Question

The condition(s) for high degree of mutual substitutional solid solubility for two metals is/are

• A. metals should have same valence
• B. metals should have same crystal structure
• C. the difference in atomic size of metals should be less than 15%
• D. the difference in electronegativity of metals should be large

Hint:

Remember the Hume-Rothery rules by thinking about what makes it easy for one atom to "fit in" and replace another: they should be about the same size, live in the same type of "house" (crystal structure), have similar chemical "personalities" (valence and electronegativity).

Answer 1

The Correct Option is A, B, C

Step 1: Understanding the Concept:
Substitutional solid solubility refers to the ability of solute atoms to replace solvent atoms in a crystal lattice to form a solid solution. The extent of this solubility is governed by a set of empirical guidelines known as the Hume-Rothery rules. The question asks to identify these conditions.
Step 2: The Hume-Rothery Rules:
For two metals to have a high degree of mutual substitutional solid solubility, they must satisfy the following four conditions:
Atomic Size Factor: The difference in the atomic radii between the solute and solvent atoms must be small, typically less than 15%. A large difference causes significant lattice strain, limiting solubility. Crystal Structure: The solute and solvent metals must have the same crystal structure (e.g., both FCC or both BCC).
Valence: The metals should have the same valence. A metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency.
Electronegativity: The metals should have similar electronegativities. A large difference in electronegativity encourages the formation of stable intermetallic compounds rather than substitutional solid solutions.
Step 3: Evaluating the Options:
- (A) metals should have same valence: Correct. This is one of the Hume-Rothery rules.
- (B) metals should have same crystal structure: Correct. This is also a key Hume-Rothery rule.
- (C) the difference in atomic size of metals should be less than 15%: Correct. This is the atomic size factor rule.
- (D) the difference in electronegativity of metals should be large: Incorrect. The rule states that the electronegativities should be similar, meaning the difference should be small. A large difference favors compound formation.
Step 4: Why This is Correct:
Options (A), (B), and (C) correctly state three of the four Hume-Rothery rules that promote extensive substitutional solid solubility. Option (D) states the opposite of the electronegativity rule.