The cell constant is necessary to convert the measured conductance to molar conductance using the formula $\Lambda_m = \frac{1000}{C \times l} \times \kappa$.