Answer: 0.0023
Explanation:
1) Balanced equilibrium equation:
HF ⇆ H⁺ + F⁻
2) Equilibrium constant of the acid, Ka:
Ka = [H⁺] [F⁻] / [HF]
- [HF] is the concentration searched
- From the stoichiometry of the balanced chemical equation [H⁺] = [F⁻]
Hence:
Ka = [H⁺] [H⁺] / [HF] = [H⁺]² / [HF]
3) From the pH value you can calculate [H⁺], using the definition:
- pH= - log [H⁺]
- Substitute: 2.90 = - log [H⁺]
- Clear [H⁺] using logarithm properties:
[tex][H^+]=10^{-2.90}=0.00126[/tex]
4) Now you can substitute [H⁺] and the value of Ka in the equation for Ka:
Ka = [H⁺]² / [HF] ⇒ [HF] = [H⁺]² / Ka = (0.00126)² / (6.8×10⁻⁴) = 0.00233.
Since the value of Ka has two significant figures, you must report the answer with two significan figures, i.e. 0.0023
