Which of the following statement is correct about the cyclic silicate `[Si_(6)O_(18)]^(n-)`?

Options

A. the value of n is 12
B. each Si atom is bonded with three oxygen atoms
C. each oxygen atom is bonded with two Si atoms
D. All of these

Explanation

To solve the question regarding the cyclic silicate \([Si_6O_{18}]^{n-}\), we will analyze the statements provided and determine which one is correct.

### Step-by-Step Solution:

1. **Understanding the General Formula**:
The cyclic silicate is represented as \([Si_6O_{18}]^{n-}\). This indicates that there are 6 silicon (Si) atoms and 18 oxygen (O) atoms in the structure.

2. **Determining the Charge**:
- Silicon typically has a valency of +4 (it can form four bonds).
- Oxygen has a valency of -2 (it can form two bonds).
- Therefore, the total positive charge contributed by silicon is \(6 \times +4 = +24\).
- The total negative charge contributed by oxygen is \(18 \times -2 = -36\).

3. **Calculating the Overall Charge**:
The overall charge of the silicate can be calculated as:
\[ +24 + (-36) = -12 \]
This means that \(n = 12\), hence the charge of the cyclic silicate is \(-12\).

4. **Analyzing the Statements**:
- **Statement A**: Claims that the value of \(n\) is 12. This is correct based on our calculation.
- **Statement B**: Claims that each silicon atom is bonded to 3 other oxygen atoms. This is incorrect because each silicon atom is actually bonded to 4 oxygen atoms in a cyclic structure.
- **Statement C**: Claims that each oxygen atom is bonded to 2 silicon atoms. This is also incorrect because terminal oxygen atoms are bonded to only one silicon atom, while the bridging oxygen atoms can bond to two.

5. **Conclusion**:
Based on the analysis, the correct statement about the cyclic silicate \([Si_6O_{18}]^{n-}\) is that \(n = 12\).

### Final Answer:
The correct statement about the cyclic silicate \([Si_6O_{18}]^{n-}\) is that \(n = 12\) (Statement A).