Electrochemistry - More Details On Plot Of Molar Conductance

Electrochemistry - More details on Plot of Molar Conductance

Molar conductance depends on the concentration of electrolyte
Plot of molar conductance vs. square root of concentration is called Kohlrausch’s law plot
Kohlrausch’s law plot helps to determine limiting molar conductance and dissociation constant of the electrolyte
It is a graphical representation of the molar conductance data
The plot is linear for strong electrolytes, but deviates for weak electrolytes

Kohlrausch’s Law Plot

Kohlrausch’s law states that molar conductance of an electrolyte at infinite dilution is the sum of the molar conductances of its cation and anion in the same solvent
The plot of molar conductance vs. square root of concentration follows the equation: Λm = Λm° - K√c
Λm is the molar conductance at a given concentration c
Λm° is the limiting molar conductance at infinite dilution
K is the Kohlrausch’s constant, which depends on the strength of the electrolyte

Interpretation of Kohlrausch’s Law Plot

Strong electrolytes: The plot is linear, and the slope represents the limiting molar conductance at infinite dilution
Weak electrolytes: The plot deviates from linearity, indicating incomplete dissociation
Degree of dissociation (α) can be calculated from the intercept of the line on the y-axis
Strong electrolytes have higher α values, while weak electrolytes have lower α values

Calculation of Limiting Molar Conductance

The intercept of the Kohlrausch’s law plot on the y-axis gives the limiting molar conductance at infinite dilution (Λm°)
Limiting molar conductance is a measure of the conductance of fully dissociated ions in a solution
It can be used to compare the conducting power of different electrolytes
Limiting molar conductance is a property of the electrolyte and independent of concentration

Calculation of Degree of Dissociation

The intercept of the Kohlrausch’s law plot on the y-axis corresponds to zero concentration, where Λm becomes Λm° (limiting molar conductance)
Using the equation Λm = Λm° - K√c, we can substitute Λm = Λm° at zero concentration (Λm = Λm° - K√0)
Simplifying the equation, we find Λm° = Λm + K√0 = Λm
Hence, the degree of dissociation (α) can be calculated using the formula α = Λm/Λm°

Limitations of Kohlrausch’s Law Plot

The Kohlrausch’s law plot method assumes that the electrolyte is a true binary electrolyte, consisting of only one cation and one anion
In reality, many electrolytes contain more complex ions or multiple cations or anions
The method is less accurate for concentrated solutions due to ion-pairing and solvation effects

Example 1

Given the molar conductance values at various concentrations for an unknown electrolyte: | Concentration (c in mol/L) | Molar Conductance (Λm in S cm² mol⁻¹) | ||–| | 0.001 | 100 | | 0.002 | 150 | | 0.003 | 180 | | 0.004 | 200 |
Calculate the limiting molar conductance at infinite dilution (Λm°) and the Kohlrausch’s constant (K)

Example 1 - Solution

Using the Kohlrausch’s law plot equation Λm = Λm° - K√c, we can rearrange it as Λm + K√c = Λm°
Comparing the equation with the given values, we have the following equations:
- at c = 0.001: 100 + K√0.001 = Λm°
- at c = 0.002: 150 + K√0.002 = Λm°
- at c = 0.003: 180 + K√0.003 = Λm°
- at c = 0.004: 200 + K√0.004 = Λm°
We have four equations with four variables (K, Λm°), which can be solved simultaneously to obtain their values

Example 1 - Solution (continued)

Solving the set of equations, we find:
- Λm° = 200 S cm² mol⁻¹
- K = 20 S cm² mol⁻¹/2
The limiting molar conductance at infinite dilution (Λm°) is 200 S cm² mol⁻¹
The Kohlrausch’s constant (K) is 20 S cm² mol⁻¹/2

Properties Deduced from Kohlrausch’s Law Plot

Strong electrolytes have a linear plot with a high limiting molar conductance at infinite dilution (Λm°)
Weak electrolytes deviate from linearity, indicating incomplete dissociation and lower limiting molar conductance
Degree of dissociation (α) can be calculated from the intercept of the plot on the y-axis
Limiting molar conductance is independent of concentration and represents the conductance of fully separated ions at infinite dilution
Kohlrausch’s law plot provides valuable information about the conducting power and dissociation behavior of electrolytes.

Electrolytic Conduction

Electrolytic conduction is the process of conducting electricity through a solution containing ions
It occurs due to the movement of ions towards oppositely charged electrodes
Positive ions (cations) move towards the cathode (negative electrode), while negative ions (anions) move towards the anode (positive electrode)
The movement of ions creates an electric current in the solution

Factors Affecting Electrolytic Conduction

Concentration of electrolyte: Higher concentration leads to increased conductance due to more ions present
Nature of electrolyte: Strong electrolytes with higher dissociation conduct better than weak electrolytes
Temperature: Increased temperature leads to increased mobility and higher conductance
Surface area of electrodes: Larger surface area provides more contact area for ions, enhancing conductance
Distance between electrodes: Shorter distance reduces resistance and increases conductance

Specific Conductance and Resistance

Specific conductance (κ) is the conductance of a solution of unit volume and unit electrode area
It is defined as the reciprocal of resistance (R) in ohms: κ = 1/R
Specific conductance depends on the nature and concentration of the electrolyte, temperature, and electrode area
Specific conductance is a measure of the conducting power of a solution

Equivalent Conductance

Equivalent conductance (Λ) is the conductance of all the ions produced by one mole of an electrolyte in a solution
It is expressed in siemens per centimeter per mole (S cm² mol⁻¹)
Equivalent conductance depends on the concentration of the electrolyte, temperature, and electrode area
It is a measure of the conducting power of a solution containing one equivalent of the electrolyte

Relationship between Specific and Equivalent Conductance

Specific conductance (κ) is related to equivalent conductance (Λ) by the formula: κ = Λ/C
C is the concentration of the electrolyte in moles per liter (mol/L)
The relationship allows us to calculate the equivalent conductance of an electrolyte at any concentration by measuring its specific conductance

Calculation of Equivalent Conductance

The equivalent conductance (Λ) of an electrolyte is given by the formula: Λ = κ/C
κ is the specific conductance of the electrolyte in siemens per centimeter (S cm⁻¹)
C is the concentration of the electrolyte in moles per liter (mol/L)
The equivalent conductance depends on the concentration of the electrolyte and can be determined experimentally

Example 2

Calculate the equivalent conductance of a 0.01 M solution of HCl, given that its specific conductance is 0.01 S cm⁻¹

Example 2 - Solution

Using the formula Λ = κ/C, we can substitute the given values:
- Λ = 0.01 S cm⁻¹ / 0.01 mol/L = 1 S cm² mol⁻¹
The equivalent conductance of the 0.01 M HCl solution is 1 S cm² mol⁻¹

Applications of Conductance Measurements

Determination of the degree of dissociation (α) of weak electrolytes
Calculation of the solubility product (Ksp) of sparingly soluble salts
Quantification of the strength of electrolytes using the dissociation constant (K)
Monitoring of reactions and conductivity changes during chemical processes
Analysis of the purity and composition of solutions and electrolytes

Summary

Electrolytic conduction is the process of conducting electricity through a solution containing ions
Specific conductance (κ) and equivalent conductance (Λ) are measures of the conducting power of a solution
Specific conductance is the reciprocal of resistance, while equivalent conductance is the conductance of all the ions produced by one mole of an electrolyte
The relationship between specific and equivalent conductance allows for the calculation of equivalent conductance at different concentrations
Conductance measurements have various applications in determining degree of dissociation, solubility product, electrolyte strength, and monitoring reactions.

Slide 21

The Kohlrausch’s law plot provides valuable information about the conducting power and dissociation behavior of electrolytes.
Strong electrolytes have a linear plot, indicating complete dissociation.
Weak electrolytes deviate from linearity, indicating incomplete dissociation.
Degree of dissociation (α) can be calculated from the intercept of the plot on the y-axis.
Limiting molar conductance is independent of concentration and represents the conductance of fully separated ions.

Slide 22

Limiting molar conductance (Λm°) is a measure of the conductance of fully dissociated ions in a solution.
It can be used to compare the conducting power of different electrolytes.
Limiting molar conductance is independent of concentration and remains constant at infinite dilution.
Strong electrolytes have higher limiting molar conductance values.
Weak electrolytes have lower limiting molar conductance values.

Slide 23

Degree of dissociation (α) is a measure of the extent of dissociation of an electrolyte in a solution.
It can be calculated from the intercept of the Kohlrausch’s law plot on the y-axis.
Degree of dissociation ranges from 0 (no dissociation) to 1 (complete dissociation).
Strong electrolytes have higher degree of dissociation values.
Weak electrolytes have lower degree of dissociation values.

Slide 24

The Kohlrausch’s law plot method assumes that the electrolyte is a true binary electrolyte, consisting of only one cation and one anion.
In reality, many electrolytes contain more complex ions or multiple cations or anions.
The method is less accurate for concentrated solutions due to ion-pairing and solvation effects.
For accurate results, careful selection of the solvent and appropriate dilution is necessary.
Despite these limitations, Kohlrausch’s law plot remains a useful tool for studying electrolytes.

Slide 25

Electrolytic conduction is the process of conducting electricity through a solution containing ions.
Positive ions (cations) move towards the cathode (negative electrode).
Negative ions (anions) move towards the anode (positive electrode).
The movement of ions creates an electric current in the solution.
Electrolytic conduction is essential in various electrochemical processes and applications.

Slide 26

Factors affecting electrolytic conduction include the concentration of the electrolyte, nature of the electrolyte, temperature, surface area of electrodes, and distance between electrodes.
Higher concentration of electrolyte leads to increased conductance due to more ions present.
Strong electrolytes with higher dissociation conduct better than weak electrolytes.
Increased temperature leads to increased mobility and higher conductance.
Larger surface area of electrodes provides more contact area for ions, enhancing conductance.
Shorter distance between electrodes reduces resistance and increases conductance.

Slide 27

Specific conductance (κ) is the conductance of a solution of unit volume and unit electrode area.
It is defined as the reciprocal of resistance (R) in ohms: κ = 1/R.
Specific conductance depends on the nature and concentration of the electrolyte, temperature, and electrode area.
Specific conductance is a measure of the conducting power of a solution.
It can be measured experimentally using conductance meters.

Slide 28

Equivalent conductance (Λ) is the conductance of all the ions produced by one mole of an electrolyte in a solution.
It is expressed in siemens per centimeter per mole (S cm² mol⁻¹).
Equivalent conductance depends on the concentration of the electrolyte, temperature, and electrode area.
It is a measure of the conducting power of a solution containing one equivalent of the electrolyte.
Equivalent conductance can be calculated using specific conductance and concentration.

Slide 29

The relationship between specific conductance (κ) and equivalent conductance (Λ) can be expressed as: κ = Λ/C.
C is the concentration of the electrolyte in moles per liter (mol/L).
The relationship allows us to calculate the equivalent conductance of an electrolyte at any concentration by measuring its specific conductance.
It provides a convenient way to compare the conducting power of different electrolytes.
The relationship holds true at a given temperature and electrode area.

Slide 30

Conductance measurements have various applications in determining the degree of dissociation of weak electrolytes, calculating the solubility product of sparingly soluble salts, quantifying the strength of electrolytes using the dissociation constant, monitoring reactions and conductivity changes, and analyzing the purity and composition of solutions and electrolytes.
The study of conductance is fundamental to understanding the behavior of electrolytes and their applications in various fields.