Topic 8: Acids and Bases

Acids and bases govern the behavior of protons in aqueous solution, from the sour bite of vinegar to the carefully balanced chemistry of your blood. In this unit you will quantify acidity with pH, predict the strength of acids using equilibrium constants and molecular structure, and analyze how buffers and titrations control proton transfer. These ideas tie together equilibrium, stoichiometry, and bonding into one of the most heavily tested topics on the exam.

The pH and pOH Scales

Water undergoes a slight self-ionization: 2 H2O reacts to form H3O+ and OH-. At 25 degrees C the ion-product constant Kw equals [H+][OH-] = 1.0 x 10^-14. Because the two ion concentrations multiply to a fixed value, increasing one decreases the other. pH is defined as -log[H+] and pOH as -log[OH-]. The two are linked by pH + pOH = 14 at 25 degrees C. A neutral solution has [H+] = [OH-] = 1.0 x 10^-7 M, giving pH 7. Solutions with pH below 7 are acidic and those above 7 are basic. Remember that a change of one pH unit means a tenfold change in [H+], so pH 3 is one hundred times more acidic than pH 5.

Strong Acids and Strong Bases

Strong acids and bases ionize essentially completely in water, so their equilibrium lies far to the right and we treat the reaction as one-directional. The six common strong acids are HCl, HBr, HI, HNO3, HClO4, and H2SO4 (first proton). Strong bases are the group 1 hydroxides plus the heavier group 2 hydroxides such as Ca(OH)2. For a strong acid, [H+] equals the acid concentration directly. A 0.010 M HCl solution has [H+] = 0.010 M and pH = -log(0.010) = 2.00. For a strong base, find [OH-] first, then pOH, then pH. Watch the stoichiometry: 0.010 M Ca(OH)2 releases 0.020 M OH- because each formula unit gives two hydroxide ions.

Weak Acid and Base Equilibria: Ka and Kb

Most acids and bases are weak, meaning they only partially ionize. A weak acid HA establishes the equilibrium HA reacts with water to give H+ and A-, described by the acid dissociation constant Ka = [H+][A-] / [HA]. A larger Ka means a stronger acid. For a weak base B, Kb = [BH+][OH-] / [B] measures how much hydroxide it generates. To find the pH of a weak acid solution, set up an ICE table: let x be the amount ionized, so Ka = x^2 / (C - x). When ionization is small (Ka small and C not tiny), approximate C - x as C, giving x = sqrt(Ka x C). Always check the 5 percent rule; if x is more than 5 percent of C, solve the full quadratic. For conjugate pairs, Ka x Kb = Kw, which lets you convert between the two constants.

Conjugate Acid-Base Pairs

The Bronsted-Lowry model defines an acid as a proton donor and a base as a proton acceptor. When an acid donates H+, what remains is its conjugate base; when a base accepts H+, the result is its conjugate acid. The pair HA and A- differ by exactly one proton. A key trend: the stronger the acid, the weaker its conjugate base, and vice versa. The conjugate base of a strong acid (such as Cl- from HCl) is so weak it has no measurable effect on pH, which is why salts like NaCl are neutral. In contrast, the conjugate base of a weak acid (such as F- from HF) is itself a weak base and makes a salt solution slightly basic.

Molecular Structure and Acid Strength

Acid strength is rooted in how easily a proton leaves and how stable the resulting anion is. For binary acids (H-X), strength increases down a group as the H-X bond weakens; thus HI is stronger than HF even though F is more electronegative. Across a period, strength increases with electronegativity, so HF is stronger than H2O. For oxoacids, more oxygen atoms bonded to the central atom pull electron density away, stabilizing the conjugate base and raising acidity: HClO4 is stronger than HClO. Greater central-atom electronegativity has the same effect, making HClO stronger than HBrO. The unifying idea is that anything stabilizing the negative charge on the conjugate base makes the acid stronger.

Buffers and How They Resist pH Change

A buffer is a solution containing comparable amounts of a weak acid and its conjugate base (or a weak base and its conjugate acid). When acid is added, the conjugate base neutralizes it; when base is added, the weak acid neutralizes it. This two-sided defense keeps pH nearly constant. Buffer capacity is the amount of acid or base a buffer can absorb before pH changes significantly, and it is greatest when the concentrations of the two components are large and roughly equal. A buffer works best within about one pH unit of the weak acid's pKa. Adding a small amount of strong acid or base shifts the ratio of the two components only slightly, so the pH barely moves.

The Henderson-Hasselbalch Equation

For a buffer, the pH can be found directly from pH = pKa + log([A-] / [HA]), where pKa = -log(Ka). This equation shows that when [A-] equals [HA], the log term is zero and pH equals pKa. To raise the pH above pKa you need more conjugate base than acid; to lower it you need more acid. The equation is valid only for buffers, where both species are present in significant, comparable amounts. Because it depends on the ratio of concentrations, diluting a buffer with water does not change its pH (both concentrations change by the same factor). Use it to design a buffer: pick a weak acid whose pKa is near your target pH, then adjust the ratio.

Worked Example: Buffer pH

Suppose you mix 0.50 mol of acetic acid (CH3COOH, Ka = 1.8 x 10^-5) and 0.30 mol of sodium acetate (its conjugate base) in 1.0 L of water. First find pKa = -log(1.8 x 10^-5) = 4.74. Then apply Henderson-Hasselbalch: pH = 4.74 + log(0.30 / 0.50) = 4.74 + log(0.60) = 4.74 + (-0.22) = 4.52. Now add 0.10 mol of strong base (OH-). It converts 0.10 mol of acetic acid into acetate: acid becomes 0.40 mol and base becomes 0.40 mol. The new pH = 4.74 + log(0.40 / 0.40) = 4.74 + 0 = 4.74. Adding strong base changed the pH by only about 0.2 units, demonstrating the buffer's resistance.

Titrations, Titration Curves, and Equivalence Points

A titration adds a solution of known concentration (the titrant) to a sample until the reaction is complete. The equivalence point is where moles of added titrant exactly equal moles of analyte, found from stoichiometry. On a strong acid-strong base titration curve, the equivalence point sits at pH 7 and shows a steep vertical jump. For a weak acid titrated with strong base, the curve rises more gradually, the equivalence point lands above pH 7 (because the conjugate base is basic), and the halfway-to-equivalence point is special: there pH = pKa, since equal amounts of acid and conjugate base remain. Indicators are weak acids that change color over a narrow pH range; choose one whose color-change interval overlaps the steep portion of the curve, for example phenolphthalein for a weak acid-strong base titration.