Step 1: Understanding the problem.
We are given elements: B, C, N, S, O, F, P, Al, Si and asked for the number of elements that cannot form compounds with valencies matching their respective group valencies.
Step 2: Group Valencies in the periodic table.
- Group 13 elements like B and Al: expected valency is 3.
- Group 14 elements like C and Si: expected valency is 4.
- Group 15 elements like N and P: expected valency is 3 (sometimes 5 for P).
- Group 16 elements like O and S: expected valency is 2 (sometimes 4 or 6 for S).
- Group 17 element F: expected valency is 1.
Step 3: Checking elements and their valency behavior.
- B (Boron): forms compounds with valency 3 (e.g. BF₃). Matches its group valency.
- C (Carbon): forms compounds mostly with valency 4. Matches its group.
- N (Nitrogen): mainly forms compounds with valency 3 (NH₃), occasionally can expand octet to 5.
- S (Sulfur): usually forms compounds with valency 2, 4, or 6. Matches or exceeds group valency.
- O (Oxygen): mostly forms compounds with valency 2 only.
- F (Fluorine): always forms compounds with valency 1 only.
- P (Phosphorus): forms compounds with valency 3 and 5.
- Al (Aluminum): forms compounds with valency 3 only.
- Si (Silicon): forms compounds with valency 4 (matches group).
Step 4: Elements that do NOT match their expected group valencies strictly.
- Oxygen (O): strictly forms compounds with valency 2, even though group 16 suggests possible higher valencies.
- Nitrogen (N): shows valency 3 mostly, but sometimes 5 (expanded octet).
- Fluorine (F): strongly limited to valency 1, no expanded valency.
Thus, elements that cannot form compounds strictly matching expected group valencies are O, N, and F.
Step 5: Final Answer.
The number of elements that cannot form compounds with valencies matching their group valencies is:
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\]