MathSci Problems
Factors Affecting Acidity and Basicity
You can think of acidity as a molecule’s willingness to give up H⁺, and basicity as a molecule’s eagerness to take it.
The more stable the conjugate base, the stronger the acid. To understand why, consider the equilibrium HA + H₂O ⇌ H₃O⁺ + A⁻. Lower product energy means a larger Ka (ΔG° = −RT ln Ka), so acidity rises.
Let’s first consider four general factors we can look at when assessing how stable the conjugate base is. Atom, Resonance, Induction, Orbital, or ARIO for short.
Atom
“Atom” asks where the negative charge sits after deprotonation and how low in energy that anion can get. Across a period, higher electronegativity stabilises negative charge because the nucleus pulls the extra electron density closer. Closer to the nucleus means lower electrostatic potential energy. That is why alcohols are far more acidic than amines on the same carbon skeleton: placing charge on oxygen (more electronegative) is calmer than putting it on nitrogen.
Down a group, larger size and higher polarizability stabilise anions for two concrete reasons. First, a bigger valence shell spreads the same charge over a larger volume, which lowers charge density and cuts electron–electron repulsion inside the anion. Lower self-repulsion lowers energy. Second, a more polarizable electron cloud can distort in response to nearby charges and solvent dipoles, which shifts density toward stabilising regions and away from destabilising ones. That reshaping allows for extra stabilisation through better ion–dipole and dispersion interactions. Put together, the larger, more deformable anion is more comfortable holding charge. Consider oxygen and sulfur. Deprotonating ethanol gives an alkoxide (charge on O); deprotonating ethanethiol gives a thiolate (charge on S). Sulfur’s larger, more polarizable cloud spreads and reshapes the added electron density more effectively than oxygen can, so the thiolate sits lower in energy. The numbers match that mechanism: ethanethiol in water is much more acidic than ethanol (pKa ≈ 10–11 vs ≈ 16).
Resonance
Resonance stabilises charge because electrons can spread out. Spreading lowers charge density, which cuts electron–electron repulsion, and it lets some of that negative charge sit on atoms that are better at holding it. A carboxylate is a good example: the two C–O bonds are equivalent because the negative charge is shared over both oxygens. That sharing drops the energy of the conjugate base by a lot, which is why acetic acid lives near pKa 4.8 while an alcohol with the same carbon skeleton sits around 16.
Induction
Induction like placing a HEPA filter beside a stinky litter box. Place a powerful filter right next to the box and it pulls most of the smelly air straight through, so that corner smells fine. Move the same filter across the room and the smell near the box lingers a little more. Swap the filter for the ultra deluxe unit and the smell clears even faster. A very electronegative neighbour, like CF₃ or a carbonyl, attracts a bit of electron density toward itself. The negative site is left with a thinner cloud, so electrons there repel each other less. Less self-repulsion means the conjugate base sits lower in energy, which makes the parent acid stronger.
For example, acetic acid has pKa ≈ 4.8 in water. Replace CH₃ with CF₃ and pKa drops to about 0.2. If you move those fluorines even one carbon away, the stabilisation falls off because the pull weakens with distance. The pKa of CF₃CH₂CO₂H ≈ 3.
Orbital (hybridisation)
Hybridisation sets how tightly electrons can sit near the nucleus. An s orbital has electron density at the nucleus; a p orbital has a node there. Mixing in more s-character pulls the electron density inward, which lowers electrostatic potential energy. An sp hybrid is 50% s, sp² is 33%, sp³ is 25%, so negative charge in an sp hybrid sits closer to the nucleus and is stabilised more than in sp² or sp³.
That is why the acidity ladder for C–H bonds goes alkyne, then alkene, then alkane. Deprotonating a terminal alkyne puts the charge in an sp hybrid on carbon and gives a conjugate base that is markedly lower in energy, so pKa lands near 25 rather than the mid-40s or ~50.
Solvent Effects
Solvent also affects acidity and basicity by changing how comfortably ions sit in that liquid. In a polar protic solvent, the molecules can donate hydrogen bonds to anions. Those hydrogen bonds stabilise the conjugate base, so the deprotonated side of the equilibrium sits lower in free energy and Kₐ is larger. You can write it generically as HA + Solv ⇌ H–Solv⁺ + A⁻, where “Solv” is any molecule with a lone pair that can hydrogen-bond; stronger stabilisation of A⁻ favours the right side of the equilibrium.
Acetic acid has pKₐ about 4.8 in water and about 12.6 in DMSO because acetate loses hydrogen-bond stabilisation in DMSO. Phenol shifts from roughly 10 in water to around 18 in DMSO for the same reason.
Each solvent also has a levelling limit. In any given solvent, no acid can be stronger than the solvent’s conjugate acid, and no base can be stronger than the solvent’s conjugate base, because the medium immediately converts anything stronger to those forms. In water, strong acids are levelled to H₃O⁺ (for example, HCl + H₂O → H₃O⁺ + Cl⁻), so H₃O⁺ is the strongest acid that can persist. Strong bases are levelled to OH⁻ (for example, NH₂⁻ + H₂O → NH₃ + OH⁻), so OH⁻ is the strongest base that can persist.
Reflect & Explore
Here are some open-ended questions to help you think more deeply about this material and connect it to related ideas.
- Ethanethiol vs ethanol in DMSO: which is more acidic and does the same “S beats O” reasoning still hold? State the atom-based reason and any solvent caveats.
- Normal amides are weak bases because the N lone pair delocalises into the carbonyl. Imagine a rigid “twisted amide” where the N–C(O) π overlap is blocked by geometry, so the lone pair cannot delocalise. a) Predict how the basicity at nitrogen changes. b) Predict what happens to acidity at the α-C–H next to the carbonyl.
- You plan a selective alkylation of a 1,3-dicarbonyl: CF₃–CH₂–CO–CH₂–CO–Et. You have NaOEt in EtOH at 0 °C. Which α position deprotonates first and why? Which competing factors are at play?