`BaTi[Si_(3)O_(9)]` is a class of

Options

A. orthosilicateq
B. cyclic silicate
C. chain silicate
D. sheet silicate

Answer

To determine the class of the compound `BaTi[Si_(3)O_(9)]`, we need to analyze its structure and the arrangement of its silicate units. Here’s a step-by-step solution:

### Step 1: Identify the components of the compound
The compound `BaTi[Si_(3)O_(9)]` consists of:
- Barium (Ba)
- Titanium (Ti)
- Silicate units (Si and O)

### Step 2: Determine the oxidation states
- Barium (Ba) has an oxidation state of +2.
- Titanium (Ti) has an oxidation state of +4.

### Step 3: Calculate the overall charge of the silicate unit
Since Ba is +2 and Ti is +4, the total positive charge contributed by these cations is:
\[ +2 (from \, Ba) + +4 (from \, Ti) = +6 \]

To balance this positive charge, the silicate unit must have a total negative charge of -6. Therefore, the silicate unit `Si_(3)O_(9)` must have a charge of -6:
\[ Si_3O_9^{6-} \]

### Step 4: Analyze the silicate structure
The silicate unit `SiO_4` is the basic building block of silicates. In the case of `Si_(3)O_(9)`, we can visualize it as three `SiO_4` tetrahedra. The arrangement of these tetrahedra can lead to different types of silicates:
- Orthosilicates (isolated tetrahedra)
- Cyclic silicates (tetrahedra linked in a ring)
- Chain silicates (tetrahedra linked in a chain)
- Sheet silicates (tetrahedra linked in sheets)

### Step 5: Determine the type of silicate
In the case of `Si_(3)O_(9)`, the structure forms a cyclic arrangement. Each `SiO_4` tetrahedron shares oxygen atoms with adjacent tetrahedra, creating a closed loop or cycle.

### Conclusion
Based on the analysis, the compound `BaTi[Si_(3)O_(9)]` is classified as a **cyclic silicate**.

### Final Answer
**The correct option is B: Cyclic silicate.**

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