Respuesta :
8.8 × 10-5 M is the [H3O+] concentration in 0.265 M HClO solution.
Explanation:
HClO is a weak acid and does not completely dissociate in water as ions.
the equation of dissociation can be written and ice table to be formed.
HClO +H2O ⇒ ClO- + H3O+
I 0.265 0 0
C -x +x +x
E 0.265-x +x +x
Now applying the equation of Ka, where Ka is given as 2.9 × 10-8.
Ka = [tex]\frac{[ClO-][H3O+]}{[HClO]}[/tex]
2.9 × 10^-8 = [tex]\frac{[x] [x]}{[0.265-x]}[/tex]
[tex]x^{2}[/tex] = 7.698 x[tex]10^{-9}[/tex]
x = 8.8 × 10-5 M
The hydronium ion concentration is 8.8 × 10-5 M in 0.265 M solution of HClO.
Considering the definition of weak acid, the correct answer is option d. the [H₃O⁺] in a 0.265 M HClO solution is 8.8×10⁻⁵ M.
A classification of acids and bases in chemistry depends on the ionization force of these substances in aqueous medium. Thus:
- an acid and a base are strong when they are completely ionized, that is, in the ionization process they are completely transformed into cations or positive ions and into anions or negative ions.
- an acid and a base are weak when they partially ionize in water, that is, in solution there will be a proportion of cations, another proportion of anions and another proportion of undissociated molecules.
Then it is called Weak Acid to one that does not completely dissociate, but there will be an equilibrium between dissociated and undissociated particles. Unlike strong acids, whose dissociation is complete and practically irreversible, weak acids hardly dissociate and in a reversible way.
So, in this case, HClO is a weak acid and the equation of dissociation can be written as:
HClO + H₂O ⇒ ClO⁻ + H₃O⁺
I 0.265 M 0 0
C -x +x +x
E 0.265 M-x +x +x
Where + x and 0.265M-X represent the concentrations of the corresponding compounds after equilibrium is established. In the case of products, the value of x is positive because they are generated, while the reactant is consumed and that is why it is negative.
When a weak acid dissociates or ionizes, an equilibrium is established between the species present in the solution. This can be expressed by an acid ionization constant, which is defined as the ratio between the multiplication of the concentration of the products over the multiplication of the concentration of the reactants:
[tex]Ka=\frac{[H_{3} O^{+}][ClO^{-}] }{[HClO]}[/tex]
The Ka of HClO is 2.9×10⁻⁸, [H₃O⁺]=x, [ClO⁻]= x and [HClO]= 0.265 M - x. Replacing:
[tex]2.9x10^{-8} =\frac{[x][x] }{0.265-x}[/tex]
Solving:
[tex]2.9x10^{-8} =\frac{x^{2} }{0.265-x}[/tex]
2.9×10⁻⁸× (0.265 M - x)= x²
2.9×10⁻⁸× 0.265 M - 2.9×10⁻⁸x= x²
7.685×10⁻⁹- 2.9×10⁻⁸x= x²
0=x² + 2.9×10⁻⁸x - 7.685×10⁻⁹
Being a quadratic function of the form ax² + bx +c, where a=1, b=2.9×10⁻⁸ and c= - 7.685×10⁻⁹
A quadratic equation is solved by the expression: [tex]x1=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]x1=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
So, solving the obtained quadratic equation, you get: x1= 8.76×10⁻⁵ and x2= - 8.76×10⁻⁵
Since x is the value of a concentration and it cannot be negative, finally the value of x is: x= 8.76×10⁻⁵≅ 8.8×10⁻⁵
Remembering that [H₃O⁺] = x, the correct answer is option d. the [H₃O⁺] in a 0.265 M HClO solution is 8.8×10⁻⁵ M.
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