Solveeit Logo

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 \text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }. Given that  Al3+ \text{ A}{{\text{l}}^{\text{3+}}}\text{ } and  SO42 \text{ SO}_{4}^{2-}\text{ } are the equivalent conductance at infinite dilution of the respective ions?

A)  Λ Al3+ 0+ Λ SO42 0\text{ }\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ }\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{0}

B) (Λ Al3+ 0+ Λ SO42 0) × 6 \text{ (}\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ }\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{0})\text{ }\times \text{ 6 }

C)  13Λ Al3+ 0+ 12Λ SO42 0\text{ }\frac{1}{3}\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ }\frac{1}{2}\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{0}

D)  2Λ Al3+ 0+ 3Λ SO42 0\text{ 2}\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ 3}\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{0}

Explanation

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 \text{ }\Lambda \text{ }. 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 \text{ }\\!\\!\Lambda\\!\\!\text{ }_{\text{m}}^{\text{0}}\text{ = }\\!\\!\lambda\\!\\!\text{ }_{\text{+}}^{\text{0}}\text{ + }\\!\\!\lambda\\!\\!\text{ }_{-}^{0}\text{ }

Where,  !!Λ!! m0\text{ }\\!\\!\Lambda\\!\\!\text{ }_{\text{m}}^{\text{0}} is equivalent conductance of electrolyte at infinite dilution,  !!λ!! +0\text{ }\\!\\!\lambda\\!\\!\text{ }_{\text{+}}^{\text{0}} and  !!λ!! 0 \text{ }\\!\\!\lambda\\!\\!\text{ }_{-}^{0}\text{ } 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 \text{ 1 }{{\text{m}}^{\text{2}}}\text{ } is known as the equivalent conductance.

Let suppose that  1 m3 \text{ 1 }{{\text{m}}^{3}}\text{ }the volume of solution contains the 1 gram equivalent of the solution then conductance of solution will be equal to equivalent conductance,  Λ \text{ }\Lambda \text{ } .

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 \text{ }\\!\\!\Lambda\\!\\!\text{ }_{\text{m}}^{\text{0}}\text{ = }\\!\\!\lambda\\!\\!\text{ }_{\text{+}}^{\text{0}}\text{ + }\\!\\!\lambda\\!\\!\text{ }_{-}^{0}\text{ }

Where,  !!Λ!! m0\text{ }\\!\\!\Lambda\\!\\!\text{ }_{\text{m}}^{\text{0}} is equivalent conductance of electrolyte at infinite dilution,  !!λ!! +0\text{ }\\!\\!\lambda\\!\\!\text{ }_{\text{+}}^{\text{0}} and  !!λ!! 0 \text{ }\\!\\!\lambda\\!\\!\text{ }_{-}^{0}\text{ }is the conductance of cation and anion.

We have given the  Al2(SO4)3 \text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }electrolyte. It dissociates into its corresponding  Al3+ \text{ A}{{\text{l}}^{\text{3+}}}\text{ } and  SO42 \text{ SO}_{4}^{2-}\text{ } as shown below,

 Al2(SO4)3  2 Al3+ + 3 SO42 \text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }\to \text{ 2 A}{{\text{l}}^{\text{3+}}}\text{ + 3 SO}_{4}^{2-}\text{ }

At infinite dilution, the equivalent conductance  Al2(SO4)3 \text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }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\text{ }\Lambda _{\text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }}^{\infty }=\text{ 2 }\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ 3 }\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{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\text{ }\Lambda _{\text{ A}{{\text{l}}_{\text{2}}}{{\text{(S}{{\text{O}}_{\text{4}}}\text{)}}_{\text{3}}}\text{ }}^{\infty }=\text{ }\Lambda _{\text{ A}{{\text{l}}^{\text{3+}}}\text{ }}^{0}+\text{ }\Lambda _{\text{ SO}_{4}^{2-}\text{ }}^{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 = (1n+ + Z+)×Λm \text{ }{{\Lambda }_{\text{eq}}}\text{ = }\left( \frac{1}{{{\text{n}}^{+}}\text{ + }{{\text{Z}}^{\text{+}}}} \right)\times {{\Lambda }_{\text{m}}}\text{ }

Where, n+{{\text{n}}^{+}} is the number of cations, and Z+{{\text{Z}}^{\text{+}}}is the charge on the cation. Through this relation, the equivalent conductance and the molar conductance of electrolyte can be determined.