Question

What is molar conductivity at zero concentration in $\Omega^{-1}$ cm$^2$ mol$^{-1}$ for aluminium sulphate, if molar ionic conductivities at zero concentration of Al$^{3+}$ and SO$_4^{2-}$ are 189 $\Omega^{-1}$ cm$^2$ mol$^{-1}$ and 50.1 $\Omega^{-1}$ cm$^2$ mol$^{-1}$ respectively?

• A. 239.1
• B. 428.1
• C. 478.2
• D. 528.3

Hint:

Always write out the proper chemical formula of the salt first! A common mistake is simply adding the two ionic conductivities together without accounting for the stoichiometric multipliers (2 and 3 in this case).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Kohlrausch’s Law of Independent Migration of Ions states that the total molar conductivity of an electrolyte is the sum of the individual contributions of its ions.

Step 2: Formula Application:
For $Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-}$. $\Lambda_m^0 = 2 \times \lambda^0(Al^{3+}) + 3 \times \lambda^0(SO_4^{2-})$.

Step 3: Explanation:
$\Lambda_m^0 = 2 \times (189) + 3 \times (50.1)$ $\Lambda_m^0 = 378 + 150.3 = 528.3$ $\Omega^{-1}$ cm$^2$ mol$^{-1}$.

Step 4: Final Answer:
The molar conductivity at zero concentration is 528.3.