Molar Conductance at Infinite Dilution

Molar conductance at infinite dilution is a measure of the conductivity of a substance when it is completely separated into its constituent ions in a solution of infinite dilution. It is denoted by the symbol Λ° and is expressed in units of ohm-1m2mol-1.

The molar conductance at infinite dilution can be calculated using the formula:

Λ° = κ / c

Where Λ° is the molar conductance at infinite dilution, κ is the specific conductance of the solution, and c is the concentration of the solution.

Given Data:
Molar conductance at infinite dilution for BaCl2 = 280 ohm-1m2mol-1
Molar conductance at infinite dilution for KCl = 150 ohm-1m2mol-1
Molar conductance at infinite dilution for K2SO4 = 300 ohm-1m2mol-1
Molar conductance at infinite dilution for Cl- = 76 ohm-1m2mol-1

Transport Number of Ba2+ in BaSO4 Solution

The transport number of an ion in a solution represents the fraction of the total current carried by that ion. It can be calculated using the formula:

Transport number (tn) = Λ° / Λ°t

Where Λ° is the molar conductance at infinite dilution of the ion and Λ°t is the molar conductance at infinite dilution of the total electrolyte.

In the case of BaSO4, it dissociates into Ba2+ and SO4 2- ions. The molar conductance at infinite dilution of BaSO4 can be calculated by subtracting the molar conductance at infinite dilution of K2SO4 (as it contains the SO4 2- ion) from the sum of the molar conductance at infinite dilution of BaCl2 and KCl (as they contain the Ba2+ and Cl- ions respectively).

Λ°BaSO4 = (Λ°BaCl2 + Λ°KCl) - Λ°K2SO4

Substituting the given values:

Λ°BaSO4 = (280 + 150) - 300
Λ°BaSO4 = 130 ohm-1m2mol-1

Now, we can calculate the transport number of Ba2+ in BaSO4 solution:

tn = Λ°Ba2+ / Λ°BaSO4

Substituting the values:

tn = 280 / 130
tn ≈ 2.154

However, the transport number should be a fractional value between 0 and 1. Therefore, we need to divide the transport number by the sum of the transport numbers of both ions (Ba2+ and SO4 2-) to obtain the desired transport number of Ba2+ in the BaSO4 solution.

Transport number of Ba2+ = tn / (tn + ts)

Where tn is the transport number of Ba2+ and ts is the transport number of SO4 2-.

Substituting the values:

Transport number of Ba2+ = 2.154 / (2.154 + 1)
Transport number of Ba2+ ≈