Question

The exact concentration of H+ ion in 10-3 molar HCI
aq. solution at 298 K ​

Answer 1

Dear student

HCl completely ionizes, and thus [H⁺] = 1 × 10⁻⁸ M

The concentration is very low, and thus the self-ionization of water must be considered.

H₂O(l) ⇌ H⁺(aq) + OH⁻(aq)

Assume that water self-ionizes to give y M of H⁺ ions and y M of OH⁻ ions.

Kw = [H⁺][OH⁻]

[y + (1 × 10⁻⁸)] y = 1 × 10⁻¹⁴

y² + (1 × 10⁻⁸)y - 1 × 10⁻¹⁴ = 0

y = 9.512 × 10⁻⁸ or y = -1.051 × 10⁻⁷ (rejected)

[H⁺] = (1 × 10⁻⁸) + (9.512 × 10⁻⁸) = 1.0512 × 10⁻⁷ M

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