Question

The McCabe $\Delta$L law states that the

• A. molar heat of vaporization of components are nearly equal
• B. linear crystal growth rate depends on the degree of supersaturation
• C. linear crystal growth rate does not depend on the crystal size
• D. linear crystal growth rate depends on the crystal size

Hint:

McCabe $\Delta$L law is essential in crystallization processes, where controlling supersaturation is key to regulating the crystal growth rate.

Answer 1

The Correct Option is B

Step 1: Understanding McCabe $\Delta$L Law.
The McCabe $\Delta$L law primarily applies to crystal growth and describes how the growth rate is influenced by the degree of supersaturation. Supersaturation is a key factor in the formation of crystals, and the growth rate is linear with respect to the degree of supersaturation in most cases. This law is not related to the molar heat of vaporization or crystal size.
Step 2: Conclusion.
The correct answer is (2), as McCabe $\Delta$L law states that the linear crystal growth rate depends on the degree of supersaturation.

Answer 2

The McCabe \(\Delta L\) law is a foundational relationship in crystallization used to describe how a population of crystals grows over time in a well-mixed crystallizer. Let's check each option against what this law actually states.

1. Molar heat of vaporization of components are nearly equal: This statement relates to phase-equilibrium behaviour in distillation, not to crystallization or crystal growth, so it has nothing to do with the \(\Delta L\) law.
2. Linear crystal growth rate depends on the degree of supersaturation: The \(\Delta L\) law describes how the linear growth rate of crystals in a magma is governed by the driving force for crystallization, the degree of supersaturation of the mother liquor; a higher supersaturation drives a faster linear growth rate for the crystal population, which is the essence of this law.
3. Linear crystal growth rate does not depend on the crystal size: While it's true that under McCabe's law all crystals in the same environment tend to grow by the same linear increment regardless of their starting size, the law is fundamentally stated in terms of what governs the growth rate itself, the supersaturation of the surrounding solution, rather than simply describing size-independence.
4. Linear crystal growth rate depends on the crystal size: This would describe a size-dependent growth model, the opposite of the uniform, environment-driven growth assumption underlying the \(\Delta L\) law.

The \(\Delta L\) law ties the linear growth rate of crystals to the supersaturation of the solution they are growing in.

Therefore, the correct answer is linear crystal growth rate depends on the degree of supersaturation.