Ka/Kb Calculator
Calculate acid and base dissociation constants.
Ka / Kb Calculator
For Conjugate Acid-Base Pairs
Enter any one value to calculate the others.
Acid Dissociation Constant
Base Dissociation Constant
Acid Ionization Constant
Base Ionization Constant
Acid-Base Relationships
For any conjugate acid-base pair, their strengths are inversely related. This relationship is defined by the ion-product constant for water (Kw) at 25°C:
- Ka × Kb = Kw = 1 x 10⁻¹⁴
- pKa + pKb = pKw = 14
Understanding Ka and Kb
Quantifying the Strength of Weak Acids and Bases.
What are Ka and Kb?
Ka and Kb are equilibrium constants that quantify the strength of weak acids and weak bases, respectively. They measure the extent to which an acid or base dissociates (ionizes) in water.
The Acid Dissociation Constant (Ka) refers to the equilibrium of a weak acid donating a proton to water.
The Base Dissociation Constant (Kb) refers to the equilibrium of a weak base accepting a proton from water.
Crucially, a larger Ka value indicates a stronger weak acid, and a larger Kb value indicates a stronger weak base.
Example: Unlike a strong acid that breaks apart 100%, a weak acid like acetic acid (vinegar) only partially dissociates, creating an equilibrium between the acid and its ions. Ka tells us the position of this equilibrium.
The Ka and Kb Expressions
For a generic weak acid dissociation, HA ⇌ H⁺ + A⁻, the Ka expression is:
Ka = [H⁺][A⁻] / [HA]
For a generic weak base dissociation, B + H₂O ⇌ BH⁺ + OH⁻, the Kb expression is:
Kb = [BH⁺][OH⁻] / [B]
Note: [ ] denotes molar concentration at equilibrium. Pure liquids like water (H₂O) are not included in the expression.
Example:For hydrofluoric acid (HF ⇌ H⁺ + F⁻), the expression is Ka = [H⁺][F⁻] / [HF].
pKa and pKb: A More Convenient Scale
Ka and Kb values are often very small numbers. To make them easier to work with, scientists use the logarithmic pKa and pKb scales:
pKa = -log(Ka)
pKb = -log(Kb)
This is similar to how pH relates to [H⁺]. Because of the negative logarithm, the relationship is inverse:
A smaller pKa means a stronger acid.
A smaller pKb means a stronger base.
Example:Acetic acid has a Ka of 1.8 x 10⁻⁵, which gives a pKa of 4.74. Hydrofluoric acid has a Ka of 6.3 x 10⁻⁴, giving a smaller pKa of 3.20, indicating it is the stronger acid.
The Relationship Between Ka, Kb, and Kw
For any conjugate acid-base pair, their strengths are inversely related. The stronger the acid, the weaker its conjugate base, and vice versa.
This relationship is mathematically defined by the ion-product constant for water, Kw (1.0 x 10⁻¹⁴ at 25°C).
The formula is: Ka * Kb = Kw
In logarithmic form, this is: pKa + pKb = 14
This is an extremely useful relationship because if you know the Ka of a weak acid, you can immediately find the Kb of its conjugate base.
Example:If you know the Ka for acetic acid (1.8 x 10⁻⁵), you can find the Kb for its conjugate base, acetate: Kb = (1.0 x 10⁻¹⁴) / (1.8 x 10⁻⁵) = 5.6 x 10⁻¹⁰.
Real-World Application: Drug Design and Buffers
The pKa of a molecule is one of its most important properties in chemistry and biology.
Pharmaceuticals: The pKa of a drug determines its charge at a given pH, which affects how well it can be absorbed by the body. A drug might be designed to be absorbed in the acidic environment of the stomach or the more neutral environment of the intestine based on its pKa.
Buffer Systems: The pH of a buffer solution is determined by the pKa of its weak acid component and the ratio of acid to conjugate base. Chemists select a buffer system with a pKa close to the desired pH they need to maintain.
Acid-Base Titrations: The shape of a titration curve and the choice of a suitable indicator depend on the pKa of the acid being titrated.
Example:The effectiveness of aspirin (acetylsalicylic acid, pKa ≈ 3.5) depends on it being in its uncharged form to pass through cell membranes. Its pKa helps predict how it will behave in different parts of the digestive system.
Key Summary
- **Ka** and **Kb** are equilibrium constants that measure the strength of weak acids and bases.
- A larger Ka or Kb means a stronger acid or base. A smaller **pKa** or **pKb** means a stronger acid or base.
- For a conjugate pair, **Ka * Kb = Kw** (1.0 x 10⁻¹⁴) and **pKa + pKb = 14**.
- These values are crucial for understanding buffer systems and the behavior of drugs in the body.
Practice Problems
Problem: The pH of a 0.1 M solution of a weak acid (HA) is measured to be 2.87. What is the Ka of the acid?
1. Calculate [H⁺] from pH ([H⁺] = 10⁻ᵖᴴ). 2. At equilibrium, [H⁺] = [A⁻]. 3. The equilibrium concentration of [HA] is approximately its initial concentration. 4. Plug these values into the Ka expression.
Solution: [H⁺] = 10⁻².⁸⁷ ≈ 1.35 x 10⁻³ M. So, [A⁻] ≈ 1.35 x 10⁻³ M. Ka = [H⁺][A⁻] / [HA] ≈ (1.35 x 10⁻³)² / 0.1 ≈ 1.8 x 10⁻⁵.
Problem: The pKa of formic acid (HCOOH) is 3.75. What is the pKb and Kb of its conjugate base, formate (HCOO⁻)?
Use the relationships pKa + pKb = 14 and Ka * Kb = Kw.
Solution: pKb = 14 - pKa = 14 - 3.75 = 10.25. Kb = 10⁻ᵖᴷᵇ = 10⁻¹⁰.²⁵ ≈ 5.6 x 10⁻¹¹.
Frequently Asked Questions
Why don't strong acids and bases have Ka or Kb values?
Strong acids and bases are assumed to dissociate 100% in water. This means the concentration of the undissociated acid [HA] is essentially zero, which would make the denominator in the Ka expression zero, and the Ka value would be infinitely large. For practical purposes, we just say they dissociate completely.
What is a conjugate acid-base pair?
A conjugate acid-base pair consists of two substances that differ only by the presence of a single proton (H⁺). When a weak acid (HA) donates its proton, what remains (A⁻) is its conjugate base. When a weak base (B) accepts a proton, the new species (BH⁺) is its conjugate acid.
How does Ka relate to pH?
Ka is an intrinsic constant for an acid, while pH is a property of a specific solution that depends on the acid's concentration. However, they are related: for a solution of a weak acid, a smaller pKa (stronger acid) will result in a lower pH at the same concentration.
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