1. Understand the Relationship
* pH and [H+]: The pH of a solution is related to the concentration of hydrogen ions ([H+]) by the equation: pH = -log[H+].
* Ka and Dissociation: The dissociation constant (Ka) is a measure of the extent to which an acid dissociates in solution. For a monobasic acid (HA), the dissociation reaction and Ka expression are:
HA(aq) ⇌ H+(aq) + A-(aq)
Ka = [H+][A-] / [HA]
2. Calculate [H+]
* Use the pH to find the [H+]:
[H+] = 10^(-pH) = 10^(-4.22) = 6.03 x 10^(-5) M
3. Set Up an ICE Table
* I: Initial Concentrations
* C: Change in Concentrations
* E: Equilibrium Concentrations
| | HA | H+ | A- |
|-----|--------|---------|---------|
| I | 0.001 | 0 | 0 |
| C | -x | +x | +x |
| E | 0.001-x | x | x |
4. Substitute Values into Ka Expression
* Ka = [H+][A-] / [HA]
* Ka = (x)(x) / (0.001-x)
5. Since the acid is weak, assume x << 0.001
* This simplifies the equation: Ka ≈ x² / 0.001
6. Solve for x (which is equal to [H+])
* x² = Ka * 0.001
* x = √(Ka * 0.001)
* We know x = 6.03 x 10^(-5) M (from step 2)
7. Calculate Ka
* 6.03 x 10^(-5) = √(Ka * 0.001)
* (6.03 x 10^(-5))² = Ka * 0.001
* Ka = (6.03 x 10^(-5))² / 0.001
* Ka ≈ 3.64 x 10^(-6)
Therefore, the dissociation constant (Ka) of the monobasic acid at 25 degrees Celsius is approximately 3.64 x 10^(-6).
