Question

Define limiting molar conductivity.

Hint:

Remember the notation: \[ \Lambda_m = \text{Molar Conductivity} \] \[ \Lambda_m^{\circ} = \text{Limiting Molar Conductivity} \] At infinite dilution, ionic interactions become negligible and molar conductivity attains its maximum value.

Answer 1

Concept: Electrical conductivity of an electrolyte solution depends upon the number of ions present and their mobility in the solution. As the solution is diluted, the distance between oppositely charged ions increases and the interionic attractions decrease. Due to reduced interionic interactions, ions move more freely through the solution, resulting in an increase in molar conductivity. The maximum value of molar conductivity is obtained when the electrolyte is diluted to such an extent that the ions become completely independent of one another. This condition is known as infinite dilution.

Step 1: Understanding molar conductivity. Molar conductivity is defined as the conductance of the volume of solution containing one mole of an electrolyte placed between two electrodes separated by a unit distance. It is represented by \[ \Lambda_m \] and is related to conductivity by \[ \Lambda_m=\frac{\kappa \times 1000}{C} \] where \[ \kappa = \text{conductivity of the solution} \] and \[ C = \text{molar concentration of the electrolyte}. \]

Step 2: Understanding infinite dilution. When an electrolyte solution is diluted continuously,

• the ions move farther apart,

• interionic attractions decrease,

• ionic mobility increases,

• molar conductivity increases.
At infinite dilution, the ions become completely independent and no longer influence each other's movement. This condition gives the maximum possible value of molar conductivity.

Step 3: Defining limiting molar conductivity. The molar conductivity obtained at infinite dilution is called the limiting molar conductivity. It is denoted by \[ \Lambda_m^{\circ} \] and is defined as: quote The molar conductivity of an electrolyte at infinite dilution, where interionic interactions become negligible and each ion contributes independently to the conductivity of the solution. quote

Step 4: Importance of limiting molar conductivity. Limiting molar conductivity is useful in:

• Determining the degree of dissociation of weak electrolytes.

• Calculating dissociation constants.

• Applying Kohlrausch's law of independent migration of ions.

• Comparing ionic conductivities of different electrolytes.
Thus, limiting molar conductivity is an important concept in electrochemistry and helps in understanding the behaviour of electrolytes at very low concentrations.

Final Definition: \[ \boxed{ \text{Limiting molar conductivity }(\Lambda_m^{\circ}) \text{ is the molar conductivity of an electrolyte at infinite dilution.} } \] At this stage, interionic interactions are negligible and each ion contributes independently to the conductivity of the solution.