The Noyes-Whitney equation relates:

Question

BlackTom AI · Accepted Answer

The Noyes–Whitney equation states the dissolution rate of a solid is proportional to its surface area and the concentration gradient across a stagnant diffusion layer: dm/dt = (D · A · (Cs − C)) / h.

1) Relevant knowledge points and concepts
- dm/dt is the dissolution rate (mass per time). 
- A is the particle’s surface area. 
- Cs is the saturation (surface) solubility and C is the bulk solution concentration; (Cs − C) is the driving concentration gradient. 
- D is the diffusion coefficient and h is the diffusion layer thickness.

2) Step‑by‑step reasoning
- Write the equation: dm/dt = D A (Cs − C) / h. 
- Treating D, (Cs − C), and h as constants for a given system, dm/dt is directly proportional to A. That means increasing surface area increases the dissolution rate linearly (all else equal). 
- The (Cs − C) term shows solubility (Cs) influences the driving force for dissolution, but the explicit proportional dependence in the equation that is most frequently emphasized is the dependence on surface area A.

3) Calculations / intermediate steps
- No numeric calculation is required; the algebraic proportionality is sufficient: dm/dt ∝ A (when D, Cs − C, h constant).

4) Why the correct answer is correct
- Option b (“dissolution rate to surface area”) matches the direct proportionality shown in the Noyes–Whitney equation: dissolution rate increases with surface area.

5) Why the other options are incorrect
- a (solubility to dissolution rate): solubility (Cs) appears in the equation as part of the driving force (Cs − C), but the canonical, emphasized relation is rate ∝ surface area; the option’s wording reverses the phrasing and is less accurate as the primary relationship. 
- c (dissolution rate to salt form): salt form can affect Cs indirectly, but it is not an explicit variable in the equation. 
- d (solubility to particle size): particle size affects surface area, not solubility directly; Noyes–Whitney does not relate solubility to particle size.

Conclusion: The correct choice is b. This matches the provided answer: b. dissolution rate to surface area.

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