From Ka to pKa: Taming a Wild Range
In the last guide you met the acid-base lens: an acid hands over a proton, a base catches it, and every reaction has two conjugate pairs in it. That tells you what is happening. It does not yet tell you how far it happens. For that we need a number that rates how willing an acid is to actually let go of its proton. Dissolve any acid HA in water and it sets up an equilibrium: HA gives up H+ to leave behind A-, the conjugate base. How far that equilibrium leans toward giving up the proton is captured by a single constant, the acid dissociation constant Ka — big Ka means the acid lets go readily, tiny Ka means it clings.
The trouble is that Ka values sprawl across an absurd range — from about 10^7 for a strong acid down to 10^-50 for an alkane C-H. Numbers spanning fifty-seven powers of ten are impossible to hold in your head. So chemists do the same trick that turned earthquake energy into the Richter scale: take the negative base-10 logarithm. That gives pKa = -log Ka, a tidy little number usually between about -10 and 50. Because it is a logarithm, every single step of 1 in pKa means a tenfold change in Ka — a tenfold change in how readily the proton comes off.
HA <=> H+ + A- Ka = [H+][A-] / [HA] pKa = -log10(Ka) HCl pKa = -7 (Ka ~ 10^7, proton flies off) CH3COOH pKa = 4.76 H2O pKa = 15.7 CH3CH2OH pKa = 16 CH4 pKa = ~50 (Ka ~ 10^-50, proton never leaves)
Reading the Table: Lower Means Stronger
Here is the one fact that trips up every beginner, so meet it head on: the smaller the pKa, the stronger the acid. It feels backwards, but the minus sign in -log Ka flips the direction — a strong acid has a big Ka, and the negative log of a big number is small (even negative). So hydrochloric acid at pKa -7 is a ferocious acid whose proton is essentially gone the instant it touches water, while an alkane at pKa ~50 holds its protons so tightly that nothing in an ordinary flask can pull one off. Think of the pKa column as a golf leaderboard: the lowest score wins the title of strongest acid.
You do not need to memorize a hundred numbers — you need about a dozen anchor points and the acidity reasoning from this rung to interpolate between them. A useful spine to carry in your head: strong mineral acids (HCl, H2SO4) live around -10 to -3; a protonated carbonyl or alcohol sits near -2 to -7; carboxylic acids cluster near 4 to 5; protonated amines near 10 to 11; phenols near 10; water at 15.7 and alcohols near 16 to 18; terminal alkynes near 25; and plain C-H bonds far off the chart near 45 to 50. Once you know where the families sit, a new molecule's pKa is rarely a surprise.
The Master Rule: Equilibrium Favors the Weaker Acid
Now the payoff — the single most practical skill in early organic chemistry. Any proton transfer is a tug-of-war between two bases competing for one proton, and there is a law that decides the winner every time: an acid-base equilibrium always runs downhill toward the weaker acid and the weaker base. Why? Because a weaker acid is a more stable, more contented arrangement of that proton, and an equilibrium settles wherever energy is lowest. The proton ends up parked on whichever base holds it most comfortably — that is, the base whose conjugate acid has the higher pKa.
Spelled out as a recipe you can run on any proton-transfer reaction:
- Find the acid on the LEFT (the one losing a proton) and look up its pKa.
- Find the acid on the RIGHT — the conjugate acid that forms when your base grabs the proton — and look up ITS pKa.
- Compare. The side with the HIGHER-pKa acid (the weaker acid) is the favored side; equilibrium leans toward it.
- Estimate how far it goes: K_eq ~ 10^(pKa of left acid - pKa of right acid). A gap of even 3-4 units means the reaction goes essentially to completion.
A Worked Prediction, Start to Finish
Let's run the rule on a real question. Suppose you have ethanol, CH3CH2OH, and you want to make its conjugate base, the ethoxide ion, to use as a nucleophile. Will sodium hydroxide (the base is OH-) do the job? Write the reaction: CH3CH2OH + OH- gives CH3CH2O- + H2O. The acid on the left is ethanol, pKa 16. The acid on the right is water, pKa 15.7. The higher-pKa (weaker) acid is ethanol — barely — so equilibrium actually leans slightly back to the LEFT. Hydroxide deprotonates ethanol only partially; you get a useless near-50/50 mixture, not clean ethoxide.
So you reach for a stronger base. Sodium hydride (the base is H-, whose conjugate acid H2 has pKa ~35) instead gives CH3CH2OH + H- -> CH3CH2O- + H2. Now the left acid is ethanol (16) and the right acid is hydrogen gas (35). The weaker acid by far sits on the right, a 19-unit gap, so K_eq is about 10^19 — the reaction stampedes to completion and bubbles off H2 gas as it goes. Same alcohol, same goal, but the pKa table told you which reagent actually works. Contrast that with a carboxylic acid (pKa ~5): even mild hydroxide rips its proton off cleanly, because the gap to water (15.7) is a comfortable ten units downhill.
Notice what the table is really telling you, looping back to last rung's acidity reasoning: the carboxylic acid is easy to deprotonate precisely because its conjugate base, the carboxylate, spreads the negative charge over two oxygens by resonance, while the ethoxide is stuck holding the charge on one. pKa is not an arbitrary lookup value — it is the numerical shadow of conjugate-base stability. The trends you reasoned out qualitatively last time are exactly what the numbers in the table encode.
Honest Limits and Common Traps
The pKa rule is powerful, but be honest about its borders. First, it predicts position, not speed. Equilibrium tells you where a reaction ends up if given time, not how fast it gets there — a thermodynamically favorable proton transfer can still be slow if there is a high barrier, and a catalyst can change the rate without nudging the equilibrium position at all. Second, simple proton transfers between electronegative atoms (O, N) are usually fast, but pulling a proton off carbon can be sluggish; do not assume a favorable pKa gap means an instant reaction.
Third, pKa values depend on the solvent, and water has a ceiling. The leveling effect means any acid much stronger than hydronium (H3O+, pKa -1.7) is fully ionized in water and just reads as H3O+, so you cannot rank HCl, HBr, and HI in water — they all look equally strong. The same flattens super-strong bases down to hydroxide. That is why a reagent like NaH or butyllithium must be used in an aprotic solvent, never water: water would simply level it. The extreme pKa values you see for very strong or very weak acids are measured in special non-aqueous conditions, so treat numbers below about -2 or above about 16 as approximate, solvent-dependent guides.