Question

Which of the following expressions indicates the correct relationship between molar conductivity of strong electrolyte and its concentration?

• A. \(\Lambda = \Lambda _0+\sqrt{c}\)
• B. \(\Lambda = \Lambda _0-a\sqrt{c}\)
• C. \(\Lambda = \Lambda _0+a\sqrt{c}\)
• D. \(\Lambda = \Lambda _0-\sqrt{c}\)

Hint:

Debye-Huckel-Onsager equation: molar conductivity falls linearly with the square root of concentration.

Answer 1

The Correct Option is B

Step 1: Approach
Reason about the physical cause and then match the form.

Step 2: Reasoning
At higher concentration the ions are closer and hold each other back, so each mole conducts less. Hence $\Lambda$ must be smaller than $\Lambda^\circ$, so the correction term is subtracted.

Step 3: Form
The correction grows with the square root of concentration, with a proportionality constant $a$ that depends on the electrolyte type:
\[ \Lambda = \Lambda^\circ - a\sqrt{c} \]
This is option (B). The versions with a plus sign predict rising conductivity with concentration, which is wrong, and the one with no $a$ cannot distinguish between electrolytes.

Final Answer:
The correct relation is $\Lambda=\Lambda_0-a\sqrt{c}$, option (B). \[ \boxed{\Lambda=\Lambda_0-a\sqrt{c}} \]