At `25^(@)C`, the dissociation constant of a base. BOH is `1.0xx10^(-12)`. The concentration of hydroxyl ions in `0.01`M aqueous solution of the base would be

Options

A. (a) `2.0xx10^(-6)mol L^(-1)`
B. (b) `1.0xx10^(-5)mol L^(-1)`
C. (c) `1.0xx10^(-6)mol L^(-1)`
D. (d) `1.0xx10^(-7)mol L^(-1)`

Explanation

To solve the problem, we need to find the concentration of hydroxyl ions (OH⁻) in a 0.01 M solution of the base BOH, given that the dissociation constant (K_b) of BOH is 1.0 x 10^(-12).

### Step-by-Step Solution:

1. **Write the dissociation equation**:
The dissociation of the base BOH can be represented as:
\[ BOH \rightleftharpoons B^+ + OH^- \]

2. **Express the dissociation constant (K_b)**:
The expression for the dissociation constant (K_b) is given by:
\[ K_b = \frac{[B^+][OH^-]}{[BOH]} \]

3. **Define the concentrations at equilibrium**:
Let the concentration of hydroxyl ions (OH⁻) at equilibrium be \( x \). Since the dissociation of BOH produces equal amounts of B⁺ and OH⁻, we have:
\[ [B^+] = x \quad \text{and} \quad [OH^-] = x \]
The initial concentration of BOH is 0.01 M, and at equilibrium, the concentration of BOH will be:
\[ [BOH] = 0.01 - x \approx 0.01 \quad \text{(since x will be very small)} \]

4. **Substitute into the K_b expression**:
Substituting the values into the K_b expression gives:
\[ K_b = \frac{x \cdot x}{0.01} = \frac{x^2}{0.01} \]

5. **Set up the equation**:
We know that \( K_b = 1.0 \times 10^{-12} \). Therefore, we can set up the equation:
\[ 1.0 \times 10^{-12} = \frac{x^2}{0.01} \]

6. **Solve for x²**:
Rearranging the equation gives:
\[ x^2 = 1.0 \times 10^{-12} \times 0.01 = 1.0 \times 10^{-14} \]

7. **Calculate x**:
Taking the square root of both sides, we find:
\[ x = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \]

8. **Conclusion**:
The concentration of hydroxyl ions (OH⁻) in the 0.01 M aqueous solution of the base BOH is:
\[ [OH^-] = 1.0 \times 10^{-7} \, \text{M} \]

### Final Answer:
The concentration of hydroxyl ions in the solution is \( 1.0 \times 10^{-7} \, \text{M} \).