Study sheet: Fundamentals of Acid-Base Chemistry

📋 Course Outline

1. Acid-base concepts and definitions
2. Acid-base reactions and strength
3. Acidity constants and pKa
4. pH, neutrality and solution domains
5. Approximations in pH calculations
6. Strong acids and strong bases
7. Weak acids and weak bases
8. Mixing acid and base solutions
9. Acid-base titrations
10. Buffer solutions and capacity

📖 1. Acid-base concepts and definitions

🔑 Key Concepts & Definitions

• Arrhenius acid : An Arrhenius acid is a compound that releases hydrogen ions when dissolved in water.
• Arrhenius base : An Arrhenius base is a compound that dissociates in water to release hydroxide ions.
• Brønsted acid : A Brønsted acid is a proton donor that can release $H^+$.
• Brønsted base : A Brønsted base is a proton acceptor that can capture $H^+$.
• Conjugate acid-base pair : A conjugate acid-base pair is formed when an acid donates a proton to become a base, or when a base accepts a proton to become an acid.

📝 Essential Points

• The Arrhenius definition is limited to aqueous solutions and fails for compounds without hydroxide ions or for ionic entities’ acid-base behavior.
• In the Brønsted model, acid-base behavior does not depend on the solvent and applies to both molecules and ions.
• Acid-base reactions proceed by proton transfer between conjugate acid-base pairs; free $H^+$ does not exist in solution.
• A conjugate acid corresponds to a base that is produced by removing one proton, and vice versa.
• Water can act as an acid or a base because it can donate or accept a proton depending on what it reacts with.

💡 Memory Hook

Conjugates flip roles: acid donates $H^+$ → base; base accepts $H^+$ → acid.

📖 2. Acid-base reactions and strength

🔑 Key Concepts & Definitions

• Acid-base reaction : An acid-base reaction is a proton transfer between two conjugate acid/base pairs in which no free protons remain in solution.
• Leveling effect of water : In water, any acid/base stronger than hydronium or hydroxide is converted so that the observable strength is capped at H3O+ or OH−.

📝 Essential Points

• An acid can donate a proton only when a base is present to accept it, so proton transfer always involves both partners.
• For two conjugate acid/base pairs, a equilibrium constant K>1 implies acid1 is stronger than acid2 and base2 is stronger than base1.
• The Golden Rule states that the strongest acids have the weakest conjugate bases and vice versa.
• In aqueous solution, it is impossible for an acid stronger than H3O+ to exist because water converts it completely to H3O+.
• All strong acids appear equally strong in water because their dissociation is leveled to the same H3O+ strength.
• Strong bases are leveled in the same way, and to rank strong acids beyond this leveling a less basic solvent such as methanol is required.

💡 Memory Hook

Leveling effect: water caps strengths—strong acids get turned into H3O+, and strong bases into OH−.

📖 3. Acidity constants and pKa

🔑 Key Concepts & Definitions

• Acidity constant Ka : The acidity constant is the thermodynamic equilibrium constant for the acid reacting with water to produce its conjugate base and hydronium.
• Basicity constant Kb : The basicity constant is the thermodynamic equilibrium constant for the base reacting with water to produce its conjugate acid and hydroxide.
• pKa : pKa is defined as the negative base-10 logarithm of Ka, linking acid strength to a convenient scale.
• Golden Rule of strength : The strength ranking connects acids and conjugate bases so that the stronger acid corresponds to the weaker conjugate base, and vice versa.

📝 Essential Points

• Using water as the standard reference, Ka and Kb are thermodynamic equilibrium constants for reactions with water at a given temperature.
• For a conjugate acid/base pair at the same temperature, the product Ka×Kb gives the self-ionization constant through cancellation of acid and base concentration terms.
• Ka and Kb are inversely proportional for the same conjugate pair at a fixed temperature.
• pKa equals −log10(Ka), so smaller pKa means a stronger acid with a weaker conjugate base.
• Higher pKa corresponds to a weaker acid and a stronger conjugate base.

💡 Memory Hook

Golden Rule: Strong acid ↔ weak conjugate base (and strong base ↔ weak conjugate acid).

📖 4. pH, neutrality and solution domains

🔑 Key Concepts & Definitions

• pH : pH is an experimental measure of how acidic a solution is based on the hydronium ion activity, expressed on a logarithmic scale.
• Neutral solution : A neutral solution is one where hydronium and hydroxide concentrations are equal because only water autoionization sets the balance.
• Hydronium concentration : Hydronium concentration is the amount of $\mathrm{H_3O^+}$ present in solution and it directly determines the pH under dilute, pure-solution conditions.
• Water autoionization equilibrium : Water autoionization equilibrium is the balance where water produces $\mathrm{H_3O^+}$ and $\mathrm{OH^-}$ with equal concentrations in pure water.
• Solution domain (acidic/basic) : Solution domains categorize solutions as acidic or basic by whether $[\mathrm{H_3O^+}]$ or $[\mathrm{OH^-}]$ is larger than the neutral benchmark set by water.

📝 Essential Points

• For ideal dilute solutions, pH can be computed from the $\mathrm{H_3O^+}$ concentration using $\mathrm{pH}=\log_{10}\!\left(\frac{[\mathrm{H_3O^+}]}{c^\circ}\right)$ with $c^\circ=1\,\mathrm{mol\,L^{-1}}$ to make the log argument dimensionless.
• In pure water, autoionization gives $[\mathrm{H_3O^+}]=[\mathrm{OH^-}]=K_e$, so neutral pH is $\mathrm{pH}=-\log_{10}(K_e)$.
• For an acidic solution, extra $\mathrm{H_3O^+}$ makes $[\mathrm{H_3O^+}]>[\mathrm{OH^-}]$, hence $\mathrm{pH}<-\log_{10}(K_e)$.
• For a basic solution, dissolving a base increases $[\mathrm{OH^-}]$ so $[\mathrm{H_3O^+}]<[\mathrm{OH^-}]$, hence $\mathrm{pH}>-\log_{10}(K_e)$.
• The pH-to-$[\mathrm{H_3O^+}]$ link assumes ideal dilute behavior where solute–solute interactions do not disrupt hydronium behavior.

💡 Memory Hook

Acid: adds $\mathrm{H_3O^+}$ → pH falls below $-\log_{10}(K_e)$; Base: adds $\mathrm{OH^-}$ → pH rises above $-\log_{10}(K_e)$.

📖 5. Approximations in pH calculations

🔑 Key Concepts & Definitions

• Species predominance : Species predominance means the major dissolved form sets the pH while minor forms can often be ignored.
• Neglecting water autoionization : Neglecting water autoionization assumes the natural $\mathrm{H_3O^+}$ or $\mathrm{OH^-}$ from water is negligible compared with that from the acid or base.
• Weak acid protolysis approximation : Weak acid protolysis approximation treats a weak acid as barely dissociated so the initial acid concentration is essentially unchanged.
• Extremely dilute strong acid : Extremely dilute strong acid is a strong-acid case where water autoionization is comparable to the acid contribution, so a full quadratic balance is needed.

📝 Essential Points

• Exact pH requires solving electroneutrality plus mass conservation with all equilibria constants, which can reduce to polynomial equations of degree 3.
• Approximations are acceptable when the predicted pH error stays within about 0.05 pH units.
• For neglecting water in acid form, use $c(\mathrm{H_3O^+})_{eq}\ge 10K_e$ or equivalently $\mathrm{pH}\le -\log_{10}(10K_e)$.
• For weak acids, the “<10% dissociation” condition is enforced via the degree of dissociation $\alpha=(c(\mathrm{A^-})_{eq})/(c(\mathrm{AH})_i)$ being less than 10%.
• For extremely dilute strong acids near $10^{-8}\,\mathrm{mol\,L^{-1}}$, compute $c(\mathrm{H_3O^+})_{eq}$ from the quadratic $c(\mathrm{H_3O^+})^2-c(\mathrm{AH})_i\,c(\mathrm{H_3O^+})-K_e=0$ and take the positive root.

💡 Memory Hook

When pH is not extreme, one species rules; only at very dilute conditions do you “bring back water” and solve the quadratic.

📖 6. Strong acids and strong bases

🔑 Key Concepts & Definitions

• Strong acid solution species : In a strong acid, the most abundant species among $\mathrm{H_3O^+}$, $\mathrm{A^-}$, $\mathrm{OH^-}$, and $\mathrm{H_2O}$ depends on concentration.
• Standard strong acid approximation : For sufficiently concentrated strong acids at 25°C with $\mathrm{pH}<6.5$, hydronium is much larger than water autoionization and dominates over conjugate-base and hydroxide contributions.
• Extremely dilute strong base : For extremely low strong-base concentration around $10^{-8}\,\mathrm{mol\,L^{-1}}$, hydroxide from water autoionization cannot be ignored.
• Complete dissociation of strong base : A strong monobase dissociates completely in water so the equilibrium hydroxide concentration equals the initial dissolved base concentration.

📝 Essential Points

• For a standard strong acid at 25°C with $\mathrm{pH}<6.5$, the abundance ranking is $c\,\mathrm{H_2O}\gg c\,\mathrm{H_3O^+}=c\,\mathrm{A^-}>c\,\mathrm{(OH^-)}$.
• For an extremely dilute strong acid, the ranking becomes $c\,\mathrm{H_2O}\gg c\,\mathrm{H_3O^+}>c\,\mathrm{A^-}>c\,\mathrm{(OH^-)}$.
• For a strong monobase with initial concentration $c\,(\mathrm{BOH})_i$, $c\,(\mathrm{OH^-})_{eq}=c\,(\mathrm{BOH})_i$ when water’s contribution to $\mathrm{OH^-}$ is neglected.
• Using $K_e=c\,(\mathrm{H_3O^+})_{eq}\,c\,(\mathrm{OH^-})_{eq}$ gives $\mathrm{pH}=\mathrm{p}K_e+\log_{10}\!\left(\frac{c\,(\mathrm{BOH})_i}{c^\circ}\right)$ for the standard strong base case.
• For extremely dilute strong bases, the resulting equation for $c\,(\mathrm{H_3O^+})_{eq}$ is quadratic and only the positive root is physically valid.

💡 Memory Hook

Dilute-strong cases lead to a quadratic, and the physical solution is the positive root for $c(\mathrm{H_3O^+})$.

📖 7. Weak acids and weak bases

🔑 Key Concepts & Definitions

• Water autoionization : Water autoionization describes the equilibrium that generates both hydronium and hydroxide ions in pure water.
• Hydronium balance : A hydronium balance is the equation that accounts for all contributions to the equilibrium hydronium concentration in solution.
• Hydroxide balance : A hydroxide balance is the equation that accounts for all contributions to the equilibrium hydroxide concentration in solution.
• Dissociation fraction alpha : The dissociation fraction alpha measures what fraction of a weak acid or weak base has dissociated at equilibrium.

📝 Essential Points

• For a weak acid, if approximations are valid then $\mathrm{pH}=\tfrac{1}{2}(\mathrm{p}K_a-\log_{10}c_i)$ after verifying the approximations work.
• Weak-acid approximation 1 is valid when water is negligible, which requires $\mathrm{pH}<6.5$.
• Weak-acid approximation 2 is valid when $\alpha<10\%$, which is equivalent to checking $\mathrm{pH}\le \mathrm{p}K_a-1$.
• If $\alpha>10\%$ for a weak acid, use $c(\mathrm{AH})_{eq}=c_i-(\mathrm{H_3O^+})_{eq}$ and solve the quadratic $c(\mathrm{H_3O^+})_{eq}^2+K_a(\mathrm{H_3O^+})_{eq}-K_a c_i=0$.
• If a weak acid is extremely dilute with $\mathrm{pH}>6.5$, include water autoionization so $c(\mathrm{H_3O^+})_{eq}=K_a c_i+K_e$ (when the acid still does not fully dissociate).
• For a weak base, if approximations are valid then $\mathrm{pH}=\tfrac{1}{2}(\mathrm{p}K_a+\mathrm{p}K_e+\log_{10}c_i)$, and validity requires $\mathrm{pH}>7.5$ and $\mathrm{pH}>\mathrm{p}K_a+1$.

📖 8. Mixing acid and base solutions

🔑 Key Concepts & Definitions

• Strong acid mixture : A strong acid mixture is treated as complete dissociation, so hydronium concentrations add directly for each acid added.
• Strong base mixture : A strong base mixture is treated as complete dissociation, so hydroxide concentrations add directly for each base added.
• Henderson approximation : The Henderson approximation assumes both members of a weak acid/conjugate base pair keep near their initial concentrations during mixing.
• Henderson-Hasselbalch equation : The Henderson-Hasselbalch equation relates pH to pKa and the concentration ratio of a conjugate base to its weak acid.

📝 Essential Points

• When mixing two strong acids, $c(H_3O^+)_{eq}=c(aci1)_i+c(aci2)_i$, and pH is computed as for a single strong acid with that total.
• When mixing two strong bases, $c(OH^-)_{eq}=c(base1)_i+c(base2)_i$, and pOH/pH is then obtained from the hydroxide concentration.
• When mixing a strong acid with a weak acid, the strong acid dominates so the mixture pH follows $pH=-\log_{10}(c_{strong\,acid})$.
• For a weak acid plus its conjugate base, Henderson gives $pH=pK_a+\log_{10}\left(\dfrac{c(base)_i}{c(acid)_i}\right)$.
• Henderson fails in highly acidic or highly basic mixtures, requiring exact mass balances via a quadratic Ka relation for acidic cases.

💡 Memory Hook

Strong beats weak: strong-dominates pH, but weak+conjugate uses Henderson-Hasselbalch via the base/acid ratio.

📖 9. Acid-base titrations

🔑 Key Concepts & Definitions

• Titration : Titration is an analytical technique that finds an unknown concentration by reacting it with a reagent of known concentration until a completion signal is reached.
• Equivalence point : The equivalence point is reached when the titrant has been added in the exact stoichiometric amount needed to react with all of the analyte.
• Weak acid–strong base titration buffer region : In a weak acid–strong base titration, added hydroxide converts AH into A− so both species coexist and the pH changes slowly before equivalence.
• Half-equivalence condition : Half-equivalence occurs when half of the weak species has been converted, making the relevant conjugate-pair concentrations equal.

📝 Essential Points

• In a strong acid–strong base titration (1:1), the pH at the equivalence point is 7.00 at 298 K.
• A strong acid–strong base titration shows a near-vertical pH jump around VE, where adding about 0.1 mL of base can shift pH by several units.
• For a weak acid–strong base titration, the half-equivalence point satisfies [AH]=[A−], so the Henderson log term becomes zero and it gives a reliable pKa measurement.
• For a weak acid–strong base titration, the pH at equivalence is always greater than 7 because the solution contains the weak base A−.
• For a weak base–strong acid titration, the pH at equivalence is always acidic (pH < 7) because all B is converted to BH+.

💡 Memory Hook

Equivalence means stoichiometry; half-equivalence means equal conjugate partners so the log term becomes 0.

📖 10. Buffer solutions and capacity

🔑 Key Concepts & Definitions

• Buffer solution : A buffer solution is an aqueous system that resists major pH changes when small amounts of acid or base are added or when it is diluted.
• Buffer capacity : Buffer capacity is the amount of strong acid or strong base a solution can absorb before it stops effectively resisting pH changes.
• Buffer capacity efficiency : Buffer efficiency is maximal when the conjugate-pair concentrations satisfy [Base]/[Acid] = 1 so the buffer works best around its pKa.

📝 Essential Points

• A higher total concentration of buffer species (acid + base) increases buffer capacity by providing more conjugate pairs to neutralize added titrant.
• A buffer works most efficiently when [Base]/[Acid] = 1, which corresponds to pH = pKa for the conjugate pair.
• A buffer maintains useful properties when 0.1 ≤ [Base]/[Acid] ≤ 10, i.e., when pH is within pKa ± 1.
• Outside the working window around pKa ± 1, buffer capacity drops significantly.

💡 Memory Hook

Capacity ↑ with total [acid+base]; efficiency peaks at [Base]=[Acid] → pH=pKa; useful window is pKa±1 (or ratio 0.1 to 10).

📅 Key Dates

1. 1923Brønsted concept introduced
2. OCTOBRE 2020Course chapter/notes reference date
3. 25°CTemperature used for strong-acid leveling/standard cases
4. 298 KCondition for strong acid–strong base titration pH at equivalence

📊 Synthesis Tables

Arrhenius vs Brønsted definitions

Model	Acid definition	Base definition	Scope
Arrhenius	Releases hydrogen ions in aqueous solution	Dissociates in water to release hydroxide ions	Strictly limited to aqueous solutions; fails for compounds lacking hydroxide ions and ionic entities’ behavior
Brønsted	Proton donor (capable of releasing H+)	Proton acceptor (capable of capturing H+)	Independent of the solvent used; applies to neutral molecules and ions

Strong vs weak species (strength criteria and consequences)

Species	Strength criterion (K with water)	Dissociation behavior	Strength ranking notes
Strong acid/base	K > 1	Virtually complete (total reaction in one direction)	Strength is leveled by water to H3O+ or OH−; all strong acids (bases) appear equally strong in water
Weak acid/base	K < 1	Partial dissociation only	Acid/base strengths are characterized by pKa; approximations apply in pH domains

⚠️ Common Pitfalls & Confusions

1. Confusing Arrhenius with Brønsted: Arrhenius is limited to aqueous solutions and hydroxide release, while Brønsted applies to any solvent and treats proton transfer for molecules and ions.
2. Thinking free H+ exists in solution: acid-base reactions are proton transfers between conjugate pairs with “no free protons remain in solution.”
3. Mixing up the Golden Rule direction: stronger acid ↔ weaker conjugate base (and stronger base ↔ weaker conjugate acid).
4. Using pH=−log10([H3O+]/c°) incorrectly by forgetting the dimensionless standard concentration c°=1 mol/L.
5. Applying the “ignore water” approximation to weak acids/bases without checking validity conditions (pH<6,5 / pH>7,5 and the α<10% equivalents).
6. Assuming Henderson-Hasselbalch always works when mixing conjugate pairs: it fails in highly acidic or highly basic mixtures where reaction extent is no longer negligible.
7. At equivalence in titrations: believing strong acid–strong base is the only case with pH=7; weak acid–strong base equivalence is always >7 and weak base–strong acid equivalence is always <7.

✅ Exam Checklist

1. State the Arrhenius definitions of acid/base and why they are limited to aqueous solutions.
2. State the Brønsted definitions of acid/base and what “conjugate acid-base pair” means (including every acid ⇄ conjugate base).
3. Explain acid-base reaction rules: proton donation requires a base acceptor, proton transfer between conjugate pairs, and no free H+ remains in solution.
4. Use competition interpretation of K>1 to conclude stronger acid and stronger base, and state the Golden Rule pairing.
5. Define Ka and Kb as thermodynamic equilibrium constants for reactions with water, and connect pKa=−log10(Ka) with strength ranking.
6. Write the water autoionization (2 H2O → H3O+ + OH−) and state pKe=−log10(Ke) and the neutral pH condition.
7. Compute/relate pH to hydronium: pH=log10([H3O+]/c°) (dimensionless log argument), and determine whether pH is above/below −log10(Ke) for acidic/basic solutions.
8. Choose the correct pH-approximation method by checking validity: neglect water (c(H3O+)eq ≥10Ke) and for weak acids/bases verify the α<10% conditions (pH<6,5 etc.).
9. Solve/identify the “extremely dilute” strong acid or strong base case requiring the quadratic in c(H3O+)eq with only the positive root physical.
10. Apply weak acid and weak base formulas when approximations are valid (pH=1/2(pKa−log10 ci) for weak acids; pH=1/2(pKa+pKe+log10 ci) for weak bases) and state when to switch to quadratic equations.
11. Use mixing rules in order of strength: strong+strong add H3O+/OH−; strong acid+weak acid gives pH from the strong acid only; weak acid+conjugate base uses Henderson-Hasselbalch and state when it fails.
12. For titrations, state equivalence/half-equivalence meanings and the key pH facts: strong acid–strong base at equivalence gives pH=7.00 (298 K), weak acid–strong base equivalence pH>7 with half-equivalence [AH]=[A−] for pKa, and weak base–strong acid equivalence pH<7.
13. Define buffer solutions and buffer capacity, then use the efficiency rule [Base]/[Acid]=1 (pH=pKa) and the working window 0.1 ≤ [Base]/[Acid] ≤ 10 (pH within pKa ± 1).