Question
Question: Which of the following expressions correctly represents the equivalent conductance at infinite dilut...
Which of the following expressions correctly represents the equivalent conductance at infinite dilution of Al2(SO4)3 . Given that Al3+ and SO42− are the equivalent conductance at infinite dilution of the respective ions?
A) Λ Al3+ 0+ Λ SO42− 0
B) (Λ Al3+ 0+ Λ SO42− 0) × 6
C) 31Λ Al3+ 0+ 21Λ SO42− 0
D) 2Λ Al3+ 0+ 3Λ SO42− 0
Solution
The conductance of a solution which contains the one equivalent weight of electrolyte is known as the equivalent conductance. It is denoted by the Λ . At infinite dilution the conductance of the electrolyte is equal to the sum of the conductance of the ions (cation and anions) in the solution. !!Λ!! m0 = !!λ!! +0 + !!λ!! −0
Where, !!Λ!! m0 is equivalent conductance of electrolyte at infinite dilution, !!λ!! +0 and !!λ!! −0 is the conductance of cation and anion.
Complete step by step answer:
The electricity passes through the solution of electrolytes due to the migration of ions when the potential difference is applied between the two electrodes.
The ease of a solution to conduct electricity is known as the conductance of the solution.
The conductance of the volume of a solution that contains the one equivalent weight of an electrolyte which is placed between the electrodes 1 meter apart and has a cross-sectional area equal to 1 m2 is known as the equivalent conductance.
Let suppose that 1 m3 the volume of solution contains the 1 gram equivalent of the solution then conductance of solution will be equal to equivalent conductance, Λ .
At infinite dilution, when electrolyte undergoes complete dissociation, each ion makes a definite contribution towards the equivalent conductance or towards the molar conductance of electrolyte irrespective of the nature of the other ion.
The conductance of a solution of an electrolyte is given by the sum of the contributions of the two ions. For example, let an electrolyte’ then conductance at the infinite dilution is:
!!Λ!! m0 = !!λ!! +0 + !!λ!! −0
Where, !!Λ!! m0 is equivalent conductance of electrolyte at infinite dilution, !!λ!! +0 and !!λ!! −0 is the conductance of cation and anion.
We have given the Al2(SO4)3 electrolyte. It dissociates into its corresponding Al3+ and SO42− as shown below,
Al2(SO4)3 → 2 Al3+ + 3 SO42−
At infinite dilution, the equivalent conductance Al2(SO4)3 would be equal to the conductance of ions in the solution. It is given as follows,
Λ Al2(SO4)3 ∞= 2 Λ Al3+ 0+ 3 Λ SO42− 0
Since we know that the equivalent conductance is given only concerning ions of the solution (irrespective of the number of ions) thus equivalent conductance at infinite dilution is as:
Λ Al2(SO4)3 ∞= Λ Al3+ 0+ Λ SO42− 0
So, the correct answer is “Option A”.
Note: The conductivity per unit concentration is expressed as equivalent conductance or molar conductance. The relation between the equivalent conductance and the molar conductance is as shown below,
Λeq = (n+ + Z+1)×Λm
Where, n+ is the number of cations, and Z+is the charge on the cation. Through this relation, the equivalent conductance and the molar conductance of electrolyte can be determined.