pKa and pKb Relationship- How to Find pKa of Conjugate Acid

What pKa and pKb Actually Mean

Before diving into the relationship, you need to understand what these values represent. pKa is the negative logarithm of the acid dissociation constant (Ka). pKb is the negative logarithm of the base dissociation constant (Kb). Both measure how strong an acid or base is in water.

The lower the pKa, the stronger the acid. The lower the pKb, the stronger the base. This is counterintuitive if you're new to chemistry, so burn this into your memory: low numbers = strong stuff.

The pKa and pKb Relationship Formula

Here's the equation that connects them:

pKa + pKb = pKw

pKw is the ion product constant for water. At 25°C, pKw = 14. This relationship is what makes calculating one value from the other possible.

So if you know the pKb of a base, you can find the pKa of its conjugate acid instantly. Same equation, rearranged:

• pKa = pKw - pKb
• pKb = pKw - pKa

Why This Relationship Exists

Every base has a conjugate acid. Every acid has a conjugate base. They're pairs—when one accepts a proton, it becomes the other. This conjugate pair relationship is why their constants multiply to give Kw.

Ka × Kb = Kw

Taking the negative log of both sides gives you the familiar pKa + pKb = pKw.

How to Find pKa of Conjugate Acid: Step-by-Step

Method 1: Using pKb of the Base

If you have the pKb of a base, finding the pKa of its conjugate acid takes about 10 seconds.

Formula: pKa (conjugate acid) = 14 - pKb (base)

Example: Ammonia (NH₃) has a pKb of 4.75. Find the pKa of its conjugate acid (NH₄⁺).

pKa = 14 - 4.75 = 9.25

That's it. Done.

Method 2: Using Ka or Kb Values

Sometimes you have Ka or Kb instead of their log versions. Here's how to handle that:

1. Find Ka or Kb from your data
2. Calculate Kb = Kw/Ka (or Ka = Kw/Kb)
3. Take pKa = -log(Ka) or pKb = -log(Kb)
4. Apply the relationship: pKa = 14 - pKb

Example: Acetic acid has Ka = 1.8 × 10⁻⁵. Find pKa.

pKa = -log(1.8 × 10⁻⁵) = 4.74

Quick Reference Table

Common Mistakes to Avoid

• Forgetting the temperature: pKw = 14 only at 25°C. At other temperatures, the value changes. If your problem specifies a different temperature, adjust accordingly.
• Confusing conjugate pairs: The conjugate acid of NH₃ is NH₄⁺. The conjugate base of NH₃ is NH₂⁻. Don't mix these up.
• Using the wrong formula: pKa + pKb = 14 works for conjugate pairs. Don't try to use it for unrelated acids and bases.

Temperature Effects on the Calculation

At 25°C, pKw = 14. But this value shifts with temperature. At 0°C, pKw ≈ 14.94. At 100°C, pKw ≈ 12.3. If you're working outside room temperature conditions, check your reference tables for the correct pKw value.

For most introductory and intermediate chemistry problems, 25°C is assumed and pKw = 14 is used.

Getting Started: Your First Calculation

Try this example to confirm you understand the relationship:

Problem: Methylamine has a pKb of 3.44. What is the pKa of the conjugate acid (CH₃NH₃⁺)?

Solution:

1. Apply the formula: pKa = 14 - pKb
2. Substitute: pKa = 14 - 3.44
3. Result: pKa = 10.56

This tells you methylammonium is a weak acid (high pKa = weak acid), which makes sense since methylamine is a moderately strong base.

When You'll Use This in Real Chemistry

Buffer calculations rely heavily on the Henderson-Hasselbalch equation, which uses pKa directly. If you're given pKb and need to work with buffer pH, converting to pKa is your first step.

Acid-base titration curves also require this relationship. Knowing the pKa of the conjugate acid tells you where you'll see the buffer region on your titration curve.

Organic chemistry uses this constantly when predicting protonation states. A base with pKb 5 has a conjugate acid with pKa 9. At pH 7, that conjugate acid will be mostly protonated.

The Bottom Line

The pKa of a conjugate acid equals 14 minus the pKb of its conjugate base. That's the entire relationship. Memorize it, apply it, move on. Every acid-base problem that involves conjugate pairs uses this equation—you don't need to overthink it.