We know, pH + pOH = 14
pOH = -log[OH⁻]
11 = -log[OH⁻]
log[OH⁻] = -11
[OH⁻] = 10⁻¹¹ M
For 10⁻⁴ M of solution, volume required is :
10⁻⁴ × 1 = 10⁻¹¹ × V₁
V₁ = 10⁷ units.
Similarly for 10⁻² M :
10⁻² × 1 = 10⁻¹¹ × V₂
V₂ = 10⁹ units.
Therefore, the ratio of volume is 10⁷/10⁹ = 10⁻² units.