In the compound `Na_(2)[B_(4)O_(5)(OH)_(4)].8H_(2)O`, it the
(i) number of `B-O-B` bonds is x
(ii) number of `B-B` bonds is y
(iii) number of `sp^(2)` hybridised B atoms is z calculate the value of `x +y + z`.

Answer

To solve the problem, we need to analyze the compound \( \text{Na}_2[\text{B}_4\text{O}_5(\text{OH})_4] \cdot 8\text{H}_2\text{O} \) and determine the values of \( x \), \( y \), and \( z \) as defined in the question.

### Step 1: Determine the structure of the compound
The compound consists of a borate ion \( [\text{B}_4\text{O}_5(\text{OH})_4]^{2-} \). To visualize the structure, we can draw the arrangement of boron (B) and oxygen (O) atoms.

### Step 2: Identify B-O-B bonds (x)
In the structure, we need to count the number of B-O-B bonds. Each boron atom can form bonds with oxygen atoms, and we can look for connections between boron atoms through oxygen atoms.

1. **Count B-O-B bonds**:
- In the structure, we can see that there are 5 B-O-B bonds formed between the boron atoms through the oxygen atoms.

Thus, \( x = 5 \).

### Step 3: Identify B-B bonds (y)
Next, we need to count the number of B-B bonds in the compound.

1. **Count B-B bonds**:
- In the given structure, there are no direct B-B bonds present. All boron atoms are connected through oxygen atoms.

Thus, \( y = 0 \).

### Step 4: Identify sp² hybridized B atoms (z)
Now, we need to determine how many boron atoms are sp² hybridized.

1. **Identify sp² hybridized B atoms**:
- In the structure, two boron atoms are bonded to three other atoms (two OH groups and one oxygen), which indicates sp² hybridization.
- The other two boron atoms are connected to four atoms (one B and three O), indicating sp³ hybridization.

Thus, \( z = 2 \) (the two boron atoms that are sp² hybridized).

### Step 5: Calculate \( x + y + z \)
Now, we can sum up the values of \( x \), \( y \), and \( z \):

\[ x + y + z = 5 + 0 + 2 = 7 \]

### Final Answer
The value of \( x + y + z \) is **7**.

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