Solid–liquid extraction (leaching) rate control: In practical leaching of a solid particle by a solvent, which step most commonly limits the overall rate of extraction?

Introduction / Context:
Leaching or solid–liquid extraction removes a soluble constituent from a solid matrix into a contacting solvent. Understanding the controlling resistance—internal diffusion within the particle or external film diffusion—guides particle-size selection, agitation, and equipment design.

Given Data / Assumptions:

• Porous solid containing a soluble solute.
• Isothermal operation; solvent does not chemically react with the matrix.
• Well-agitated slurry such that external films can be minimized.

Concept / Approach:
Overall extraction rate often depends on the slowest step. In many practical systems with adequate agitation, dissolution at the surface is rapid and external mass-transfer resistance is relatively small, leaving internal diffusion through solvent-filled pores as the controlling mechanism. This is particularly true for larger particles or tortuous pore networks.

Step-by-Step Solution:
Identify candidate resistances: interfacial dissolution, internal diffusion, external diffusion.Assess typical magnitudes: interfacial dissolution is fast; agitation reduces external film thickness.Internal diffusion depends on pore tortuosity and path length and is often rate-limiting.Therefore, select internal diffusion (option b) as the common controlling step.

Verification / Alternative check:
Shrinking-core/ash-layer models predict linear-to-parabolic kinetics when diffusion through the product/porous layer controls, aligning with many experimental leaching curves.

Why Other Options Are Wrong:
(a) Interfacial phase change/dissolution is seldom controlling for soluble solids in good solvents.

(c) External diffusion can dominate only at low agitation or very viscous slurries; it is not the general case.

(d) 'All' overstates the contribution of interfacial phase change in typical leaching.

Common Pitfalls:

• Ignoring the impact of particle size: reducing size shortens diffusion paths and accelerates extraction.
• Overlooking clogging or swelling that can alter internal diffusivity during operation.

Final Answer:
Diffusion of solute through solvent-filled pores to the outside of the particle (internal diffusion)