If pH of a saturated solution of Ba(OH)₂ is 12, the value of its Ksp is

Options

(a) 4.00 ˣ 10⁻⁶ M³
(b) 4.00 ˣ 10⁻⁷ M³
(c) 5.00 ˣ 10⁻⁶ M³
(d) 5.00 ˣ 10⁻⁷ M³

Correct Answer:

5.00 ˣ 10⁻⁷ M³

Explanation:

We Know, pH + pOH = 14,
Here, 12 + pOH = 14,
pOH = 2,
⇒ [OH⁻] = 10⁻².
Ba(OH)₂ ⇌ Ba²⁺ + 2OH⁻.

2s = [OH⁻] = 10⁻².
s = 10⁻²/2 = 5×10⁻³ M.
K(sp) = [Ba²⁺][OH⁻]² = (5×10⁻³)(10⁻²)²,
K(sp) = 5×10⁻⁷.