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Química Geral · Acid–base and solubility equilibria

Curvas de titulação ácido–base

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O que você vai aprender

  • Calculate the pH at any point of a strong acid–strong base titration: at the start, before, at and after the equivalence point.
  • Calculate the pH along weak acid–strong base and weak base–strong acid titrations, including half-equivalence (pH = pKa) and salt hydrolysis at equivalence.
  • Choose an indicator whose colour-change range lies on the steep part of the curve around the equivalence point.
  • Read the equivalence points and pKa values from the titration curve of a polyprotic acid.
  • Work back from titration data to the concentration, molar mass and Ka of an unknown acid.

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Reading a titration curve

A titration curve plots pH against the volume of titrant added. The equivalence point is where the moles of titrant added exactly match the moles of analyte by the balanced equation; the end point is where the indicator changes colour, and a good indicator makes the two coincide. Every curve is solved in two stages: first do the stoichiometry in millimoles (the strong titrant reacts completely), then decide which species are left and do the equilibrium. Five regions recur: the start (analyte alone), before equivalence (analyte partly neutralized), half-equivalence, equivalence (only the salt remains) and after equivalence (excess titrant). Concentrations always use the total volume, analyte plus titrant added. All values here are at 25 °C with Kw = 1.0 × 10⁻¹⁴, and volumes are taken as additive.

Strong acid with strong base

Take 20.0 mL of 0.100 M HCl (2.00 mmol) titrated with 0.100 M NaOH. At the start [H₃O⁺] = 0.100 M, pH 1.00. After 5.0 mL, 0.50 mmol OH⁻ has removed 0.50 mmol H₃O⁺, leaving 1.50 mmol in 25.0 mL: 0.0600 M, pH 1.22. At 20.0 mL (equivalence) only NaCl and water remain; Na⁺ and Cl⁻ are the conjugates of a strong base and a strong acid, so neither reacts with water and pH = 7.00. After 25.0 mL, 0.50 mmol OH⁻ is in excess in 45.0 mL: [OH⁻] = 0.0111 M, pOH 1.95, pH 12.05. The pH rises slowly, then jumps from about 3 to about 11 within a fraction of a millilitre around equivalence; diluting both solutions tenfold leaves the equivalence volume and pH 7.00 unchanged but shortens the jump by about one pH unit at each end.

Weak acid with strong base

Take 50.0 mL of 0.100 M acetic acid (5.00 mmol, Ka = 1.8 × 10⁻⁵, pKa 4.74) titrated with 0.100 M NaOH. Start: a weak acid alone, [H₃O⁺] = √(Ka·C) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M, pH 2.87. After 10.0 mL: 1.00 mmol acetate and 4.00 mmol acetic acid form a buffer, so pH = pKa + log(1.00/4.00) = 4.74 − 0.60 = 4.14 (the volume cancels in the ratio). At half-equivalence, 25.0 mL, [HA] = [A⁻] and pH = pKa = 4.74. At equivalence, 50.0 mL, only acetate is left, 5.00 mmol in 100.0 mL = 0.0500 M; it is a weak base with Kb = Kw/Ka = 5.6 × 10⁻¹⁰, so [OH⁻] = √(Kb·C) = 5.3 × 10⁻⁶ M, pOH 5.28 and pH 8.72, above 7. Past equivalence the excess OH⁻ controls the pH (55.0 mL: 0.50 mmol in 105.0 mL, pH 11.68) and the curve merges with that of a strong acid. Compared with HCl at the same concentration, the curve starts higher, has a flat buffer region and a shorter jump, yet needs exactly the same volume of base: neutralization of a weak acid by OH⁻ goes to completion.

Weak base with strong acid

The mirror image: 20.0 mL of 0.100 M NH₃ (Kb = 1.8 × 10⁻⁵, pKb 4.74) titrated with 0.100 M HCl starts at [OH⁻] = √(Kb·C) = 1.34 × 10⁻³ M, pOH 2.87, pH 11.13, and the pH falls as acid is added. Before equivalence NH₃ and NH₄⁺ form a buffer; use pKa(NH₄⁺) = 14.00 − 4.74 = 9.26 in pH = pKa + log([NH₃]/[NH₄⁺]). At half-equivalence pH = 9.26. At equivalence, 20.0 mL, only NH₄⁺ remains at 0.0500 M; it is a weak acid with Ka = Kw/Kb = 5.6 × 10⁻¹⁰, so [H₃O⁺] = √(Ka·C) = 5.3 × 10⁻⁶ M and pH 5.28, below 7. After equivalence the excess H₃O⁺ sets the pH.

Choosing an indicator

An indicator is a weak acid, HIn, whose acid form and conjugate base In⁻ have different colours. pH = pKa(HIn) + log([In⁻]/[HIn]), and the eye sees a change roughly while the ratio goes from 1/10 to 10, so the colour-change range is about pKa(HIn) ± 1. Choose an indicator whose range lies on the near-vertical part of the curve that contains the equivalence pH. Common ranges: methyl orange 3.1–4.4, methyl red 4.4–6.2, bromothymol blue 6.0–7.6, phenolphthalein 8.2–10.0 (colourless to pink, drawn in its colourless form). A strong acid–strong base titration at 0.1 M jumps across all of these, so any of them works. A weak acid–strong base titration needs a basic-range indicator such as phenolphthalein; a weak base–strong acid titration needs an acidic-range indicator such as methyl red. An indicator that changes colour in the buffer region gives an end point well before equivalence.

Polyprotic acids and bases

A polyprotic acid whose pKa values are several units apart is titrated one proton at a time and shows one jump per proton that can be titrated. The equivalence points fall at V, 2V, …, because each proton needs the same amount of base. Halfway between the first and second equivalence points the two neighbouring species are equal, so pH = pKa2, just as pH = pKa1 at the first half-equivalence point when the acid is not too strong. At an intermediate equivalence point the solution holds an amphiprotic ion, and its pH is approximately the average of the two pKa values that bracket it. Sodium carbonate titrated with HCl shows this: the first equivalence point (all HCO₃⁻) lies near ½(6.35 + 10.33) = 8.34, where phenolphthalein loses its pink colour, and the second (H₂CO₃, which loses CO₂) lies near pH 4, where methyl orange changes. A proton with pKa near 12 or higher gives no visible jump in water, because the acid is too weak to react completely with OH⁻ and the excess OH⁻ already holds the pH near 12.

Working back from titration data

The equivalence volume gives the amount of analyte: n(acid) = c(titrant) × V(equivalence) times the mole ratio, whatever the strength of the acid. The pH at half-equivalence gives pKa directly; at any other point in the buffer region, use the millimoles that remain: pKa = pH − log(n(A⁻)/n(HA)), where n(A⁻) is the base added and n(HA) is the starting acid minus the base added. The initial pH also gives Ka once the concentration is known: Ka = [H₃O⁺]²/(C − [H₃O⁺]). Example: 25.00 mL of an unknown monoprotic acid needs 18.00 mL of 0.1000 M NaOH, so it holds 1.800 mmol and is 0.0720 M; the pH at 9.00 mL is 3.85, so pKa = 3.85 and Ka = 10⁻³·⁸⁵ = 1.4 × 10⁻⁴. Adding water to the flask before titrating changes neither the moles of acid nor the equivalence volume.

What to carry forward

Do stoichiometry first, in millimoles, then equilibrium. Before any titrant: the analyte alone. In the buffer region: Henderson–Hasselbalch, with pH = pKa at half-equivalence. At equivalence: the conjugate salt alone, neutral for strong–strong, basic for a weak acid, acidic for a weak base. After equivalence: the excess titrant over the total volume. Pick an indicator whose colour change falls on the steep jump, and read concentrations from equivalence volumes and pKa from half-equivalence.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 4

Working back from titration data

  • Extra water in the flaskPredict which features of a weak acid titration curve change when the analyte is diluted before titrating.

Indicators and polyprotic curves

  • Locating the second equivalence pointPredict the second equivalence volume of a diprotic acid from the first.

Weak acid–strong base

  • Halfway to equivalence with benzoic acidPredict the composition and pH at the half-equivalence point of a weak acid titration.

Weak base–strong acid

  • pH halfway through an ammonia titrationPredict the pH at the half-equivalence point of a weak base titration from Kb.

Classificar 1

  • Where on the curve is this point?Classify a point on a weak base–strong acid titration by region and choose the matching pH method.

Comparar 5

Indicators and polyprotic curves

  • Where does each equivalence point lie?Rank strong–strong, weak acid and weak base titrations by the pH at their equivalence points.

Strong acid–strong base

  • Diluting both solutions tenfoldCompare strong acid–strong base titration curves at two concentrations.

Weak acid–strong base

  • Five millilitres past equivalenceCompare the pH of weak and strong acid titrations after the equivalence point.
  • Equivalence pH and acid strengthRank weak acids by the pH at their equivalence points with NaOH using Ka values.
  • Acetic acid versus HClCompare the titration curves of a weak acid and a strong acid at the same concentration.

Calcular 15

Working back from titration data

  • pKa from a point that is not half-equivalenceCalculate pKa from one point in the buffer region using the millimoles of acid and conjugate base present.
  • Acetic acid in vinegarCalculate the concentration of a weak acid in an undiluted sample from the equivalence volume of a titrated aliquot.

Indicators and polyprotic curves

  • Indicator ratio inside its rangeCalculate the ratio of base to acid form of an indicator at a given pH from its pKa.
  • pH at phosphoric acid's first equivalence pointEstimate the pH at an intermediate equivalence point of a polyprotic acid from the bracketing pKa values.

Strong acid–strong base

  • pH past the equivalence pointCalculate the pH after the equivalence point of a strong acid–strong base titration from the excess hydroxide.
  • Titrating NaOH with HClCalculate the pH before equivalence when a strong base is titrated with a strong acid.
  • pH partway to equivalence: HCl with NaOHCalculate the pH of a strong acid partly neutralized by strong base, using the total volume.
  • How steep is the jump?Quantify the pH change over 0.20 mL around the equivalence point of a strong acid–strong base titration.

Weak acid–strong base

  • pH in the buffer regionCalculate the pH in the buffer region of a weak acid–strong base titration from millimoles of acid and conjugate base.
  • pH at the equivalence point of acetic acidCalculate the equivalence-point pH of a weak acid–strong base titration from the hydrolysis of the conjugate base.
  • Starting pH of a formic acid titrationCalculate the starting pH of a weak acid titration from Ka and the acid concentration.

Weak base–strong acid

  • Excess acid after an ammonia titrationCalculate the pH after the equivalence point of a weak base–strong acid titration from the excess strong acid.
  • pH in the ammonia buffer regionCalculate the pH in the buffer region of a weak base–strong acid titration.
  • pH at the equivalence point of ammoniaCalculate the equivalence-point pH of a weak base–strong acid titration from the hydrolysis of the conjugate acid.
  • Starting pH of an ammonia titrationCalculate the starting pH of a weak base titration from Kb and the base concentration.

Encontre o erro 3

Working back from titration data

  • Find the student's mistakeDiagnose an error in a pKa calculated from a buffer-region titration point.

Strong acid–strong base

  • The pKa of HCl from a titration?Diagnose why the half-equivalence rule cannot give the pKa of a strong acid.

Weak base–strong acid

  • Phenolphthalein in an ammonia titrationDiagnose the error caused by using an indicator that changes colour in the buffer region of a weak base titration.

Interprete as evidências 5

Working back from titration data

  • Reading the equivalence volume from dataLocate the equivalence volume of a weak acid titration from tabulated pH readings.
  • Ka of an unknown acid from its curveDetermine Ka of an unknown weak acid from the pH at half the equivalence volume.

Indicators and polyprotic curves

  • pKa2 of phosphoric acid from its curveRead the second pKa of a polyprotic acid from the pH midway between its first and second equivalence points.

Strong acid–strong base

  • The shape of an HCl–NaOH curveRecognize the titration curve of a strong acid titrated with a strong base.

Weak base–strong acid

  • The shape of an ammonia–HCl curveRecognize the titration curve of a weak base titrated with a strong acid.

Trabalhe de trás para frente 2

Working back from titration data

  • Identify the unknown acidIdentify an unknown monoprotic acid from its molar mass and pKa determined by titration.
  • Ka from the starting pH and the equivalence volumeWork back from the equivalence volume and the initial pH to the Ka of a weak acid.

Planeje uma síntese 1

  • An indicator for acetic acidChoose an indicator for a weak acid–strong base titration from its colour-change range.

Explique por quê 4

Indicators and polyprotic curves

  • How does an indicator change colour?Explain how an acid–base indicator works and why it changes colour over about two pH units.
  • Where is the third equivalence point?Explain why the third proton of phosphoric acid gives no visible equivalence jump in water.

Strong acid–strong base

  • Why pH 7 at this equivalence point?Explain why the equivalence point of a strong acid–strong base titration is neutral.

Weak acid–strong base

  • Why is the equivalence point basic?Explain the basic equivalence point of a weak acid–strong base titration by hydrolysis of the conjugate base.

Travou em curvas de titulação ácido–base? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

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