8 Acids and Bases

Calculate the values of pH and pOH, based on Kw and the concentration of all species present in a neutral solution of water.

• The concentrations of hydronium ion and hydroxide ion are often reported as pH and pOH, respectively. EQN: pH = −log[H3O+] EQN: pOH = −log[OH−] The terms “hydrogen ion” and “hydronium ion” and the symbols H+(aq) and H3O+(aq) are often used interchangeably for the aqueous ion of hydrogen. Hydronium ion and H3O+(aq) are preferred, but H+(aq) is also accepted on the AP Exam.
• Water autoionizes with an equilibrium constant Kw. EQN: Kw = [H3O+][OH−] = 1.0 × 10−14 at 25°C
• In pure water, pH=pOH is called a neutral solution. At 25°C, pKw = 14.0 and thus pH = pOH = 7.0. EQN: pKw = 14 = pH + pOH at 25°C
• The value of Kw is temperature dependent, so the pH of pure, neutral water will deviate from 7.0 at temperatures other than 25°C.

Calculate pH and pOH based on concentrations of all species in a solution of a strong acid or a strong base.

• Molecules of a strong acid (e.g., HCl, HBr, HI, HClO4, H2SO4, and HNO3) will completely ionize in aqueous solution to produce hydronium ions and the conjugate base of the acid. As such, the concentration of H3O+ in a strong acid solution is equal to the initial concentration of the strong acid, and thus the pH of the strong acid solution is easily calculated.
• When dissolved in solution, strong bases (e.g., group I and II hydroxides) completely dissociate to produce hydroxide ions. As such, the concentration of OH− in a strong base solution is equal to the initial concentration of a group I hydroxide and double the initial concentration of a group II hydroxide, and thus the pOH (and pH) of the strong base solution is easily calculated.

Explain the relationship among pH, pOH, and concentrations of all species in a solution of a monoprotic weak acid or weak base. Acids and Bases UNIT 8

• Weak acids react with water to produce hydronium ions. However, only a small percentage of molecules of a weak acid will ionize in this way. Thus, the concentration of H + 3O is much less than the initial concentration of the molecular acid, and the vast majority of the acid molecules remain un-ionized.
• A solution of a weak acid involves equilibrium between an un-ionized acid and its conjugate base. The equilibrium constant for this reaction is Ka, often reported as pKa. The pH of a weak acid solution can be determined from the initial acid concentration and the pKa. EQN: K [H O] [A ] [HA] a 3= +− EQN: pKa = −log Ka
• Weak bases react with water to produce hydroxide ions in solution. However, ordinarily just a small percentage of the molecules of a weak base in solution will ionize in this way. Thus, the concentration of OH− in the solution does not equal the initial concentration of the base, and the vast majority of the base molecules remain un-ionized.
• A solution of a weak base involves equilibrium between an un-ionized base and its conjugate acid. The equilibrium constant for this reaction is Kb, often reported as pKb. The pH of a weak base solution can be determined from the initial base concentration and the pKb. EQN: K [OH ][HB ] [B] b = −+ EQN: pKb = −log Kb
• The percent ionization of a weak acid (or base) can be calculated from its pKa (pKb) and the initial concentration of the acid (base). The percent ionization can also be calculated from the initial concentration of the acid (base) and the equilibrium concentration of any of the species in the equilibrium expression.
• For any conjugate acid-base pair, the acid ionization constant and base ionization constant are related by Kw: EQN: Kw = Ka × Kb EQN: pKw = pKa + pKb

Explain the relationship among the concentrations of major species in a mixture of weak and strong acids and bases. Acids and Bases UNIT 8

• When a strong acid and a strong base are mixed, they react quantitatively in a reaction represented by the equation: H+(aq) + OH−(aq) → H2O(l). The pH of the resulting solution may be determined from the concentration of excess reagent.
• When a weak acid and a strong base are mixed, they react quantitatively in a reaction represented by the equation: HA(aq) + OH−(aq)  A−(aq) H2O(l). If the weak acid is in excess, then a buffer solution is formed, and the pH can be determined from the Henderson-Hasselbalch ( H−H) equation (see
• When a weak base and a strong acid are mixed, they will react quantitatively in a reaction represented by the equation: B(aq) + H3O+(aq)  HB+(aq) + H2O(l). If the weak base is in excess, then a buffer solution is formed, and the pH can be determined from the H−H equation. If the strong acid is in excess, then the pH can be determined from the moles of excess hydronium ion and the total volume of solution. If they are equimolar, then the (slightly acidic) pH can be determined from the equilibrium represented by the equation: HB+(aq) + H2O(l)  B(aq) + H3O+(aq).
• When a weak acid and a weak base are mixed, they will react to an equilibrium state whose reaction may be represented by the equation: HA(aq) + B(aq)  A−(aq) + HB+(aq).

Explain results from the titration of a mono- or polyprotic acid or base solution, in relation to the properties of the solution and its components. Acids and Bases UNIT 8

• An acid-base reaction can be carried out under controlled conditions in a titration. A titration curve, plotting pH against the volume of titrant added, is useful for summarizing results from a titration.
• At the equivalence point for titrations of monoprotic acids or bases, the number of moles of titrant added is equal to the number of moles of analyte originally present. This relationship can be used to obtain the concentration of the analyte. This is the case for titrations of strong acids/bases and weak acids/bases.
• For titrations of weak acids/bases, it is useful to consider the point halfway to the equivalence point, that is, the half-equivalence point. At this point, there are equal concentrations of each species in the conjugate acid-base pair, for example, for a weak acid [HA] = [A−]. Because pH = pKa when the conjugate acid and base have equal concentrations, the pKa can be determined from the pH at the halfequivalence point in a titration.
• At the equivalence point, pH is determined by the major species in solution. Strong acid and strong base titrations result in neutral pH at the equivalence point. However, in titrations of weak acids (weak bases), the conjugate base of the weak acid (conjugate acid of the weak base) is present at the equivalence point and can undergo proton-transfer reactions with the surrounding water, producing basic (acidic) solutions.
• For polyprotic acids, titration curves can be used to determine the number of acidic protons. In doing so, the major species present at any point along the curve can be identified, along with the pKa associated with each proton in a weak polyprotic acid.
  • Exclusion: Computation of the concentration of each species present in the titration curve for polyprotic acids will not be assessed on the AP Exam. Such computations for titration of monoprotic acids are within the scope of the course (see

Explain the relationship between the strength of an acid or base and the structure of the molecule or ion.

• The protons on a molecule that will participate in acid-base reactions, and the relative strength of these protons, can be inferred from the molecular structure.
  • i. Strong acids (such as HCl, HBr, HI, HClO4, H2SO4, and HNO3) have very weak conjugate bases that are stabilized by electronegativity, inductive effects, resonance, or some combination thereof.
  • ii. Carboxylic acids are one common class of weak acid.
  • iii. Strong bases (such as group I and II hydroxides) have very weak conjugate acids.
  • iv. Common weak bases include nitrogenous bases such as ammonia as well as carboxylate ions.
  • v. Electronegative elements tend to stabilize the conjugate base relative to the conjugate acid, and so increase acid strength.

Explain the relationship between the predominant form of a weak acid or base in solution at a given pH and the pKa of the conjugate acid or the pKb of the conjugate base.

• The protonation state of an acid or base (i. the relative concentrations of HA and A−) can e., be predicted by comparing the pH of a solution to the pKa of the acid in that solution. When solution pH < acid pKa, the acid form has a higher concentration than the base form. When solution pH > acid pKa, the base form has a higher concentration than the acid form.
• Acid-base indicators are substances that exhibit different properties (such as color) in their protonated versus deprotonated state, making that property respond to the pH of a solution.
• T o ensure accurate results in a titration experiment, acid-base indicators should be selected that have a pKa close to the pH at the equivalence point.

Explain the relationship between the ability of a buffer to stabilize pH and the reactions that occur when an acid or a base is added to a buffered solution.

• A buffer solution contains a large concentration of both members in a conjugate acid-base pair. The conjugate acid reacts with added base and the conjugate base reacts with added acid. These reactions are responsible for the ability of a buffer to stabilize pH.

Identify the pH of a buffer solution based on the identity and concentrations of the conjugate acid-base pair used to create the buffer.

• The pH of the buffer is related to the pKa the acid and the concentration ratio of the of conjugate acid-base pair. This relation is a consequence of the equilibrium expression associated with the dissociation of a weak acid, and is described by the HendersonHasselbalch equation. Adding small amounts of acid or base to a buffered solution does not significantly change the ratio of [A−]/[HA] and thus does not significantly change the solution pH. The change in pH on addition of acid or base to a buffered solution is therefore much less than it would have been in the absence of the buffer. EQN: pH = pKa + [] − log [A ] HA
  • Exclusion: Computation of the change in pH resulting from the addition of an acid or a base to a buffer will not be assessed on the AP Exam. Derivation of the Henderson-Hasselbalch equation will not be assessed on the AP Exam.

Explain the relationship between the buffer capacity of a solution and the relative concentrations of the conjugate acid and conjugate base components of the solution.

• Increasing the concentration of the buffer components (while keeping the ratio of these concentrations constant) keeps the pH of the buffer the same but increases the capacity of the buffer to neutralize added acid or base.
• When a buffer has more conjugate acid than base, it has a greater buffer capacity for addition of added base than acid. When a buffer has more conjugate base than acid, it has a greater buffer capacity for addition of added acid than base.

Identify the qualitative effect of changes in pH on the solubility of a salt.

• The solubility of a salt is pH sensitive when one of the constituent ions is a weak acid, a weak base, or the hydroxide ion. These effects can be understood qualitatively using Le Châtelier’s principle.
  • Exclusion: Computations of solubility as a function of pH will not be assessed on the AP Exam.