Acid Dissociation Constant (Kₐ)
What Exactly is an Acid?
Before diving into Kₐ, let's recall what an acid is. You might know that lemon juice and vinegar taste sour; that's because they are acids. Scientifically, an acid is a substance that can donate a proton (H⁺ ion). When an acid is mixed with water, a fascinating dance occurs: some acid molecules give away their H⁺ to water molecules. This process is called dissociation.
For a general acid, HA, the dissociation reaction in water is:
Here, HA is the acid, H₂O is water, A⁻ is the conjugate base, and H₃O⁺ is the hydronium ion. The double arrow (⇌) is the most important part—it means the reaction is reversible and can go back and forth until a balance, or equilibrium, is reached.
Introducing the Kₐ Expression
At equilibrium, the concentrations of the products and reactants become constant. The Acid Dissociation Constant (Kₐ) is the special ratio that describes this balance for an acid's dissociation. For our general acid HA, the Kₐ expression is written as:
The square brackets [ ] mean "concentration of" in moles per liter (M). Notice that the concentration of water ([H₂O]) is not included in the equation. This is because in dilute solutions, the concentration of water is so large compared to the other substances that it is essentially constant and is folded into the value of Kₐ itself.
What does this ratio tell us? If an acid dissociates a lot, it means there is a high concentration of products ([A⁻] and [H₃O⁺]) and a low concentration of the original acid ([HA]). This makes the Kₐ value large. Conversely, if the acid barely dissociates, the concentration of HA remains high while the products are low, resulting in a small Kₐ value.
Strong Acids vs. Weak Acids
The value of Kₐ is the key to classifying acids as either strong or weak.
Strong Acids dissociate completely in water. Almost every molecule of a strong acid donates its proton. This means at equilibrium, [HA] is nearly zero, and [A⁻] and [H₃O⁺] are very high. Therefore, the Kₐ for a strong acid is very large, often much greater than 1. Because the dissociation is complete, we don't usually talk about Kₐ for strong acids; it's more straightforward to use concentration to find pH.
Weak Acids only partially dissociate in water. They establish a clear equilibrium where a significant amount of the original acid (HA) remains. This results in a Kₐ value that is less than 1, and often much less. Most acids you encounter in nature, like acetic acid in vinegar, are weak acids.
| Acid Name | Formula | Kₐ Value | Strength |
|---|---|---|---|
| Hydrochloric Acid | HCl | ~10⁷ | Strong |
| Acetic Acid | CH₃COOH | 1.8 × 10⁻⁵ | Weak |
| Carbonic Acid | H₂CO₃ | 4.3 × 10⁻⁷ | Weak |
| Hydrofluoric Acid | HF | 6.8 × 10⁻⁴ | Weak |
A Handy Shortcut: pKₐ
Because Kₐ values can be very small and involve negative exponents (like 1.8 × 10⁻⁵), scientists often use a more convenient number called pKₐ. It is defined as the negative logarithm of Kₐ:
This mathematical trick turns very small numbers into more manageable positive numbers. The relationship is simple:
- A low pKₐ value means a high Kₐ and a stronger acid.
- A high pKₐ value means a low Kₐ and a weaker acid.
For example, acetic acid has a Kₐ of 1.8 × 10⁻⁵. Its pKₐ is calculated as -log(1.8 × 10⁻⁵) = 4.74. A strong acid like HCl, with a Kₐ of ~10⁷, would have a pKₐ of about -7, which is why we typically don't bother calculating it.
Kₐ in Action: Calculating the pH of a Weak Acid
Let's see how Kₐ is used in a practical calculation. Suppose we have a 0.1 M (molar) solution of acetic acid (CH₃COOH), which we'll abbreviate as HAc. Its Kₐ is 1.8 × 10⁻⁵. We want to find the pH of this solution.
Step 1: Write the balanced dissociation equation.
Step 2: Set up an ICE (Initial, Change, Equilibrium) table. This helps us track concentrations.
| Species | HAc | H⁺ | Ac⁻ |
|---|---|---|---|
| Initial (M) | 0.1 | 0 | 0 |
| Change (M) | -x | +x | +x |
| Equilibrium (M) | 0.1 - x | x | x |
Step 3: Apply the Kₐ expression.
Step 4: Solve for x. Since Kₐ is very small, x will be very small compared to 0.1. We can make the approximation that 0.1 - x ≈ 0.1. This simplifies the equation to:
$ x^2 = 1.8 \times 10^{-6} $
$ x = \sqrt{1.8 \times 10^{-6}} $
$ x \approx 1.34 \times 10^{-3} $
So, [H⁺] = x ≈ 1.34 × 10⁻³ M.
Step 5: Calculate pH. pH = -log[H⁺] = -log(1.34 × 10⁻³) ≈ 2.87.
This example shows how a relatively small Kₐ value leads to a low concentration of H⁺ ions, resulting in a pH that is not extremely low (remember, pH 7 is neutral, and lower numbers are acidic).
Important Questions
What is the difference between Kₐ and pH?
Can Kₐ change?
Do bases have a similar constant?
Footnote
¹ Kb: Base Dissociation Constant. The equilibrium constant for the reaction of a base with water.