CSIR-NET/GATE/SLET
According to the Debye-Hückel Limiting Law, the mean activity coefficient ($\gamma_{\pm}$) of an electrolyte is related to the ionic strength ($I$) of the solution by which of the following expressions (at 25°C in water)?
- (A) $\log \gamma_{\pm} = -0.509 |z_+ z_-| \sqrt{I}$
- (B) $\log \gamma_{\pm} = -0.509 |z_+ z_-| I$
- (C) $\log \gamma_{\pm} = 0.509 |z_+ z_-| \sqrt{I}$
- (D) $\log \gamma_{\pm} = -0.509 |z_+ z_-| I^2$
Correct Answer: (A) $\log \gamma_{\pm} = -0.509 |z_+ z_-| \sqrt{I}$
Explanation:
The Debye-Hückel Limiting Law describes how the activity coefficient of an electrolyte decreases as the ionic strength of the solution increases.
Key Components:
- $z_+, z_-$: The charges of the cation and anion.
- $I$: The Ionic Strength, calculated as $I = \frac{1}{2} \sum c_i z_i^2$.
- 0.509: A constant for aqueous solutions at 25°C.
The law is a "limiting" law because it is only accurate for very dilute solutions (typically less than 0.01 M). As concentration increases, the interactions become too complex for this simple linear relationship between $\log \gamma_{\pm}$ and $\sqrt{I}$.