What is the Ka of HA if 0.10 M solution has pH = 3.50?
The correct answer and explanation is :
To find the acid dissociation constant (Ka) of HA, we need to use the information given about the solution and apply the principles of acid-base chemistry.
Given:
- The concentration of HA: 0.10 M
- The pH of the solution: 3.50
Step 1: Calculate the concentration of ([H^+])
The pH of a solution is related to the concentration of hydrogen ions (([H^+])) by the formula:
[
\text{pH} = -\log[H^+]
]
To find ([H^+]), we rearrange the equation:
[
[H^+] = 10^{-\text{pH}}
]
Substitute the given pH value:
[
[H^+] = 10^{-3.50} = 3.16 \times 10^{-4} \, \text{M}
]
Step 2: Set up an ICE table
HA dissociates according to the following reaction:
[
\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-
]
Using an ICE (Initial, Change, Equilibrium) table, we can express the changes in concentrations as the dissociation occurs:
| HA (M) | H⁺ (M) | A⁻ (M) | |
|---|---|---|---|
| Initial | 0.10 | 0 | 0 |
| Change | -x | +x | +x |
| Equilibrium | 0.10 – x | x | x |
At equilibrium, the concentration of (H^+) is equal to (x), which we found to be 3.16 × 10⁻⁴ M. Therefore, (x = [H^+] = 3.16 \times 10^{-4} \, \text{M}).
Step 3: Calculate Ka
The expression for the acid dissociation constant, Ka, is:
[
K_a = \frac{[H^+][A^-]}{[HA]}
]
At equilibrium, ([H^+] = [A^-] = 3.16 \times 10^{-4} \, \text{M}), and ([HA] = 0.10 – x = 0.10 – 3.16 \times 10^{-4} \approx 0.0997 \, \text{M}).
Now, substitute these values into the Ka expression:
[
K_a = \frac{(3.16 \times 10^{-4})(3.16 \times 10^{-4})}{0.0997}
]
[
K_a = \frac{9.97 \times 10^{-8}}{0.0997}
]
[
K_a \approx 1.00 \times 10^{-6}
]
Final Answer:
The acid dissociation constant, Ka, for HA is approximately:
[
K_a = 1.00 \times 10^{-6}
]
Explanation:
In this problem, we used the pH to calculate the concentration of (H^+) ions in the solution. From there, we used an ICE table to set up an equilibrium expression and apply it to the formula for Ka. This allowed us to calculate the acid dissociation constant, which quantifies the strength of the acid HA. A Ka of (1.00 \times 10^{-6}) suggests that HA is a weak acid, as its dissociation in water is minimal.