Unit 8 Beta

Acids and Bases: the one-page sheet

8.1 Introduction to Acids and Bases

Water ionizes itself slightly, so every water solution holds both H₃O⁺ and OH⁻, tied together by Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. pH and pOH are base-10 logarithm scales of the two concentrations, adding to 14.00 at 25 °C. Neutral means equal concentrations, which falls at pH 7 only at 25 °C.

Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, in every water solution. Know one ion and you know the other.
pH = −log[H₃O⁺] and pOH = −log[OH⁻]; at 25 °C pH + pOH = 14.00. One pH unit is ten times the [H₃O⁺].
Acidic: [H₃O⁺] > [OH⁻]. Basic: [OH⁻] > [H₃O⁺]. Neutral: equal. Neutral is pH 7.00 only at 25 °C.
Significant figures: the pH gets as many decimal places as the concentration has significant figures.

pure water always holds equal, tiny amounts of H₃O⁺ and OH⁻ Kw = [H₃O⁺][OH⁻] has one value at a given temperature: 1.0 × 10⁻¹⁴ at 25 °C some of the added H₃O⁺ reacts with OH⁻ until the product is back to Kw, so [OH⁻] falls chemists report them as pH = −log[H₃O⁺], where each unit is a factor of ten warm water has a larger Kw, so neutral water there has a pH below 7

Kw: The ion product of water, Kw = [H₃O⁺][OH⁻]. It equals 1.0 × 10⁻¹⁴ at 25 °C and rises with temperature, because water's self-ionization, 2 H₂O ⇌ H₃O⁺ + OH⁻, absorbs heat.
pH: pH = −log[H₃O⁺], a base-10 logarithm scale of hydronium concentration; pOH = −log[OH⁻]. At 25 °C, pH + pOH = 14.00. One pH unit is a factor of ten in [H₃O⁺].
acidic solution: A solution is acidic when [H₃O⁺] > [OH⁻], basic when [OH⁻] > [H₃O⁺], and neutral when they are equal. Neutral is pH 7.00 only at 25 °C.

8.2 pH and pOH of Strong Acids and Bases

Strong acids and strong bases ionize fully, so [H₃O⁺] or [OH⁻] comes straight from the concentration (doubled for hydroxides such as Ba(OH)₂). When they are mixed, the H₃O⁺ and OH⁻ cancel mole for mole; the pH comes from whatever is left over, divided by the total volume.

Strong acids: HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ (first proton). Strong bases: group 1 hydroxides, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂.
Strong acid: [H₃O⁺] = C. Strong base: [OH⁻] = C × (number of OH⁻ per formula unit), then pOH, then pH.
Mixing: moles first, subtract, divide the excess by the total volume, then take the log.
At equivalence, strong acid + strong base gives a neutral salt solution: pH 7.00 at 25 °C.

no acid molecules remain, and [H₃O⁺] equals the acid concentration [OH⁻] equals the base concentration times the OH⁻ per formula unit mixing strong acid and strong base leaves only the excess of whichever had more moles its concentration, and then the pH, comes from the excess moles over the total volume

strong acid: An acid that ionizes fully in water, so [H₃O⁺] equals the acid concentration: HCl, HBr, HI, HNO₃, HClO₄ and the first proton of H₂SO₄. A strong base dissociates fully into OH⁻: the group 1 hydroxides and Ca(OH)₂, Sr(OH)₂ and Ba(OH)₂.

8.3 Weak Acid and Base Equilibria

A weak acid or base reacts with water only partly, so its pH comes from an equilibrium. With Ka (or Kb) and the concentration, an ICE table and the small-x approximation give [H₃O⁺] ≈ √(Ka·C). Percent ionization rises on dilution, and a conjugate pair obeys Ka × Kb = Kw.

Weak acid: Ka ≪ 1, mostly un-ionized. Larger Ka (smaller pKa) = stronger acid.
Weak acid pH: [H₃O⁺] = x ≈ √(Ka × C). Check x < 5% of C; if not, solve the quadratic.
Weak base: same method with Kb to find [OH⁻], then pOH, then pH.
Ka × Kb = Kw for a conjugate pair; pKa + pKb = 14.00 at 25 °C. Kb is not 1/Ka.

HA + H₂O ⇌ H₃O⁺ + A⁻ reaches equilibrium with most HA un-ionized (Ka ≪ 1) an ICE table gives Ka = x²/(C − x) ≈ x²/C, so [H₃O⁺] ≈ √(Ka·C) Q falls below Ka, so a larger fraction ionizes: percent ionization rises Ka × Kb = Kw, so the weaker the acid, the stronger its conjugate base

weak acid: An acid that ionizes only partly in water (Ka much less than 1), so at equilibrium most of it stays as whole HA molecules. A weak base, such as NH₃, accepts protons from water only partly.
acid dissociation constant: The acid dissociation constant, Ka = [H₃O⁺][A⁻]/[HA], the equilibrium constant for HA + H₂O ⇌ H₃O⁺ + A⁻; pKa = −log Ka, so a smaller pKa means a stronger acid. Kb and pKb do the same for a base.
percent ionization: The share of a weak acid that has ionized at equilibrium: [H₃O⁺]eq / [HA]initial × 100%. It rises as the acid is diluted.
Ka × Kb = Kw: For an acid and its conjugate base, Ka × Kb = Kw (1.0 × 10⁻¹⁴ at 25 °C), so pKa + pKb = 14.00. The weaker the acid, the stronger its conjugate base.

8.4 Acid-Base Reactions and Buffers

When a strong acid or base meets a weak one, the reaction goes to completion, so you react the moles first and then ask what is left. Leftover weak acid plus its conjugate base is a buffer, with [H₃O⁺] = Ka × [HA]/[A⁻]; only the conjugate base left means a basic solution; excess strong base sets the pH by itself.

Strong + weak acid-base reactions go to completion (K = Ka/Kw or Kb/Kw, huge). Use moles, react first, then find the pH.
At equivalence: strong acid + strong base gives pH 7; weak acid + strong base gives a basic solution; weak base + strong acid an acidic one.
A buffer is a weak acid with its conjugate base (or a weak base with its conjugate acid) in similar amounts.
Make a buffer by mixing HA with a salt of A⁻, or by adding strong base to a weak acid (less than one mole of base per mole of acid).

the reaction goes essentially to completion: do it first, with moles the mixture is a buffer, and [H₃O⁺] = Ka × [HA]/[A⁻] the solution is basic at equivalence, not neutral the added ions are used up and the pH changes only a little

buffer: A solution of a weak acid and its conjugate base (or a weak base and its conjugate acid) in similar amounts. Added acid reacts with the base of the pair and added base with the acid, so the pH changes only a little.

8.5 Acid-Base Titrations

A titration curve shows four regions. The equivalence volume gives the moles of analyte; half that volume is the half-equivalence point, where [HA] = [A⁻] and pH = pKa. The equivalence pH is 7 only for a strong acid with a strong base; it is basic for a weak acid and acidic for a weak base. A polyprotic acid shows one equivalence point per proton.

Equivalence volume → moles of analyte → its concentration. The steep rise is centered on it.
Half-equivalence (half the equivalence volume): [HA] = [A⁻], so pH = pKa. Do not confuse it with equivalence.
Equivalence pH: 7 for strong/strong; above 7 for weak acid + strong base; below 7 for weak base + strong acid.
Weak base titrated with strong acid: pH at half-equivalence is the pKa of the conjugate acid (14.00 − pKb), not pKb.
Polyprotic acids: one equivalence point per proton; pKa₁, pKa₂ at each half-equivalence.

the flask holds HA and A⁻ together, so the pH climbs slowly (the buffer region) [HA] = [A⁻], so Ka = [H₃O⁺] and pH = pKa each drop changes the pH sharply: the steep rise the equivalence point of a weak acid is above pH 7 a diprotic acid shows two equivalence points, equally spaced in volume

titration curve: A graph of pH against volume of titrant added. Its steep rise (or fall) is centered on the equivalence point; its shape shows whether the acid or base is strong or weak.
half-equivalence point: The point in a weak acid (or weak base) titration where half the analyte has reacted, at half the equivalence volume. There [HA] = [A⁻], so pH = pKa.
buffer region: The flat, slowly rising part of a weak acid or weak base titration curve before the equivalence point, where the weak species and its conjugate are both present.
polyprotic acid: An acid that can give up more than one proton, one at a time (diprotic H₂A, triprotic H₃A). Each proton has its own Ka, and a titration curve can show one equivalence point per proton.

8.6 Molecular Structure of Acids and Bases

An acid is strong when the ion it leaves behind is stable. Electronegative atoms pull electron density from the acidic group, resonance spreads the charge of the conjugate base, and a large atom holds charge over a larger volume; each makes Ka larger. Amines are weak bases that accept a proton on the nitrogen lone pair.

Acid strength follows conjugate base stability. Stabilize A⁻ and Ka goes up.
Oxyacids: more O atoms, or a more electronegative central atom, means a stronger acid (HOI < HOBr < HOCl < HOClO).
Carboxylic acids: the carboxylate is stabilized by resonance; electron-withdrawing groups (Cl, F) nearby make the acid stronger.
Binary acids: across a period electronegativity rules (CH₄ < NH₃ < H₂O < HF); down a group bond strength rules (HF < HCl < HBr < HI).
Amines (–NH₂) are weak bases: the proton goes on the N lone pair.

the more stable A⁻ is, the further HA + H₂O ⇌ H₃O⁺ + A⁻ lies to the right the negative charge of A⁻ is less concentrated, so A⁻ is more stable and Ka is larger carboxylic acids are far stronger than alcohols, and oxyacids with more O are stronger HF < HCl < HBr < HI and H₂O < H₂S < H₂Se in acid strength amines are weak bases that accept a proton on nitrogen

acid strength: How fully an acid gives up its proton, measured by Ka. An acid is stronger when its conjugate base is more stable: the negative charge spread by resonance, pulled by electronegative atoms, or held on a large atom.
oxyacid: An acid in which the acidic H is bonded to an O that is bonded to a central atom (H–O–X), such as HOCl or HNO₃. More O atoms or a more electronegative central atom makes it stronger.
carboxylic acid: A carboxylic acid (–COOH) is a weak acid whose conjugate base, the carboxylate (–COO⁻), is stabilized by resonance. An amine (–NH₂) is a weak base that accepts a proton on its nitrogen lone pair.

8.7 pH and pKa

Comparing pH with pKa tells you which form of an acid is in the majority: protonated below pKa, deprotonated above it, equal at pKa, with a tenfold change in ratio for every pH unit. An indicator is a weak acid whose two forms have different colors, so it changes over about pKa ± 1; choose one whose pKa matches the equivalence-point pH.

pH < pKa: protonated form (HA, or BH⁺) predominates. pH > pKa: deprotonated form (A⁻, or B). pH = pKa: equal.
Every pH unit away from pKa is a factor of 10 in [A⁻]/[HA]: ratio = 10^(pH − pKa).
An indicator HIn changes color over about pKa ± 1.
Pick the indicator whose pKa is near the equivalence-point pH: phenolphthalein for weak acid + strong base, a pKa near 5 for weak base + strong acid.

[A⁻]/[HA] = Ka/[H₃O⁺] = 10^(pH − pKa) the ratio is below 1: the protonated form HA predominates the deprotonated form A⁻ predominates; at pH = pKa they are equal its color switches over about pKa ± 1, where neither form outnumbers the other more than tenfold choose an indicator whose pKa is close to the equivalence-point pH

protonated form: Which form of an acid is in the majority: the protonated form (HA) when pH < pKa, the deprotonated form (A⁻) when pH > pKa, equal amounts when pH = pKa. Each pH unit away from pKa is a tenfold ratio.
acid-base indicator: An acid-base indicator is a weak acid, HIn, whose two forms differ in color; it changes color over about pKa ± 1. Choose one whose pKa is close to the equivalence-point pH.

8.8 Properties of Buffers

A buffer resists pH change because its two components react with whatever is added: the conjugate base takes up added acid and the weak acid takes up added base. Only the ratio [A⁻]/[HA] sets the pH, so additions shift it slightly and dilution barely at all.

Buffer action: added acid is consumed by A⁻; added base is consumed by HA. The added ion is turned into a member of the pair.
Buffer pH depends on the ratio [A⁻]/[HA], not on the amounts. Same ratio, same pH.
Diluting a buffer barely changes its pH.
A buffer limits pH change; it does not stop it. Each addition shifts the ratio a little.

H₃O⁺ + A⁻ → HA + H₂O runs to completion, so the added H₃O⁺ does not stay free OH⁻ + HA → A⁻ + H₂O runs to completion, so the added OH⁻ does not stay free the ratio [A⁻]/[HA] changes slightly, so [H₃O⁺] = Ka × [HA]/[A⁻] changes slightly the ratio, and so the pH, stays almost the same

buffer action: How a buffer resists pH change: added H₃O⁺ reacts with the conjugate base and added OH⁻ reacts with the weak acid, so the ratio [A⁻]/[HA], and the pH, change only slightly. Dilution leaves the ratio, and so the pH, almost unchanged.

8.9 Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation, pH = pKa + log([A⁻]/[HA]), is the Ka expression in log form. It gives a buffer's pH from its ratio, and works backwards to design a buffer: pick an acid with pKa near the target, find the ratio 10^(pH − pKa), and turn it into amounts. Use base-10 log, and pKa of the conjugate acid for a weak base buffer.

pH = pKa + log([A⁻]/[HA]), base on top, base-10 log (never ln).
Moles can replace concentrations: both share one volume, which cancels.
Weak base buffer (NH₃/NH₄⁺): use pKa of the conjugate acid, 14.00 − pKb.
To make a buffer: choose pKa ≈ target pH, find the ratio 10^(pH − pKa), then the amounts (or the volume of NaOH for partial neutralization).

taking −log of both sides gives pH = pKa + log([A⁻]/[HA]) log 1 = 0, so pH = pKa moves the pH by exactly one unit (base-10 log) pick an acid whose pKa is within about 1 of the target pH, then set the ratio

Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]), the Ka expression in log form, for a buffer of a weak acid HA and its conjugate base A⁻. The log is base 10; for a weak base buffer, use pKa of its conjugate acid.

8.10 Buffer Capacity

Buffer capacity is how much strong acid or base a buffer can absorb before its pH changes sharply. It depends on the moles of the components, not the pH: more of each, more capacity, with capacity for base set by HA and for acid by A⁻. Capacity is balanced at pH = pKa, and the buffer fails once one component is used up.

Buffer capacity grows with the moles of HA and A⁻. Same ratio, more material: same pH, bigger capacity.
Capacity for added base depends on HA; capacity for added acid depends on A⁻.
A buffer works best within pKa ± 1, where neither component is less than a tenth of the other.
Once a component is used up, find the pH from the excess strong acid or base, not from Henderson-Hasselbalch.

the moles of the components set how much acid or base the buffer can absorb has a larger capacity, even at the same pH capacity for acid and for base is balanced, at pH = pKa the next addition stays free and the pH jumps, as in the steep part of a titration curve

buffer capacity: How much strong acid or base a buffer can absorb before its pH changes greatly. It grows with the moles of weak acid and conjugate base, and is greatest in both directions when the two are about equal (pH near pKa).

8.11 pH and Solubility

The solubility of a salt depends on pH when its anion is a base. Added H₃O⁺ reacts with the anion, its concentration drops, Q falls below Ksp, and more solid dissolves; Ksp itself does not change. Salts of anions from strong acids are unaffected by pH. On the exam this is reasoned qualitatively.

Lowering the pH dissolves more of a salt whose anion is a base: F⁻, CO₃²⁻, PO₄³⁻, S²⁻, OH⁻.
Explain with Q and Ksp: H₃O⁺ removes the anion, Q < Ksp, more solid dissolves. Ksp itself does not change.
Anions from strong acids (Cl⁻, Br⁻, I⁻, NO₃⁻) are unaffected, so those salts' solubility does not depend on pH.
The weaker the conjugate acid, the stronger the base, and the more the solubility depends on pH.

H₃O⁺ reacts with it: F⁻ + H₃O⁺ → HF + H₂O Q = [Ca²⁺][F⁻]² falls below Ksp more solid dissolves until Q = Ksp again, so solubility rises as pH falls its salts' solubility does not depend on pH

pH-dependent solubility: A slightly soluble salt whose anion is a base (the conjugate base of a weak acid, such as F⁻, CO₃²⁻ or OH⁻) dissolves more as pH falls: H₃O⁺ removes the anion, Q drops below Ksp, and more solid dissolves. Salts of anions from strong acids (Cl⁻, NO₃⁻) are not affected.