Why Module 6 is the calculation backbone of HSC Chemistry
Module 6 sits at the centre of the HSC syllabus because every other module (organic, electrochemistry, analytical) eventually returns to acid-base equilibria for buffers, pH-dependent reactions, or titration analysis. NESA examiners reward students who can move fluently between conceptual definitions and numerical calculations.
Bronsted-Lowry theory and conjugate pairs
A Bronsted-Lowry acid donates a proton; a base accepts one. The pair before and after proton transfer is the conjugate pair. Amphiprotic species (water, bicarbonate, dihydrogen phosphate) act as either.
Recognising the conjugate pair is the first step in any acid-base question. Examiners often disguise this by giving an organic acid or weak base structure; identify the labile proton.
The pH scale, Kw and temperature
At 25 degrees C Kw=[H+][OH−]=1.0×10−14. Taking logs gives pH+pOH=14.
Two HSC traps:
Kw grows with temperature because auto-ionisation is endothermic, so neutral pH falls below 7 above 25 degrees C even though the solution is still neutral.
Strong-acid pH calculations need a sanity check: 0.10 M HCl has pH 1, but 0.10 M H2SO4 (a diprotic strong acid) has pH close to 0.7 because both protons dissociate.
Strong versus weak: Ka and dissociation
Strong acids and bases fully dissociate; weak ones partially dissociate, governed by the dissociation constant Ka or Kb. The relationship KaKb=Kw links the strength of an acid and its conjugate base.
For a 0.10 M weak acid HA with Ka=1.8×10−5:
Ka=0.10−xx2≈0.10x2
x=[H+]=1.8×10−6=1.34×10−3 M,pH=2.87
Check the approximation: x is 1.3 percent of 0.10, so the approximation is valid.
Buffers and the Henderson-Hasselbalch equation
A buffer is a solution of a weak acid and its conjugate base (or weak base and conjugate acid) that resists pH change when small amounts of acid or base are added.
pH=pKa+log10([HA][A−])
Practical design: to make a buffer at pH 5.0, choose acetic acid (pKa=4.74) and adjust the ratio. The buffer is effective within plus or minus 1 pH unit of pKa.
Worked example: blood is buffered by the carbonic acid / bicarbonate system. pKa of H2CO3 is about 6.4, and blood pH is 7.4, so [HCO3−]/[H2CO3] is approximately 101.0, that is 10 to 1. Respiratory and renal compensation adjust both species.
Titrations and titration curves
A titration delivers titrant of known concentration to analyte until the equivalence point, when moles of acid equal moles of base.
Four shapes to recognise:
Strong acid plus strong base: equivalence at pH 7, steep transition.
Weak acid plus strong base: equivalence above pH 7 (the conjugate base is basic). At half-equivalence, pH=pKa.
Weak base plus strong acid: equivalence below pH 7.
Half-equivalence in case 2 is gold for examiners: you can read pKa directly off the graph.
Strong-acid plus strong-base curve: a near-vertical jump through pH 7 at the equivalence volume; any indicator changing colour between pH 4 and pH 10 brackets the jump.Acetic acid titrated with NaOH: read pKa straight off the y-axis at half-equivalence, and pick an indicator (phenolphthalein) whose colour change brackets the slightly basic equivalence pH.The Henderson-Hasselbalch line has slope 1 and crosses pH equals pKa at equal acid and conjugate-base concentrations; the buffer is effective within ± 1 pH unit of pKa.
Worked example: NaOH into acetic acid
25.00 mL of 0.100 M acetic acid is titrated with 0.100 M NaOH. Calculate pH at four points.
Initial: weak acid only. pH=2.87 (above).
After 12.50 mL NaOH (half-equivalence): equal moles of HA and A−, pH=pKa=4.74.
At equivalence (25.00 mL): all converted to A− in 50.00 mL total. [A−]=0.0500 M. Kb=Kw/Ka=5.6×10−10. [OH−]=Kbc=5.3×10−6. pOH=5.28, pH=8.72.
After 35.00 mL NaOH (excess base): excess OH− in 60.00 mL. [OH−]=(0.100×0.010)/0.0600=0.0167 M, pH=12.22.
Indicator selection
Indicators are themselves weak acids: HIn⇌H++In−. Colour change occurs over pKin±1.
Match indicator pH range to the equivalence pH:
Bromothymol blue (6.0 to 7.6): strong-strong.
Phenolphthalein (8.2 to 10.0): weak acid plus strong base.
Methyl orange (3.1 to 4.4): weak base plus strong acid.
Using phenolphthalein for a HCl-NaOH titration would still work but adds a small systematic error; using methyl orange for acetic acid-NaOH gives a large error because methyl orange changes well before equivalence.
Common HSC examiner trap list
Forgetting Kw is temperature-dependent.
Reporting pH to more sig fig than the input concentrations support (the digits after the decimal in pH are the significant ones).
Treating a weak acid as if 100 percent dissociated.
Picking the wrong indicator for the conjugate-pair behaviour at equivalence.
Confusing equivalence (stoichiometric) with end-point (indicator colour change).
Check your knowledge
A mix of definitional, calculation/explanation, and exam-style multi-part questions covering this topic. Aim to answer all under exam conditions, then check against the solutions block.
Define an amphiprotic species and identify three examples relevant to Module 6, writing the equation for each acting as both a Bronsted-Lowry acid and a base. (4 marks)
Methanoic acid (formic acid) is found in the venom of green-tree ants (Oecophylla smaragdina) common to northern Australia. Calculate the pH and the percentage dissociation of a 0.0500 M aqueous methanoic acid solution. Ka=1.77×10−4. (5 marks)
The accompanying titration table records pH against volume of 0.100 M NaOH added to 25.00 mL of an unknown monoprotic acid. (a) At 0.00 mL the pH is 2.87. (b) At 12.50 mL the pH is 4.74. (c) At 25.00 mL the pH is 8.72. (d) At 37.50 mL the pH is 12.30. Identify whether the acid is strong or weak, justify your answer using two specific data points, and estimate Ka. (5 marks)
A buffer is needed for an enzyme assay at pH 7.20. From the candidates below, choose the most suitable conjugate acid-base system and calculate the mole ratio of conjugate base to acid required. Candidates: ethanoic / ethanoate (pKa=4.74); dihydrogen phosphate / hydrogen phosphate (pKa=7.20); ammonium / ammonia (pKa=9.25). (a) Identify the chosen system, (b) calculate the required ratio at pH 7.20, (c) propose how to prepare 500 mL of 0.100 M total buffer. (6 marks)
(a) Calculate the pH of pure water at 50 degrees C given that Kw=5.48×10−14 at this temperature. (b) Explain why the water is still neutral despite the pH being less than 7. (c) State whether the autoionisation of water is endothermic or exothermic, justifying with a Le Chatelier argument. (5 marks)
30.00 mL of 0.200 M ammonia (Kb=1.80×10−5) is titrated with 0.250 M HCl. Calculate (a) the volume of HCl required to reach equivalence, (b) the pH at equivalence, (c) the pH after 30.00 mL of HCl has been added (past equivalence). Kw=1.0×10−14. (6 marks)
Two students measure the pH of a 0.10 M solution of H2SO4. Student A reports pH 1.00; student B reports pH 0.74. Account for the difference, given that H2SO4 is a strong acid for the first dissociation but the second dissociation (HSO4−⇌H++SO42−, Ka2=1.2×10−2) is only partial. State which student is more accurate and support with calculation. (5 marks)
A 250.0 mL flask contains 1.00×10−3 mol of NaH2PO4 and 1.00×10−3 mol of Na2HPO4. The pKa values of phosphoric acid are pKa1=2.15, pKa2=7.20, pKa3=12.35. (a) Calculate the pH of the buffer. (b) Calculate the pH after adding 1.00×10−4 mol of solid NaOH (assume no volume change). (c) Explain in approximately 100 words why this phosphate buffer is critical for maintaining intracellular pH in human cells, referencing the relevant pKa and one consequence of buffer failure. (7 marks)