The weak acid hypochlorous acid (HClO) is formed in bleach solutions. If the pH of a 0.12 M solution of
HClO is 4.19, what is the value of the Ka of this weak acid?
The correct answer and explanation is :
To find the value of the acid dissociation constant (Ka) of hypochlorous acid (HClO), we need to work through the problem step-by-step using the information provided: a 0.12 M solution of HClO with a pH of 4.19.
Step 1: Understanding the Dissociation of HClO
Hypochlorous acid (HClO) dissociates in water as follows:
[
\text{HClO} \rightleftharpoons \text{H}^+ + \text{ClO}^-
]
We are given that the pH of the solution is 4.19. The pH is related to the concentration of hydrogen ions (([H^+])) by the following equation:
[
\text{pH} = -\log[\text{H}^+]
]
From this equation, we can calculate the concentration of ( [\text{H}^+] ) (hydrogen ion concentration).
[
[\text{H}^+] = 10^{-\text{pH}} = 10^{-4.19} \approx 6.46 \times 10^{-5} \, \text{M}
]
Step 2: Set Up the Equilibrium Expression
We can now set up an ICE (Initial, Change, Equilibrium) table to represent the dissociation of HClO:
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HClO | 0.12 | -x | 0.12 – x |
| H(^+) | 0 | +x | x |
| ClO(^-) | 0 | +x | x |
Where ( x ) is the change in concentration due to dissociation. At equilibrium, we know that ( [\text{H}^+] = 6.46 \times 10^{-5} \, \text{M} ). Therefore, ( x = 6.46 \times 10^{-5} \, \text{M} ).
Step 3: Use the Ka Expression
The acid dissociation constant (Ka) for HClO is given by:
[
K_a = \frac{[\text{H}^+][\text{ClO}^-]}{[\text{HClO}]}
]
Substitute the equilibrium concentrations into the expression:
[
K_a = \frac{(6.46 \times 10^{-5})(6.46 \times 10^{-5})}{0.12 – 6.46 \times 10^{-5}}
]
Since ( 6.46 \times 10^{-5} ) is much smaller than 0.12, we can approximate ( 0.12 – 6.46 \times 10^{-5} \approx 0.12 ). Thus, the Ka expression simplifies to:
[
K_a \approx \frac{(6.46 \times 10^{-5})^2}{0.12}
]
Now, calculate ( K_a ):
[
K_a \approx \frac{4.18 \times 10^{-9}}{0.12} = 3.48 \times 10^{-8}
]
Final Answer:
The value of the acid dissociation constant ( K_a ) for hypochlorous acid (HClO) is approximately 3.48 × 10⁻⁸.
Explanation:
This result shows that HClO is a weak acid because its dissociation constant ( K_a ) is quite small. A small ( K_a ) means that only a small fraction of HClO dissociates into hydrogen ions and hypochlorite ions in solution, which is characteristic of weak acids. The lower the ( K_a ), the weaker the acid, as it indicates that the equilibrium lies more toward the undissociated form (HClO).