Consider the following silicates
(a) `BaTi(Si_(3)O_(9))`
(b) `ZnCa_(2)Si_(2)O_(7)`
Then calculate X+Y, where X and Y are total number of monovalent and divalent oxygen atoms in both silicates respectively.

Answer

To solve the problem, we need to determine the total number of monovalent (X) and divalent (Y) oxygen atoms in the given silicates, `BaTi(Si₃O₉)` and `ZnCa₂Si₂O₇`.

### Step 1: Analyze the first silicate `BaTi(Si₃O₉)`

1. **Identify the oxidation states**:
- Barium (Ba) has an oxidation state of +2.
- Titanium (Ti) has an oxidation state of +4.
- The total positive charge from Ba and Ti is +2 + +4 = +6.

2. **Determine the charge of the silicate**:
- To balance the +6 charge, the silicate must have a charge of -6.
- The formula indicates that there are 3 silicon (Si) atoms and 9 oxygen (O) atoms.

3. **Identify the types of oxygen**:
- In the structure of `Si₃O₉`, there are 3 oxygen atoms that are part of the cyclic structure (divalent).
- The remaining 6 oxygen atoms are attached to silicon (monovalent).

4. **Count the oxygen atoms**:
- Monovalent oxygen atoms (X) = 6
- Divalent oxygen atoms (Y) = 3

### Step 2: Analyze the second silicate `ZnCa₂Si₂O₇`

1. **Identify the oxidation states**:
- Zinc (Zn) has an oxidation state of +2.
- Calcium (Ca) has an oxidation state of +2, and since there are 2 calcium atoms, the total charge from calcium is +4.
- The total positive charge from Zn and Ca is +2 + +4 = +6.

2. **Determine the charge of the silicate**:
- To balance the +6 charge, the silicate must have a charge of -6.
- The formula indicates that there are 2 silicon (Si) atoms and 7 oxygen (O) atoms.

3. **Identify the types of oxygen**:
- In `Si₂O₇`, there is 1 oxygen atom that is shared between the two silicon atoms (divalent).
- The remaining 6 oxygen atoms are attached to silicon (monovalent).

4. **Count the oxygen atoms**:
- Monovalent oxygen atoms (X) = 6
- Divalent oxygen atoms (Y) = 1

### Step 3: Calculate X + Y

1. **Sum the total monovalent oxygen atoms (X)**:
- From the first silicate: 6
- From the second silicate: 6
- Total X = 6 + 6 = 12

2. **Sum the total divalent oxygen atoms (Y)**:
- From the first silicate: 3
- From the second silicate: 1
- Total Y = 3 + 1 = 4

3. **Calculate X + Y**:
- X + Y = 12 + 4 = 16

### Final Answer:
The value of X + Y is **16**.

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