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: Understanding the Concept
For a strong electrolyte, the molar conductivity increases slightly as the solution is diluted, because ion-ion attractions weaken.

Step 2: Key Formula or Approach
Debye-Huckel-Onsager (Kohlrausch) equation:
\[ \Lambda=\Lambda^\circ-a\sqrt{c} \]
Here \(\Lambda^\circ\) is the limiting molar conductivity, \(c\) is the concentration and \(a\) is a constant that depends on the solvent, temperature and type of electrolyte.

Step 3: Check the options
Options (A) and (C) have a plus sign, which would make conductivity rise with concentration. This is the opposite of what is seen. Option (D) is missing the constant \(a\), which carries the dependence on the type of electrolyte. Option (B) has the minus sign and the constant, so it is correct.

Step 4: Graph meaning
A plot of \(\Lambda\) against \(\sqrt c\) is a straight line with intercept \(\Lambda^\circ\) and slope \(-a\).

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