Question

Which of the following statement(s) is/are correct regarding the plot between ${\Lambda }_{m}vs\sqrt{C}$?

${\Lambda }_m$ - Molar conductivity
$C$ - concentration of electrolyte

• A. ${\Lambda }_m$ increase slowly with increase in dilution for strong electrolyte
• B. ${\Lambda }_m$ increase steeply as dilution is increased, for weak electrolyte
• C. The plot curve is a straight line with negative slope for weak electrolyte
• D. Both (a) and (b)

Answer 1

The correct option is D Both (a) and (b)

Variation in ${\Lambda }_m$ for weak electrolyte:
Weak electrolytes like acetic acid have lower degree of dissociation.
With dilution of an ionic solution, the degree of dissociation ($\alpha$) of the electrolyte increases which result in increase in the number of ions in solution. Near lower concentration, there will be a steep increase in molar conductance.

Plot of ${\Lambda }_{m}vs\sqrt{C}$

From above it is evident that curve for ${\Lambda }_{m}vs\sqrt{C}$ for a weak electrolyte (here acetic acid) is rectangular hyperbola. It does not intercept the y-axis.

Variation in ${\Lambda }_m$ for strong electrolyte:
For strong electrolyte ${\Lambda }_m$ increases due to decreased ion- ion force of attraction.

As strong electrolytes are mostly in ionized state, no abrupt change in the number of ions with dilution.

Thus, ${\Lambda }_m$ increases slowly with dilution.

In concentrated solution there will be a strong attraction between ions which slows down the movement of ion.

On dilution of strong electrolyte, distance between the ions increases which results in decrease in ion-ion attraction. So, there will be overall increase in molar conductance of the solution.

Variation in molar conductivity of strong electrolyte due to ion-ion interaction is given by an empirical relation proposed by kohlrausch.

${\Lambda }_m={\Lambda }_m^0-A\sqrt{C}$
${\Lambda }_m$ - Molar conductivity
${\Lambda }_m^0$ - Limiting molar conductivity
$C$ is concentration of electrolyte
$A$ is constant for a given solvent and temperature.

${\Lambda }_m={\Lambda }_m^0-A\sqrt{C}$
This equation is in the form of straight line equation,
$y=c+mx$
$\therefore$
Plot of ${\Lambda }_{m}vs\sqrt{C}$

Intercept : ${\Lambda }_m^0$
Slope : $-A$
Thus, the extrapolation of line gives ${\Lambda }_m^0$ for strong electrolytes.