Equilibria (A Level)

• Every constant in this chapter is a Kc in disguise: write the equilibrium, leave out the solid or the solvent, and the expression, the units and the calculation follow — and no calculation ever needs a quadratic.
• Strong acid c, strong alkali through Kw, weak acid √(Kac), buffer Ka[HA]/[A−]. Resists, not prevents. Ksp never changes; the solubility does.

• 25.1.1 I can understand — understand and use the terms conjugate acid and conjugate base
• 25.1.2 I can define — define conjugate acid-base pairs, identifying such pairs in reactions
• 25.1.3 I can define — define mathematically the terms pH, K_a, pK_a and K_w and use them in calculations (K_b and the equation K_w = K_a × K_b will not be tested)
• 25.1.4 I can calculate — calculate [H+(aq)] and pH values for: (a) strong acids (b) strong alkalis (c) weak acids
• 25.1.5 I can — (a) define a buffer solution (b) explain how a buffer solution can be made (c) explain how buffer solutions control pH; use chemical equations in these explanations (d) describe and explain the uses of buffer solutions, including the role of HCO3- in controlling pH in blood
• 25.1.6 I can calculate — calculate relevant concentrations and the pH of buffer solutions, given appropriate data
• 25.1.7 I can understand — understand and use the term solubility product, Ksp
• 25.1.8 I can — write an expression for Ksp
• 25.1.9 I can calculate — calculate Ksp from concentrations and vice versa
• 25.1.10 I can — (a) understand and use the common ion effect to explain the different solubility of a compound in a solution containing a common ion (b) perform calculations using Ksp values and concentration of a common ion
• 25.2.1 I can state — state what is meant by the term partition coefficient, Kpc
• 25.2.2 I can calculate — calculate and use a partition coefficient for a system in which the solute is in the same physical state in the two solvents
• 25.2.3 I can understand — understand the factors affecting the numerical value of a partition coefficient in terms of the polarities of the solute and the solvents used

Units and significant figures are marked. The syllabus states that failure to quote units, the inclusion of units in quantities defined as ratios, and answers given to an inappropriate number of significant figures are all liable to be penalised. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as procedure, recording and evaluation rather than as theory.

• “[H+] = √(Kac) works for any solution I am given.” Correct It is for weak acids only. A strong acid has [H+] = c. A strong alkali gives [OH−] = c, and you go through Kw: [H+] = Kw/[OH−]. A buffer uses [H+] = Ka[HA]/[A−]. Decide which of the four cases you have before you touch the calculator (pH calculator).
• “0.0500 mol dm−3 Ba(OH)2 has [OH−] = 0.0500.” Correct Two hydroxide ions per formula unit: [OH−] = 2 × 0.0500 = 0.100 mol dm−3, pH 13.00.
• “A buffer keeps the pH constant.” Correct A buffer resists changes in pH when small amounts of acid or alkali are added. The pH still moves a little, and a large addition overwhelms it.
• “Adding a common ion lowers Ksp.” Correct Ksp depends only on temperature. The solubility falls; Ksp is what stays the same, and that is what lets you calculate the new solubility.
• “The conjugate base of H2SO4 is SO42−.” Correct A conjugate pair differs by exactly one proton: H2SO4/HSO4−, then HSO4−/SO42−.
• “Kpc has units of mol dm−3 and depends on how much solvent I use.” Correct It is a ratio of two concentrations in the same unit, so it has no unit, and at a fixed temperature it is fixed by the solute and the two solvents. The volumes change how much is extracted, not Kpc.
• “The conjugate base of H2SO4 is SO42−.” Repair A conjugate pair differs by one proton: H2SO4/HSO4−, then HSO4−/SO42−.
• “In NH3 + H2O ⇌ NH4+ + OH−, NH3 and OH− are a conjugate pair.” Repair They differ by more than a proton. The pairs are NH3/NH4+ and H2O/OH−.
• “pH 4 is twice as acidic as pH 8.” Repair Each pH unit is a factor of ten: pH 4 has 104 times the [H+] of pH 8.
• “0.100 mol dm−3 ethanoic acid has pH 1.00.” Repair [H+] = c only for a strong acid. For a weak acid, [H+] = √(Kac): pH 2.88 with Ka 1.7 × 10−5.
• “0.100 mol dm−3 NaOH: [H+] = 0.100, so pH = 1.00.” Repair The concentration of an alkali gives [OH−]. Convert with Kw: [H+] = 1.00 × 10−13, pH 13.00.
• “[OH−] in 0.0500 mol dm−3 Ba(OH)2 is 0.0500.” Repair Two OH− per formula unit: 0.100 mol dm−3.
• “pH = 2.4 is precise enough.” Repair With concentrations to three significant figures, give pH to two decimal places: 2.40. The digit before the point only locates the power of ten.
• “A buffer keeps the pH constant.” Repair It resists changes in pH when small amounts of acid or alkali are added; the pH changes slightly.
• “The buffer works because the equilibrium shifts to oppose the change.” (no equations) Repair Write one equation for each addition — A− + H+ → HA for acid, HA + OH− → A− + H2O for alkali — and say both reservoirs are large compared with the addition.
• “Diluting a buffer lowers its pH.” Repair Its pH depends on the ratio [HA]/[A−], which dilution leaves unchanged.
• “Ksp(PbCl2) = [Pb2+][Cl−], units mol2 dm−6.” Repair The power is the coefficient: [Pb2+][Cl−]2, mol3 dm−9. And with solubility s, [Cl−] = 2s, not s.
• “Adding NaCl lowers the Ksp of AgCl.” Repair Ksp is constant at a given temperature; the solubility falls, because [Cl−] rises and [Ag+] must fall to keep the product at Ksp.
• “Kpc depends on the volumes of solvent used.” Repair It depends on the solute, the two solvents and the temperature only. The volumes decide the mass extracted, not the ratio of concentrations.
• “One extraction with all the solvent is as good as two with half each.” Repair Two portions recover more: 1.68 g against 1.5 g in worked example 5, because each fresh portion re-establishes Kpc with what is left.

• Read the command word before you decide how much to write. This syllabus has twenty-two of them: analyse, calculate, compare, consider, contrast, deduce, define, demonstrate, describe, determine, discuss, evaluate, examine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Comment, estimate, name and outline are not among them: where a question wants something named it says identify, which the syllabus glosses as “name/select/recognise”. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Deduce and determine want a conclusion reached from the information given, with the reasoning visible.
• Interleave with the chapters that use this one. Topic 28 (stability constants) reuses the Kc logic of this chapter: re-answer “write the expression, leave out the water, work out the units” there. Topic 37 (chromatography) is partition repeated: re-answer why a non-polar solute moves further in a non-polar mobile phase. And any organic chapter that separates a product with a separating funnel is 25.2.2 in practice. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Chemistry 9701 has five components. Topic 25 is A Level content, so it is examined in Papers 4 and 5. A Level content: examined in Paper 4 (A Level structured, which also requires the AS content) and, as practical context, Paper 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E.
• There is no multiple-choice paper on A Level content, so topic 25 is met in structured questions. They ask you to define pH, Ka, Kw, a buffer, Ksp or Kpc; to identify conjugate pairs in an equation; to explain how a buffer works with an equation for each addition, or the common-ion effect through Le Chatelier and an unchanged Ksp; and to calculate.
• pH of strong acids, strong alkalis, weak acids and buffers; Ka from a pH; Ksp from a solubility and back, with and without a common ion; masses extracted with Kpc. Kw = 1.00 × 10−14 mol2 dm−6 is in the Data section; every Ka, Ksp and Kpc is given in the question. pH is quoted to two decimal places.
• A pH-meter titration of a weak acid, planned and analysed so that the pH at half the equivalence volume gives pKa; and the titration of a saturated solution to find a solubility and Ksp. A planning or evaluation question asks for the table, the graph, the precision of each reading, calibration and the largest error.
• Read the command word before you decide how much to write. This syllabus has twenty-two of them: analyse, calculate, compare, consider, contrast, deduce, define, demonstrate, describe, determine, discuss, evaluate, examine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Comment, estimate, name and outline are not among them: where a question wants something named it says identify, which the syllabus glosses as “name/select/recognise”. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Deduce and determine want a conclusion reached from the information given, with the reasoning visible.