Respuesta :
Answer:
The pH of the 0.100 M solution of hydobromous acid HBrO is 4.843
Explanation:
Here we have the reaction given as follows;
HBrO ⇄ H⁺ + BrO⁻¹
Therefore;
HBrO ⇄ H⁺ + BrO⁻¹
Initial concentration of HBrO = 0.100 M decomposes partly to form x moles of each of H⁺ and BrO⁻¹. That is
HBrO ⇄ H⁺ + BrO⁻¹
Initial 0.1 0 0
Change -x +x +x
Equilibrium 0.1 - x x x
Hence;
[tex]Ka = \frac{[H^+][BrO^{-1}]}{[HBrO]} =\frac{x \times x }{0.1 - x} = \frac{x^2}{0.1 -x} = 2.06 \times 10^{-9}[/tex]
(0.1 - x) × 2.06×10⁻⁹ = x²
x² + 2.06×10⁻⁹·x - 0.1 = 0
Factorizing gives;
(x + 1.4354×10⁻⁵)(x - 1.4352×10⁻⁵) = 0
Therefore, x = 1.4352×10⁻⁵ M or -1.4354×10⁻⁵ M
We take the positive value as x is the concentration of the ions in the solution;
From the above [H⁺] = 1.4352×10⁻⁵ M
pH = -log[H⁺] = -log(1.4352×10⁻⁵) = 4.843
The pH of the 0.100 M solution of hydobromous acid HBrO at 298 K where the Ka = 2.06×10⁻⁹ = 4.843.
