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Química Geral · Exam review

Equilíbrio, ácidos e bases: revisão para a prova

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O que você vai aprender

  • Write K expressions for homogeneous and heterogeneous equilibria, manipulate K for reversed, scaled and combined equations, and convert between Kc and Kp.
  • Compare Q with K to predict the direction of net reaction, and solve ICE tables with the small-x approximation or the quadratic formula.
  • Predict how concentration, volume, inert gas, dilution, temperature and catalysts affect an equilibrium and its K.
  • Calculate pH, pOH and percent ionization for strong and weak acids and bases, and work backwards from pH to concentration.
  • Predict whether a salt solution is acidic, basic or neutral and calculate its pH from Ka or Kb.
  • Handle polyprotic acids: dominant first ionization, the anion of the last step, amphiprotic ions and the major species at a given pH.

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K, Q and manipulating K

For aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / ([A]^a[B]^b). Leave out pure solids and liquids (including water as the solvent): Zn(OH)₂(s) + 2 OH⁻(aq) ⇌ [Zn(OH)₄]²⁻(aq) has K = [Zn(OH)₄²⁻]/[OH⁻]². Rules: reversing an equation inverts K; multiplying the coefficients by n raises K to the power n (halving takes the square root); adding equations multiplies their K values. For gases, Kp = Kc(RT)^Δn, with Δn = moles of gaseous product − moles of gaseous reactant and R = 0.08206 L atm mol⁻¹ K⁻¹. Example: 2 SO₂ + O₂ ⇌ 2 SO₃ has Δn = −1, so at 1000 K a Kc of 2.8 × 10² gives Kp = 280/(0.08206 × 1000) = 3.4. The reaction quotient Q has the same form as K but uses the concentrations present right now. Q < K: net forward reaction; Q > K: net reverse reaction; Q = K: at equilibrium. Example: for PCl₅ ⇌ PCl₃ + Cl₂ with Kc = 0.040, a mixture with [PCl₅] = 0.50 M and [PCl₃] = [Cl₂] = 0.10 M has Q = (0.10)(0.10)/0.50 = 0.020 < K, so more PCl₅ dissociates. Only temperature changes K; concentrations, pressure and catalysts change Q or the rate, not K.

ICE tables

Write Initial, Change and Equilibrium rows in mol/L. Find the direction from Q first, then let the change follow the coefficients (2x for a coefficient of 2). Example: 0.50 M PCl₅ with Kc = 0.040 gives x²/(0.50 − x) = 0.040. Dropping x gives x = √0.020 = 0.141 M, which is 28 % of 0.50 M, so the 5 % test fails. Solve x² + 0.040x − 0.020 = 0 instead: x = [−0.040 + √(0.0016 + 0.080)]/2 = 0.123 M. Keep only the root that leaves every concentration positive. If both sides start with the same power, as in A + B ⇌ 2C from equal amounts, take the square root of K instead of solving a quadratic. If an equilibrium concentration is measured, the change row follows from it directly: if 0.200 M of a diatomic gas X₂ gives 0.0060 M of X atoms at equilibrium, the molecules have lost 0.0030 M (half as much, from the 1 : 2 coefficients) and 0.197 M of X₂ remains.

Le Châtelier's principle

A disturbed equilibrium shifts in the direction that partly undoes the change. Adding a species shifts away from it; removing one shifts toward it, including removal by another reaction (OH⁻ added to an equilibrium that contains H₃O⁺ removes H₃O⁺). Halving the volume of a gas mixture shifts toward fewer moles of gas; if Δn = 0 there is no shift. An inert gas added at constant volume changes no partial pressure, so there is no shift. Diluting a solution shifts toward the side with more dissolved particles; to check, multiply every concentration in Q by the dilution factor and compare with K. Heating favours the endothermic direction: K rises with temperature for an endothermic reaction and falls for an exothermic one. A catalyst speeds up both directions equally, so equilibrium is reached sooner but K and the equilibrium composition do not change. Adding the conjugate base of a weak acid (a common ion) shifts HA ⇌ H₃O⁺ + A⁻ to the left, lowering [H₃O⁺] and the percent ionization.

pH of strong and weak acids and bases

At 25 °C, Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴, pH + pOH = 14.00 and, for a conjugate pair, Ka × Kb = Kw. Strong acids (HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ first proton) and group 1 and heavier group 2 hydroxides ionize completely: count the H₃O⁺ or OH⁻ per formula unit. A weak acid needs an ICE table: Ka = x²/(C − x). For 0.10 M benzoic acid (drawn; Ka = 6.3 × 10⁻⁵), x = √(6.3 × 10⁻⁶) = 2.5 × 10⁻³ M, pH 2.60, 2.5 % ionized, so the approximation holds. If x would exceed 5 % of C, use the quadratic. A weak base works the same way with Kb and gives [OH⁻]: 0.10 M NH₃ (Kb = 1.8 × 10⁻⁵) has [OH⁻] = 1.34 × 10⁻³ M, pOH 2.87 and pH 11.13. Common traps: reporting pOH as pH, using the pKa as the pH, forgetting the square root, and confusing equal concentration with equal pH (at equal pH a weak acid solution holds far more total acid than a strong one).

Salts

Look at each ion separately. Cations of strong bases (Na⁺, K⁺, Ca²⁺) and anions of strong acids (Cl⁻, Br⁻, NO₃⁻, ClO₄⁻) do not change the pH. The conjugate base of a weak acid makes OH⁻, with Kb = Kw/Ka; the conjugate acid of a weak base makes H₃O⁺, with Ka = Kw/Kb. Example: 0.10 M sodium benzoate (drawn): Kb = 1.0 × 10⁻¹⁴/6.3 × 10⁻⁵ = 1.6 × 10⁻¹⁰, [OH⁻] = √(1.6 × 10⁻¹¹) = 4.0 × 10⁻⁶ M, pOH 5.40, pH 8.60. The weaker the parent acid, the stronger the conjugate base and the higher the pH of its sodium salt at equal concentration.

Polyprotic acids

A polyprotic acid loses protons one at a time, with Ka1 > Ka2 > Ka3. When Ka1 is much larger than Ka2, the first step sets the pH and the second adds a negligible amount of H₃O⁺. For carbonic acid (drawn; Ka1 = 4.3 × 10⁻⁷, Ka2 = 5.6 × 10⁻¹¹) at 0.020 M, [H₃O⁺] = √(4.3 × 10⁻⁷ × 0.020) = 9.3 × 10⁻⁵ M, pH 4.03, and [CO₃²⁻] ≈ Ka2 = 5.6 × 10⁻¹¹ M because [H₃O⁺] ≈ [HCO₃⁻]. The fully deprotonated anion is a base whose conjugate acid is the last proton donor, so Kb(CO₃²⁻) = Kw/Ka2 = 1.8 × 10⁻⁴. An amphiprotic ion such as HCO₃⁻ can act as either: compare its Ka (Ka2) with its Kb (Kw/Ka1 = 2.3 × 10⁻⁸); the larger one decides whether its sodium salt is acidic or basic. At a given pH, the major species is the one whose pKa values bracket that pH: below pKa1 the fully protonated acid, between pKa1 and pKa2 the singly deprotonated ion, and so on.

What to carry forward

Write K from the balanced equation (no solids or pure liquids), compute Q before any ICE table, and remember that only temperature changes K. For pH, decide first whether each species is strong, weak or spectator; use [H₃O⁺] = √(Ka·C) or [OH⁻] = √(Kb·C) and check the 5 % rule; get Kb of an anion from Kw/Ka of the acid it came from; for polyprotic acids let the first step set the pH and match the last proton donor to the fully deprotonated anion.

Problemas de prática (40)

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ICE tables and Le Châtelier

  • Adding base to orange dichromatePredict the shift of an aqueous equilibrium when a reagent removes one of its species by neutralization.
  • Diluting a chromate–dichromate equilibriumPredict the direction of shift on dilution by working out the factor by which Q changes when every dissolved species is diluted.
  • Sodium nitrite added to nitrous acidPredict the effect of a common ion on the pH and percent ionization of a weak acid using Le Châtelier's principle.
  • Getting more CO from CO₂ and H₂Choose the one change that shifts an endothermic gas equilibrium with no change in moles of gas toward products.

Equilibrium constants and Q

  • K for an antacid dissolving in acidWrite the equilibrium-constant expression for a heterogeneous equilibrium that contains a solid, a solvent and aqueous ions.
  • Which way will the SbCl₅ mixture shift?Calculate Q from a gas mixture's concentrations and compare it with Kc to predict the direction of net reaction.

Salts and polyprotic acids

  • Which equation does Ka2 describe?Match the second acid-ionization constant of a diprotic acid to its equilibrium equation.

Classificar 1

  • Which salt makes an acidic solution?Classify salt solutions as acidic, basic or neutral by identifying which ion reacts with water.

Comparar 4

pH of acids and bases

  • Equal pH, unequal acidCompare the amount of base needed to neutralize strong and weak acid solutions of equal pH by working out their total acid concentrations.
  • Which base solution has the lowest pH?Compare the pH of equal-concentration weak-base solutions from their Kb values.
  • Rank 0.010 M solutions by pHRank strong and weak acids and bases of equal concentration by pH, using complete ionization for strong electrolytes and Ka or Kb for weak ones.

Salts and polyprotic acids

  • Rank salt solutions by pHRank salt solutions by pH by comparing the Ka of acidic cations and the Kb of basic anions derived from Kw.

Calcular 19

Equilibrium constants and Q

  • K for bicarbonate reacting with itselfBuild the equilibrium constant for proton transfer between two amphiprotic ions from the stepwise Ka values of a diprotic acid.
  • Water vapour pressure over copper sulfate hydratesUse a heterogeneous Kp that contains only one gas, raised to a power, to find that gas's equilibrium pressure.
  • K for half the reverse of ICl formationFind K for an equation that is both reversed and halved from a given equilibrium constant.
  • Kc for ethane dehydrogenation from KpConvert Kp to Kc for a gas reaction in which the moles of gas increase.
  • Kc from equilibrium amounts of NO₂, NO and O₂Convert equilibrium amounts in moles to molarities and evaluate Kc for a reaction with squared terms.
  • K for nitrous acid reacting with ammoniaCombine Ka, Kb and Kw to find the equilibrium constant for a weak acid reacting with a weak base.

ICE tables and Le Châtelier

  • Kc for bromine dissociating into atomsUse the measured equilibrium concentration of one product and the 1 : 2 stoichiometry in an ICE table to find Kc.
  • How much carbonyl bromide decomposes?Solve an ICE table with the quadratic formula when K is too large for the small-x approximation.
  • Equilibrium I₂ from equal starting amountsSolve a perfect-square ICE table by taking the square root of K instead of using the quadratic formula.
  • SbCl₅ equilibrium from a mixture with too much productUse Q to find the direction of reaction before setting up an ICE table, then pick the physically meaningful root of the quadratic.

pH of acids and bases

  • Percent ionization of dilute chloroacetic acidCalculate the percent ionization of a weak acid when the 5 % test fails and the quadratic is required.
  • How much more H₃O⁺ in lemon juice?Convert a difference in pH into a ratio of hydronium-ion concentrations.
  • pH of 0.250 M hydrazoic acidCalculate the pH of a weak acid with the small-x approximation and confirm the approximation with the 5 % test.
  • pH of dilute strontium hydroxideCalculate the pH of a strong base that releases two hydroxide ions per formula unit.

Salts and polyprotic acids

  • pH of methylammonium chlorideCalculate the pH of the salt of a weak base by deriving Ka of its cation from Kb.
  • pH of a sodium hypochlorite solutionCalculate the pH of the salt of a weak acid by deriving Kb of its anion from Ka.
  • pH of 0.10 M sodium sulfiteCalculate the pH of the fully deprotonated salt of a diprotic acid by choosing the Ka that belongs to its conjugate acid.
  • pH of 0.10 M sulfurous acidCalculate the pH of a diprotic acid whose first ionization is too large for the small-x approximation.
  • pKb of the lactate ionFind pKb of a conjugate base from the Ka of its acid using pKa + pKb = pKw.

Encontre o erro 2

ICE tables and Le Châtelier

  • Does argon push methanation forward?Diagnose the error in claiming that an inert gas added at constant volume shifts a gas-phase equilibrium.

pH of acids and bases

  • Is hydroxylamine solution acidic?Diagnose the error of reporting pOH as pH in a weak-base calculation.

Interprete as evidências 2

Salts and polyprotic acids

  • Main citrate species at pH 5.50Identify the major species of a triprotic acid at a given pH from its three pKa values.

Equilibrium constants and Q

  • Reading K values at two temperaturesDeduce the sign of ΔH° from how K changes with temperature and predict the direction of a mixture at the higher temperature from Q.

Trabalhe de trás para frente 1

  • Ammonia concentration for pH 11.00Work backwards from a target pH to the initial concentration of a weak base.

Planeje uma síntese 2

pH of acids and bases

  • Pick the acid for a pH 3 solutionPlan which weak acid to use for a target pH by estimating the pH each candidate gives at a fixed concentration.

ICE tables and Le Châtelier

  • Drying copper sulfate pentahydrate at 25 °CPlan conditions that make Q smaller than K for a solid hydrate equilibrium, using the equilibrium water vapour pressure.

Explique por quê 2

Salts and polyprotic acids

  • Is sodium hydrogen sulfite acidic or basic?Explain whether the salt of an amphiprotic anion is acidic or basic by comparing the anion's Ka with its Kb.

Equilibrium constants and Q

  • Which statement about K is true?Identify the correct statement about what does and does not change an equilibrium constant.

Travou em equilíbrio, ácidos e bases: revisão para a prova? Escaneie o problema.

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