🔬 Acid–Base Basics: The Big Picture

We start with the fundamental acid–base equilibrium:

mathrm{HA + H_2O ightleftharpoons H_3O^+ + A^-}

• HA = the acid
• A⁻ = the conjugate base
• This equilibrium tells us how much the acid dissociates in water.

⚖️ Ka – The Acid Dissociation Constant

• Ka measures how strongly an acid dissociates.
• It is assigned to the acid (HA).
• Higher Ka → more dissociation → stronger acid

Key idea:

Acid strength = how much HA wants to become A⁻

Ka values are:

• Fixed for a given acid
• Only change with temperature (which we ignore here)

🔢 pKa – A Logarithmic Convenience

Instead of using Ka directly, we usually use pKa:

oxed{mathrm{pKa = -log(Ka)}}

🔁 Inverse Relationship

• Low pKa → High Ka → Strong acid
• High pKa → Low Ka → Weak acid

This inverse relationship is critical and comes up constantly in biochemistry exams.

🧪 Conjugate Bases: Kb and pKb

For the conjugate base (A⁻):

• You can define Kb and pKb
• These describe how likely the base is to accept a proton

🔗 Acid–Base Pair Rule (Very Important)

For a conjugate acid–base pair in water:

oxed{mathrm{pKa + pKb = 14}}

This means:

• Strong acid → weak conjugate base
• Weak acid → strong conjugate base

You cannot have both strong at the same time.

🧠 What pKa vs pH Really Mean

• pKa → intrinsic property of the molecule (“How much does this acid want to dissociate?”)
• pH → property of the environment (“How many protons are actually around?”)

The balance between pH and pKa determines whether the molecule is mostly:

• Protonated (HA)
• Deprotonated (A⁻)

📐 Henderson–Hasselbalch Equation

This equation connects everything:

oxed{mathrm{pH = pKa + logleft(rac{A^-}{HA} ight)}}

🔑 Rules to remember

• Base (A⁻) goes on top
• Acid (HA) goes on bottom
• pKa is fixed
• pH depends on the environment

🔄 Three Key Scenarios (Must Know)

1️⃣ pH < pKa → Acid form dominates

• Environment is acidic
• Lots of H⁺ available
• Protonation favored
• (mathrm{HA > A^-})

🧠 Think: “Low pH = hold onto protons”

2️⃣ pH > pKa → Base form dominates

• Environment is basic
• Fewer protons available
• Deprotonation favored
• (mathrm{A^- > HA})

3️⃣ pH = pKa → 50/50 mixture

mathrm{HA = A^-}

This point is special:

• Exactly half protonated
• Exactly half deprotonated

🏥 Real Example: Drugs in the Stomach

Let’s apply this to a physiological setting.

Given:

• Stomach pH ≈ 1.5
• Two drugs with different pKa values:
  • Drug A: pKa = 2.5
  • Drug B: pKa = 4.5

We rearrange Henderson–Hasselbalch:

mathrm{pH - pKa = logleft(rac{A^-}{HA} ight)}

🧮 Drug A (pKa = 2.5)

1.5 - 2.5 = -1

rac{A^-}{HA} = 10^{-1} = 0.1

➡️ Some dissociation ➡️ Moderate amount of A⁻

🧮 Drug B (pKa = 4.5)

1.5 - 4.5 = -3

rac{A^-}{HA} = 10^{-3} = 0.001

➡️ Almost no dissociation ➡️ Mostly protonated (HA)

🧠 Final Takeaway from the Drug Example

• Lower pKa (stronger acid) → more dissociation at the same pH
• Higher pKa (weaker acid) → much less dissociation

Even a 2-unit difference in pKa leads to a 100-fold difference in protonation state.

That’s enormous in biochemistry and pharmacology.

✅ Core Concepts to Lock In

• Ka and pKa describe acid strength
• pKa is fixed, pH is environment-dependent
• Protonation state depends on pH vs pKa
• Henderson–Hasselbalch lets you quantify ratios
• Small pKa differences → huge biological effects