Fick’s law of dissolution vs Noyes Whitney equation
The Correct Answer and Explanation is:
Correct Answer:
Fick’s Law of Diffusion is the fundamental principle underlying the Noyes-Whitney equation, which specifically describes the rate of dissolution of solids in liquids.
Explanation
Fick’s Law of Diffusion and the Noyes-Whitney equation are closely related, but they serve different purposes in understanding solute transport and dissolution processes.
Fick’s First Law of diffusion states that the rate of diffusion (flux) of a substance across a unit area is proportional to the concentration gradient: J=−DdCdxJ = -D \frac{dC}{dx}
Where:
- JJ = diffusion flux
- DD = diffusion coefficient
- dC/dxdC/dx = concentration gradient
Fick’s law is a general law that applies to the movement of molecules in a medium due to concentration differences. It doesn’t account for the solid state of the solute or the interfacial area.
On the other hand, the Noyes-Whitney equation is derived from Fick’s law and specifically models the dissolution rate of a solid substance into a solvent: dCdt=DA(Cs−C)h\frac{dC}{dt} = \frac{DA (C_s – C)}{h}
Where:
- dCdt\frac{dC}{dt} = dissolution rate
- DD = diffusion coefficient
- AA = surface area of the dissolving solid
- CsC_s = saturation solubility of the solute
- CC = concentration of solute at time tt
- hh = thickness of the diffusion layer
This equation applies Fick’s principle to a solid-liquid interface, describing how a solute dissolves over time depending on surface area, solubility, and diffusion dynamics. The key assumption is that dissolution is diffusion-controlled — meaning the rate-limiting step is diffusion through a boundary layer.
In summary, Fick’s law provides the theoretical framework for diffusion, while the Noyes-Whitney equation is a practical application of this theory to the pharmaceutical and chemical industries to predict dissolution rates of tablets and other solid dosage forms.
