← SciSim / Chemistry
CHEMSIM v1.0

Acid-Base Theories: Brønsted, Lewis & HSAB

Three frameworks for one fundamental concept · Donor–acceptor chemistry · Hard & Soft Acids and Bases
⚗️ INTERACTIVE SIMULATION
Brønsted: Proton Transfer
Lewis: Lone-Pair Donation
HSAB Match
Conjugate Pairs
Acid Strength Ladder
ΔG of Transfer
HOMO–LUMO
Hard–Soft Map
pKa Ladder
pKa (HA)
—
pKb (B)
—
ΔG (kJ/mol)
—
Keq
—
η (hardness)
—
HSAB match
—
χ (electroneg.)
—
Direction
—

CONTROLS

PRESET PAIR
pKa of HA 4.76
pKb of B 4.75
Temperature (K) 298
η acid (eV) 7.0
η base (eV) 7.0
χ acid (eV) 5.0
χ base (eV) 5.0
Speed 1.0×

TOGGLES

Show lone pairs
Show partial charges
Show curly arrows
Show orbital lobes
Trail particles
💡 THE IDEA, STEP BY STEP
START — THE EVERYDAY PICTURE
Lemon juice tastes sour; oven cleaner feels slippery and turns greasy stains into soap. For centuries chemists asked what every acid has in common, and what every base has in common. The simplest honest answer is that an acid hands something off and a base takes it. The whole subject is just an argument about what gets handed off — and three theories give three answers, each one broader than the last.
BUILD — BRØNSTED: PASS THE PROTON
Brønsted–Lowry says the thing handed off is a proton, $\mathrm{H^+}$ (a bare hydrogen nucleus). An acid donates it; a base accepts it. How willingly an acid lets go is captured by one number, the $pK_a$: small or negative means "lets go easily" (strong), large means "holds on tight" (weak). Put an acid HA beside a base B and the proton hops to whichever side binds it more tightly. Worked number: vinegar ($pK_a=4.76$) meets ammonia, whose conjugate acid $\mathrm{NH_4^+}$ has $pK_a=9.25$. The gap $\Delta pK_a = 9.25-4.76 = 4.49$ gives an equilibrium constant $K_{eq}=10^{4.49}\approx 3\times10^{4}$ — so the proton ends up almost entirely on the ammonia.
DEEPEN — LEWIS & HSAB: FOLLOW THE ELECTRON PAIR
Lewis zooms out: stop watching the proton, watch the electron pair. A Lewis base donates a lone pair into a Lewis acid's empty orbital, which is why $\mathrm{BF_3}$ — with no proton at all — is still an acid. Brønsted turns out to be just the special case where the empty orbital belongs to $\mathrm{H^+}$. Energetically the drive is $\Delta G^\circ = -RT\ln K_{eq} = -5.71\,\Delta pK_a$ kJ/mol at 298 K, so each unit of $\Delta pK_a$ is worth about 5.7 kJ/mol. HSAB then refines which pair reacts best: "hard" species (small, high-charge, like $\mathrm{F^-}$ and $\mathrm{Li^+}$) prefer hard partners, "soft" ones (big, polarisable, like $\mathrm{I^-}$ and $\mathrm{Hg^{2+}}$) prefer soft partners, because matched HOMO–LUMO gaps maximise the stabilisation $\Delta E^{(2)}\propto 1/(\eta_A+\eta_B)$. The sliders map straight onto this: $pK_a$ and $pK_b$ set the proton-transfer drive and $\Delta G$; the $\eta$ sliders set hardness and the HSAB-match score; the $\chi$ sliders set charge transfer; and $T$ feeds the $\Delta G$ readout live.
TRY THIS IN THE SIM ABOVE
• Load HCl + NH₃ in Brønsted mode and watch the proton fly fully across; then load HF + H₂O and see it barely budge — that is the difference between a strong and a weak acid.
• Switch to HSAB mode and compare Hg²⁺ + I⁻ (soft–soft) with Li⁺ + F⁻ (hard–hard): both score a high match. Now drag the two η sliders apart to force a hard–soft mismatch and watch the match percentage collapse.
• In any mode, drag the Temperature slider and watch ΔG and Keq update in real time.
📐 EQUATION DERIVATION
Brønsted–Lowry Equilibrium & The Conjugate Pair Relation
$$\mathrm{HA}\ +\ \mathrm{B}\ \rightleftharpoons\ \mathrm{A^-}\ +\ \mathrm{HB^+}\qquad K_{eq}=\frac{K_{a}(\mathrm{HA})}{K_{a}(\mathrm{HB^+})}=10^{\,pK_a(\mathrm{HB^+})\,-\,pK_a(\mathrm{HA})}$$
Pearson HSAB Hardness & Electronegativity (DFT formulation)
$$\eta=\frac{I-A}{2},\qquad \chi=\frac{I+A}{2},\qquad \Delta E_{\rm match}\propto -\frac{1}{\eta_A+\eta_B}$$
SymbolMeaningUnit
$K_a$Acid dissociation constant of HA in watermol L⁻¹
$pK_a$$-\log_{10} K_a$dimensionless
$K_{eq}$Equilibrium constant of the proton transferdimensionless
$\Delta G^\circ$Standard Gibbs free energy of transferkJ mol⁻¹
$I$First ionisation energyeV
$A$Electron affinityeV
$\eta$Chemical hardness (resistance to charge transfer)eV
$\chi$Mulliken absolute electronegativityeV
$R$Universal gas constant8.314 J K⁻¹ mol⁻¹
$T$Absolute temperatureK
STEP 1 — START FROM TWO ACID DISSOCIATIONS
Write the two independent water-referenced equilibria: $$\mathrm{HA}+\mathrm{H_2O}\rightleftharpoons \mathrm{A^-}+\mathrm{H_3O^+},\quad K_a^{(1)}=\frac{[\mathrm{A^-}][\mathrm{H_3O^+}]}{[\mathrm{HA}]}$$ $$\mathrm{HB^+}+\mathrm{H_2O}\rightleftharpoons \mathrm{B}+\mathrm{H_3O^+},\quad K_a^{(2)}=\frac{[\mathrm{B}][\mathrm{H_3O^+}]}{[\mathrm{HB^+}]}$$
STEP 2 — SUBTRACT (HESS-LIKE) TO REMOVE H₃O⁺
Subtracting reaction 2 from reaction 1 cancels $\mathrm{H_3O^+}$ and gives the proton-transfer equilibrium directly: $$\mathrm{HA}+\mathrm{B}\rightleftharpoons \mathrm{A^-}+\mathrm{HB^+}$$ By Hess' law applied to equilibrium constants (multiplication, not addition): $$\boxed{K_{eq}=\dfrac{K_a^{(1)}}{K_a^{(2)}}=10^{\,pK_a^{(2)}-pK_a^{(1)}}}$$
STEP 3 — RELATE TO ΔG VIA THE BOLTZMANN BRIDGE
Using $\Delta G^\circ = -RT\ln K_{eq}$ and converting from natural to common log: $$\Delta G^\circ = -RT\ln 10\,\big(pK_a^{(2)}-pK_a^{(1)}\big) = -5.71\,\Delta pK_a\;\text{kJ/mol at 298 K}$$ Thus a $\Delta pK_a = +5$ corresponds to $\Delta G^\circ \approx -28.6$ kJ/mol — a strongly favourable transfer.
STEP 4 — LEWIS PICTURE: HOMO–LUMO STABILISATION
In the Lewis framework the base donates a lone pair (HOMO) into the acid's empty orbital (LUMO). Second-order perturbation gives the stabilisation: $$\Delta E^{(2)} = -\frac{|\langle\phi_{\rm HOMO}|\hat H|\phi_{\rm LUMO}\rangle|^2}{E_{\rm LUMO}-E_{\rm HOMO}}$$ The smaller the HOMO–LUMO gap, the larger the orbital interaction.
STEP 5 — DERIVE PEARSON'S HARDNESS FROM DFT
Parr & Pearson defined hardness as the curvature of $E$ vs $N$ (number of electrons): $$\eta = \tfrac{1}{2}\left(\frac{\partial^2 E}{\partial N^2}\right)_v \approx \frac{I-A}{2}$$ where $I$ is the ionisation energy and $A$ the electron affinity (finite-difference approximation). Hard species: large gap, ionic. Soft species: small gap, polarisable.
STEP 6 — KOOPMANS' THEOREM: η FROM HOMO–LUMO
By Koopmans' theorem $I\approx -E_{\rm HOMO}$ and $A\approx -E_{\rm LUMO}$, so: $$\eta \approx \frac{E_{\rm LUMO}-E_{\rm HOMO}}{2}$$ The HSAB principle "hard prefers hard, soft prefers soft" emerges: matched gaps maximise $\Delta E^{(2)}$ in step 4. This is the unification of the three theories: Brønsted = special case of Lewis where the acceptor is H⁺; HSAB = orbital-energy refinement of Lewis.
MAPPING TO SIMULATION
• pKa, pKb sliders → $pK_a^{(1)}$ and $pK_a^{(2)}$ of the conjugate acid of B (note $pK_a + pK_b = 14$ in water).
• η sliders → hardness of acid and base; affects HSAB-map x-y position.
• χ sliders → electronegativities; charge transferred $\Delta N=(\chi_A-\chi_B)/2(\eta_A+\eta_B)$ shown in Lewis mode.
• T slider → enters $\Delta G^\circ = -RT\ln K_{eq}$ in real time.
• Mode tabs select which theory's animation runs (proton transfer / lone-pair donation / hardness-match shading).
WORKED EXAMPLE — CH₃COOH + NH₃ at 298 K
$pK_a(\mathrm{CH_3COOH}) = 4.76$ and $pK_a(\mathrm{NH_4^+}) = 9.25$. Therefore for $\mathrm{CH_3COOH}+\mathrm{NH_3}\rightleftharpoons\mathrm{CH_3COO^-}+\mathrm{NH_4^+}$:
$\Delta pK_a = 9.25-4.76 = 4.49$  ⟹  $K_{eq} = 10^{4.49} = 3.1\times10^{4}$
$\Delta G^\circ = -RT\ln K_{eq} = -(8.314)(298)\ln(3.1\times10^4)/1000 = -25.6$ kJ/mol.
The reaction lies far to the right, exactly as observed when ammonia is bubbled through vinegar.
📖 Reference: Atkins & de Paula — Physical Chemistry, 11th Ed., Ch. 7 "Chemical Equilibrium" §7E "Proton transfer equilibria"; Housecroft & Sharpe — Inorganic Chemistry, 5th Ed., Ch. 7 "Acids, bases and ions in aqueous solution"; Pearson, R. G. — J. Am. Chem. Soc. 85, 3533 (1963) "Hard and Soft Acids and Bases".
❓ FREQUENTLY ASKED QUESTIONS
ConceptualIf Brønsted, Lewis and HSAB all describe acid-base behaviour, which one is "the right" theory?
All three are correct — they just operate at different levels of generality. Brønsted-Lowry is a special case of Lewis where the electron-pair acceptor happens to be a proton (H⁺ has an empty 1s). Lewis is the broadest structural theory, applying even where no proton moves (BF₃ + NH₃, AlCl₃ catalysis, metal coordination). HSAB is not a separate theory but a quantitative refinement of Lewis, using HOMO–LUMO energies to predict which Lewis acid prefers which Lewis base. Use Brønsted for aqueous proton chemistry, Lewis for general donor–acceptor reactions, and HSAB to pick between several Lewis bases.Key Takeaway: Brønsted ⊂ Lewis, and HSAB tells you which Lewis pair will react fastest.
Real LifeWhere does HSAB matter outside textbooks?
Everywhere extraction, catalysis or biology happens. (i) Mining: soft Hg²⁺ binds soft S²⁻ — that's why mercury contaminates fish via metallothionein cysteines. (ii) Drug design: chelation therapy uses hard Ca-EDTA for hard Pb²⁺, but soft BAL (dimercaprol, two SH groups) for soft As³⁺ and Hg²⁺. (iii) Heterogeneous catalysis: Pd⁰ (soft) prefers alkenes (soft) — basis of hydrogenation. (iv) Geochemistry: "chalcophile" elements (Cu, Zn, Pb, Hg, Ag — all soft) cluster in sulfide ores; "lithophile" (Mg, Al, Si — hard) sit in silicates with hard O²⁻.Key Takeaway: The periodic table's ore distribution is HSAB written into the Earth's crust.
SimulationWhat exactly do the curly arrows in the Lewis mode mean?
A double-barbed curly arrow shows the movement of an electron pair, always starting at the lone pair (or bond) of the donor and ending where the new bond forms — at the empty orbital of the acceptor. In the simulation, the arrow's tail sits on the base's lone pair (purple lobes) and the head lands on the acid's empty p-orbital lobe (yellow). The animation timing is proportional to $\exp(-\Delta E^\ddagger / RT)$, so when you raise temperature you'll see arrows fire more frequently.Key Takeaway: Curly arrows are not decoration — they encode where electrons go and which bond forms.
Non-ObviousWhy is H₂O amphoteric but HCl is not?
Amphoterism requires having both a removable proton and a free lone pair on the same molecule. Water has two O–H bonds (can lose a proton to give OH⁻) and two lone pairs on oxygen (can accept a proton to give H₃O⁺). HCl has only one removable proton and Cl's lone pairs are far too low in energy (Cl is too electronegative) to act as a useful base in water — protonating HCl to H₂Cl⁺ requires superacid conditions like FSO₃H/SbF₅. So amphoterism is not just about geometry; it requires the lone pair to be high enough in energy to be a base and the X–H bond strong enough to retain the proton most of the time.Key Takeaway: Amphoterism = a usable lone pair on the same atom that can release a proton.
MathematicalIf $pK_a$(HF) = 3.17, what is $\Delta G^\circ$ for HF + H₂O ⇌ F⁻ + H₃O⁺ at 298 K?
$K_a = 10^{-3.17} = 6.76\times10^{-4}$. Then $\Delta G^\circ = -RT\ln K_a = -(8.314)(298)\ln(6.76\times10^{-4})/1000 = +18.1$ kJ/mol. The positive sign tells us the equilibrium lies on the HF side — HF is a weak acid even though F⁻ is a hard, electronegative atom. The reason is the unusually strong H–F bond (565 kJ/mol) and the small, highly hydrated F⁻ ion that stabilises the un-ionised form via hydrogen bonding.Key Takeaway: $\Delta G^\circ = 5.71\times pK_a$ kJ/mol at 298 K — a number worth memorising.
Deep / AdvancedIs there a connection between hardness η and chemical reactivity in general?
Yes — it is captured by the Maximum Hardness Principle (Pearson, Parr): at fixed external potential and chemical potential, molecules arrange themselves to maximise η. Stable configurations are hard; transition states are softer. The principle is rigorously derivable from density functional theory and explains, for example, why aromatic molecules (benzene η ≈ 5.3 eV) are remarkably stable while their excited states or biradicals (η < 2 eV) are reactive. HSAB is one corollary of this deeper principle.Key Takeaway: Nature prefers hardness — reactivity flows toward soft species and through soft transition states.
Real LifeWhy does soap (RCOO⁻Na⁺) feel slippery and clean grease?
Soap exhibits two acid-base behaviours simultaneously. (i) The carboxylate head is a Brønsted base — it raises the local pH and saponifies skin oils. (ii) The whole molecule is a Lewis amphiphile: the polar head binds hard water cations (Ca²⁺, Mg²⁺) which is why soap "scums" in hard water — those hard ions prefer the hard COO⁻ over the soft tail. Detergents replace COO⁻ with sulfonate (RSO₃⁻), which is borderline-hard and still works in hard water.Key Takeaway: Soap chemistry is HSAB applied to washing.
📖 Best resource for self-study: LibreTexts Chemistry — "Acid-Base Theories" (Inorganic Chemistry Library), https://chem.libretexts.org; Chemguide.co.uk — Jim Clark, "Theories of Acids and Bases"; Khan Academy — Acids, Bases & pH unit.
⚠️ COMMON MISCONCEPTIONS
❌ "Strong acid mane concentrated acid — same jinish."
✅ Strong vs concentrated are unrelated dimensions. Strength is about fraction ionised: HCl is "strong" because >99% dissociates regardless of concentration. Concentration is about amount per volume. A 0.001 M HCl solution is dilute but still 100% ionised — every HCl molecule gives H₃O⁺. Conversely a 17 M acetic acid (glacial) is concentrated but weak — fewer than 1% of molecules are ionised, so [H⁺] is actually lower than in 0.1 M HCl.
📖 Atkins & de Paula, Physical Chemistry 11e, §7E.1; Skoog et al., Fundamentals of Analytical Chemistry 9e, Ch. 9.
❌ "BF₃ er kono H nai, tahole ki kore acid hote pare?"
✅ BF₃ is the textbook example of a Lewis acid precisely because it has no proton. The boron atom is sp² hybridised with an empty p-orbital perpendicular to the BF₃ plane — that empty orbital accepts a lone pair from any donor (NH₃, F⁻, ether O). Brønsted's definition is too narrow to capture this. Lewis generalised acidity to "any electron-pair acceptor", which immediately explains why BF₃, AlCl₃, FeCl₃, Cu²⁺ etc. behave as acids in non-aqueous solvents and as Friedel-Crafts catalysts.
📖 Housecroft & Sharpe, Inorganic Chemistry 5e, §7.7; Clayden, Greeves & Warren, Organic Chemistry 2e, Ch. 8.
❌ "Hardness mane hard physically — like diamond hard."
✅ Pearson's "hardness" is a chemistry-specific term, not mechanical. It quantifies how much energy is required to add or remove an electron — formally $\eta = (I-A)/2$. Hard species (F⁻, O²⁻, Mg²⁺, H⁺) have a large HOMO–LUMO gap; their charge is concentrated and not easily polarised. Soft species (I⁻, S²⁻, Cu⁺, Hg²⁺) have a small gap and a diffuse, polarisable electron cloud. The word was chosen by analogy to "hard to deform electronically", not to physical hardness.
📖 Pearson, R. G. J. Chem. Educ. 45, 581 (1968); Housecroft & Sharpe, 5e §7.10.
❌ "Conjugate base of a strong acid is a strong base."
✅ It is the exact opposite. Conjugate base of a strong acid is a negligibly weak base. Cl⁻ is the conjugate base of HCl ($pK_a = -7$); the corresponding $pK_b$ of Cl⁻ is $14-(-7)=21$, meaning Cl⁻ in water is a vastly poorer base than even water itself. This is the quantitative content of $pK_a + pK_b = pK_w = 14$. Strong acids have weak conjugate bases because the proton has already left and the anion has no driving force to take it back.
📖 Atkins & de Paula, 11e §7E.2; Silberberg, Chemistry: The Molecular Nature of Matter and Change 8e, Ch. 18.
❌ "HSAB just ekta rule — exception onek."
✅ HSAB is not a hard rule but a quantitative tendency derivable from second-order perturbation theory: $\Delta E^{(2)} \propto 1/(\eta_A+\eta_B)$. Apparent exceptions usually arise when steric effects, solvent or charge magnitude dominate. For instance, OH⁻ binding Al³⁺ (both hard) is HSAB-favoured, but in water solvation cages the kinetics may differ. The exceptions are not failures of HSAB; they are reminders that HSAB is one term among several in $\Delta G$.
📖 Pearson, R. G. Chemical Hardness, Wiley-VCH (1997), Ch. 1–2; Parr & Yang, Density-Functional Theory of Atoms and Molecules, OUP (1989), §5.3.
❌ "Lewis acid = electron deficient species, like cation; Lewis base = anion. Bas ei rule."
✅ Lewis acidity/basicity is about frontier orbitals, not net charge. Neutral molecules can be strong Lewis acids: BF₃, BCl₃, AlCl₃, SO₃ all have empty acceptor orbitals. Cations need not be Lewis acids: NMe₄⁺ has no accessible empty orbital and is essentially inert. Anions need not be Lewis bases: ClO₄⁻ is a textbook non-coordinating anion despite carrying −1 charge, because its lone pairs are very low-lying. Always look at HOMO/LUMO, not at the ± sign.
📖 Housecroft & Sharpe, 5e §7.7; Taber, K. S. Chemical Misconceptions: Prevention, Diagnosis and Cure, RSC (2002), Vol. II Ch. 6.
📖 Education research: Cooper, M. M. et al. — J. Chem. Educ. 93, 1703 (2016) "Lewis structures, formal charge, and oxidation numbers"; Bhattacharyya, G. — CERP 15, 594 (2014) "Trusting the textbook: students and acid-base concepts"; Taber, K. S. — Chemical Misconceptions, RSC (2002), Vol. II.