Grade 12th passPhysical Chemistry

the hydrogen ion concentration of 10^-8M hcl aueous solution at 298K(Kw=10^-14)

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poorav saraswat

8 Years agoGrade 12th pass

2 Answers

Arun

8 Years ago

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

Regards

Arun (askIITians forum expert)

Rishi Sharma

5 Years ago

Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards