Respuesta :
Answer:
The concentration of [tex][H_3O^+][/tex] is[tex]0.725 \times 10^{-4} \ M[/tex].
Explanation:
Let the initial concentration of weak acid be c m/liter and [tex]\alpha[/tex] be change of concentration.
The reaction of an acid with water is given by the general expression
[tex]HA(aq) +H_2O(l) \rightleftharpoons H_3O^+(aq)+A^-[/tex]
Initial Concentration c 0 0
Change in concentration -[tex]\alpha[/tex] +[tex]\alpha[/tex] +[tex]\alpha[/tex]
Equilibrium Concentration c-[tex]\alpha[/tex] [tex]\alpha[/tex] [tex]\alpha[/tex]
[tex]K_a=\frac{[A^-][H_3O^+]}{[HA]}[/tex]
[tex]=\frac{(\alpha)(\alpha)}{c-\alpha}[/tex]
[tex]=\frac{\alpha^2}{c-\alpha}[/tex]
[tex]=\frac{\alpha^2}{c}[/tex] [ For weak acid , the value of [tex]\alpha[/tex] is so small, ∴[tex]c-\alpha \approx c[/tex]]
[tex]\therefore K_a= \frac{\alpha^2}{c}[/tex]
[tex]\Rightarrow \alpha^2={K_a}\times{c}[/tex]
[tex]\Rightarrow \alpha = \sqrt{K_a\times c}[/tex]
The concentration of [tex][H_3O^+][/tex] is [tex]\alpha[/tex] [tex]=\sqrt {K_a\times c}[/tex]
Given equation is
[tex]HOCl(aq) +H_2O(l)\rightleftharpoons H_3O^+(aq)+OCl^-(aq)[/tex]
The initial concentration of the hypochlorous acid solution is 0.150 M.
The ionization constant [tex]K_a= 3.5 \times 10^{-8}[/tex]
The concentration of [tex][H_3O^+][/tex] is [tex]\alpha[/tex] [tex]=\sqrt {K_a\times c}[/tex]
= [tex]\sqrt {3.5 \times 10^{-8}\times 0.150[/tex] M
[tex]= 0.725 \times 10^{-4}[/tex] M
