`B_(10)C_(2)H_(12)` is isostructural & isoelectronic with borate ion of formula `B_(x)H_(y)^(2-)` give `x+y

Answer

To solve the problem, we need to determine the values of \( x \) and \( y \) in the borate ion \( B_xH_y^{2-} \) that is isostructural and isoelectronic with the compound \( B_{10}C_2H_{12} \).

### Step-by-Step Solution:

1. **Identify the Total Number of Electrons in \( B_{10}C_2H_{12} \)**:
- Boron (B) has an atomic number of 5, so each boron atom contributes 5 electrons.
- Carbon (C) has an atomic number of 6, so each carbon atom contributes 6 electrons.
- Hydrogen (H) has an atomic number of 1, so each hydrogen atom contributes 1 electron.
- Calculate the total number of electrons:
\[ \text{Total electrons} = (10 \times 5) + (2 \times 6) + (12 \times 1) = 50 + 12 + 12 = 74 \text{ electrons} \]

2. **Determine the Total Number of Electrons in the Borate Ion \( B_xH_y^{2-} \)**:
- The borate ion has a charge of \( 2- \), which means it has 2 extra electrons.
- Therefore, the total number of electrons in \( B_xH_y^{2-} \) can be expressed as:
\[ \text{Total electrons} = (x \times 5) + (y \times 1) + 2 \]
- Set this equal to the total number of electrons from \( B_{10}C_2H_{12} \):
\[ (x \times 5) + (y \times 1) + 2 = 74 \]

3. **Rearranging the Equation**:
- Rearranging gives:
\[ 5x + y = 72 \]

4. **Finding Suitable Values for \( x \) and \( y \)**:
- We know that the borate ion typically has a structure where \( x \) (the number of boron atoms) and \( y \) (the number of hydrogen atoms) are integers.
- To find suitable values, we can try different integers for \( x \) and solve for \( y \):
- If \( x = 12 \):
\[ 5(12) + y = 72 \implies 60 + y = 72 \implies y = 12 \]

5. **Calculating \( x + y \)**:
- Now that we have \( x = 12 \) and \( y = 12 \):
\[ x + y = 12 + 12 = 24 \]

### Final Answer:
Thus, the answer to the question is \( x + y = 24 \).