Sum of the number of oxygen shared in between two silicon atoms in `Si_(3)O_(9)^(6-)` and `Si_(3)O_(10)^(8-)` is:

Answer

To solve the problem of finding the sum of the number of oxygen atoms shared between two silicon atoms in \( \text{Si}_3\text{O}_9^{6-} \) and \( \text{Si}_3\text{O}_{10}^{8-} \), we can follow these steps:

### Step 1: Analyze the structure of \( \text{Si}_3\text{O}_{10}^{8-} \)

1. **Identify the number of silicon and oxygen atoms**: In \( \text{Si}_3\text{O}_{10}^{8-} \), there are 3 silicon (Si) atoms and 10 oxygen (O) atoms.
2. **Determine the connectivity**: The structure is a two-dimensional silicate. Each silicon atom can share oxygen atoms with neighboring silicon atoms.
3. **Count the shared oxygen atoms**: When drawing the structure, we can see that there are 3 oxygen atoms shared between the silicon atoms.

### Step 2: Analyze the structure of \( \text{Si}_3\text{O}_9^{6-} \)

1. **Identify the number of silicon and oxygen atoms**: In \( \text{Si}_3\text{O}_9^{6-} \), there are 3 silicon atoms and 9 oxygen atoms.
2. **Determine the connectivity**: This structure is a three-dimensional cyclic silicate.
3. **Count the shared oxygen atoms**: In this structure, we can see that there are 2 oxygen atoms shared between the silicon atoms.

### Step 3: Calculate the total number of shared oxygen atoms

1. **Add the shared oxygen atoms from both structures**:
- From \( \text{Si}_3\text{O}_{10}^{8-} \): 3 oxygen atoms shared.
- From \( \text{Si}_3\text{O}_9^{6-} \): 2 oxygen atoms shared.

Therefore, the total number of shared oxygen atoms is:
\[ 3 + 2 = 5 \]

### Final Answer

The sum of the number of oxygen atoms shared between two silicon atoms in \( \text{Si}_3\text{O}_9^{6-} \) and \( \text{Si}_3\text{O}_{10}^{8-} \) is **5**.

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