Lyophobic colloids are unstable in nature but can be stabilized by specific mechanisms. The key reasons for their stability are:

Step 1: Understanding Lyophobic Colloids
Lyophobic colloids (e.g., gold sol, arsenic sulphide sol) have no affinity for the dispersion medium. They are inherently unstable and tend to coagulate easily unless stabilized.

Step 2: Primary Stabilization Mechanism - Electrical Double Layer
The main reason for stability is the presence of an electrical double layer. Colloidal particles preferentially adsorb ions from the solution onto their surface. This creates a fixed layer of ions (e.g., negative ions adsorbed on a particle, making it negatively charged). Around this fixed layer, a diffused layer of opposite charges (counter-ions) forms due to electrostatic attraction. The potential difference between these two layers (known as zeta potential) prevents particles from coming close and coagulating.

Mathematically, the stability is due to the repulsive forces from the double layer. The zeta potential $\zeta$ is given by:
$\zeta =\frac{4}{\pi ϵ}\sigma \delta$
where $\sigma$ is the charge density, $ϵ$ is the dielectric constant, and $\delta$ is the thickness of the diffused layer.

Step 3: Evaluating the Options
- Preferential adsorption of solvent: This is for lyophilic colloids, not lyophobic. Lyophobic colloids have no such adsorption.
- Attraction between opposite charges: This would cause coagulation, not stability.
- Preferential adsorption of ions: Correct. This creates the charge on particles.
- Potential difference between fixed and diffused layers: Correct. This zeta potential provides repulsive force.

Final Answer: The correct reasons are preferential adsorption of ions on their surface and the potential difference between the fixed and diffused layers.

Related Topics and Formulae

Electrical Double Layer Theory:
When a colloidal particle adsorbs ions, it becomes charged. The fixed layer (Stern layer) is strongly attached, while the diffused layer is mobile. The zeta potential is the potential at the slipping plane between these layers.

Formula for Zeta Potential:
$\zeta =\frac{4\pi \eta u}{E}$
where $\eta$ is viscosity, $u$ is electrophoretic mobility, and $E$ is electric field strength.

Lyophilic vs. Lyophobic:
Lyophilic colloids are stabilized by solvent adsorption (solvation), while lyophobic colloids rely on electrical charge.