Complexes: How an Insoluble Salt Is Persuaded to Dissolve

Silver bromide is one of the least soluble things in this course. A saturated solution of it in pure water holds 0.13 mg per litre, which is why a LibreTexts treatment of the same problem observes that washing the unused silver bromide out of a single roll of film with water alone “would require tens of thousands of liters of water and a great deal of time”. Yet a tray of fixer clears a film in a couple of minutes and takes the silver bromide away completely. Nothing about the silver bromide has changed. What has changed is the solution it finds itself in.

What a complex is

A complex is a metal ion with other species attached to it by bonds in which the attached species donates both of the electrons. OpenStax’s account is exact: it is a Lewis acid-base interaction, the metal ion being the electron acceptor and the attached species — the ligand — the donor. Any atom, molecule or ion with a lone pair to offer can be a ligand.

Three words come with it.

• The coordination sphere is the metal ion plus the ligands bound to it. Square brackets enclose it in a formula, and anything written outside those brackets is not part of it: in Na₃[Ag(S₂O₃)₂] the sodium ions are counter-ions, not ligands.
• The coordination number is the number of donor atoms bonded to the metal. OpenStax gives the silver case explicitly: in [Ag(NH₃)₂]⁺ it is two.
• A ligand that binds through one atom is monodentate; one that binds through several is polydentate, and a polydentate ligand gripping a metal ion is a chelate, from the Greek for a claw.

A complex ion is a different chemical species from the free metal ion, and that is the whole point. It has its own solubility, its own colour, its own stability and — as the last page showed — its own redox potential. Appendix L makes the last point unmistakable: Ag⁺/Ag is +0.7996 V, the same silver in a chloride lattice is +0.222 V, held by two ammonia molecules it is +0.373 V, and held by two thiosulfate ions it is +0.017 V. Wrapping a ligand round an ion changes what the ion is.

A silver ion, free and complexed, beside the lattice it came from

1. 1Silver bromide lattice — each silver ion surrounded by bromide; the arrangement is the reason it is insoluble
2. 2Free silver ion, Ag⁺ — vanishingly rare above solid AgBr: 7.1 × 10⁻⁷ mol/L, or 0.13 mg/L
3. 3The complex, [Ag(S₂O₃)₂]³⁻ — coordination number two; soluble, and carrying a 3− charge

Same element in all three, three different chemical species. The last page's potentials say the same thing in volts: +0.22 in the lattice, +0.80 free, +0.02 complexed.

Formation constants, and what a big one buys

The formation constant, Kf (also called a stability constant), is the equilibrium constant for building a complex from its metal ion and its ligands. Large means stable; and these numbers are very large, so they are always quoted as powers of ten.

Complex	Equilibrium	Kf	Where the course meets it
[AgCl₂]⁻	Ag⁺ + 2 Cl⁻	1.8 × 10⁵	chloride emulsions, and why excess chloride is not a fixer
[Ag(NH₃)₂]⁺	Ag⁺ + 2 NH₃	1.7 × 10⁷	historical ammoniacal silver; Part II’s prohibition
[Ag(SCN)₄]³⁻	Ag⁺ + 4 SCN⁻	1.2 × 10¹⁰	thiocyanate fixers and toners, Part XX
[Ag(S₂O₃)₂]³⁻	Ag⁺ + 2 S₂O₃²⁻	4.7 × 10¹³	fixing
[Ag(CN)₂]⁻	Ag⁺ + 2 CN⁻	1 × 10²¹	the historical cyanide fixer; Part XXVI, studied and not used
[Fe(C₂O₄)₃]³⁻	Fe³⁺ + 3 C₂O₄²⁻	2.0 × 10²⁰	ferric oxalate, Parts XXIV and XXV

The silver values with one exception are from OpenStax Appendix K; the thiosulfate constant is the one used in OpenStax’s own worked photographic example, and the iron oxalate figure is from the LibreTexts map of Petrucci.

!Compilations disagree, and the course says so

The formation constant of the silver-thiosulfate complex is given as 4.7 × 10¹³ by OpenStax and as 2.9 × 10¹³ by the LibreTexts map of Petrucci, which attributes its table to Lange’s Handbook of Chemistry, 15th edition. The same two sources also differ on the solubility product of silver bromide, 5.0 × 10⁻¹³ against 5.35 × 10⁻¹³, which is the difference the solubility page already noted. Carried through to the net constant for fixing, the pair give 24 and 15 respectively.

This page uses the OpenStax values throughout, for consistency with the rest of Part III, and states here that the other exists. A factor of 1.6 between compilations is normal for constants of this magnitude, and nothing in the argument below turns on it — the conclusion is that the constant is enormous, and both numbers are enormous.

Formation is stepwise. A ligand joins, then another, and each step has its own constant; the overall constant is the product of the stepwise ones, so that the logarithms add. Silver and thiosulfate build up through a series of species:

Ag⁺ + S₂O₃²⁻ ⇌ [Ag(S₂O₃)]⁻

First step: one thiosulfate per silver

[Ag(S₂O₃)]⁻ + S₂O₃²⁻ ⇌ [Ag(S₂O₃)₂]³⁻

Second step: the bis(thiosulfato) complex, the one the constants above describe

[Ag(S₂O₃)₂]³⁻ + S₂O₃²⁻ ⇌ [Ag(S₂O₃)₃]⁵⁻

Third step: a higher complex, formed where thiosulfate is in large excess

The photographic literature describes all three, and which of them predominates at a given thiosulfate concentration matters to fixing. The course has not found stepwise constants for the silver-thiosulfate system in a source it has read, and so does not give any. What it can give, sourced, is the overall constant for the second complex, and the practical consequences below, which follow from the overall equilibrium and from what manufacturers actually publish.

Coupled equilibria: the whole trick of fixing

Silver bromide dissolving in water is an equilibrium that goes almost nowhere:

AgBr ⇌ Ag⁺ + Br⁻

Dissolution: Ksp = 5.0 × 10⁻¹³ at 25 °C

Thiosulfate consuming silver ion is an equilibrium that goes almost to completion:

Ag⁺ + 2 S₂O₃²⁻ ⇌ [Ag(S₂O₃)₂]³⁻

Complex formation: Kf = 4.7 × 10¹³ at 25 °C

Put them in the same beaker and they share a species — the silver ion. The second reaction removes what the first produces, so the first keeps going. Add the two equations and multiply the two constants:

AgBr + 2 S₂O₃²⁻ ⇌ [Ag(S₂O₃)₂]³⁻ + Br⁻

Fixing, as one equilibrium: K = Ksp × Kf = 5.0 × 10⁻¹³ × 4.7 × 10¹³ = 24

A constant of 24 does not look impressive next to 10¹³, and that is exactly why it is worth pausing on. Twenty-four is a perfectly ordinary equilibrium constant, comfortably greater than one, describing a reaction that goes. It has been produced by multiplying an appallingly small number by an enormously large one. The whole art is in the coupling: an equilibrium that would not move on its own has been dragged forward by a second equilibrium that shares a species with it.

One equilibrium dragging another

1. 1Alone in water — the ion product reaches Ksp almost at once and dissolution stops
2. 2The silver ion, removed as it appears — two thiosulfate ions take it into the complex
3. 3The solid keeps dissolving — because [Ag⁺][Br⁻] never reaches Ksp

The solubility product is unchanged and unbreakable; it is simply never reached. Removing a product drives a reaction forward, which is Le Chatelier's principle doing the most useful thing it does in this course.

🧮How much thiosulfate does a gram of silver bromide need?

OpenStax works this in full, and it is worth following because it is the arithmetic behind every fixer capacity figure you will ever read.

Dissolving 1.00 g of silver bromide (molar mass 187.77) in 1.00 L gives 0.00532 mol/L of bromide and the same of the complex. Rearranging the combined equilibrium expression for the thiosulfate needed to sustain that:

[S₂O₃²⁻] = √( [complex] × [Br⁻] ÷ K )

From the combined equilibrium

The square root is there because the combined equilibrium constant carries the thiosulfate concentration squared — two ions per silver. So it is the square root of (0.00532 × 0.00532) ÷ 24, the square root of 1.18 × 10⁻⁶, giving 0.0011 mol/L of free thiosulfate left over at equilibrium. On top of that, each complex has locked up two thiosulfate ions, which is 2 × 0.00532 = 0.01064 mol/L. Total thiosulfate required: 0.0117 mol/L.

As the anhydrous salt (molar mass 158.1) that is 1.85 g/L. Photographic fixers are usually mixed from the pentahydrate, whose molar mass PubChem gives as 248.19, so the same quantity of thiosulfate is 2.90 g of crystals — the hydrate conversion of Part II, used and not re-derived. Note what dominates: nine-tenths of the thiosulfate is locked in complexes, and only a tenth is left free. That is the fact the next section turns into a capacity.

Why a fixer exhausts, and why a weak one fixes badly

Take the combined equilibrium seriously for a moment and it predicts fixer behaviour without any further information.

Let a fixer start with T moles of thiosulfate per litre and let x moles per litre of silver halide have been dissolved so far. Each dissolved silver has taken two thiosulfate ions with it, so the free thiosulfate remaining is T − 2x. Meanwhile the equilibrium demands a certain amount of free thiosulfate to hold the silver already in solution: rearranging K = [complex][Br⁻] ÷ [S₂O₃²⁻]² with [complex] = [Br⁻] = x gives a required free concentration of x ÷ √24, or x ÷ 4.9.

Those two lines cross, and the crossing is exhaustion.

What is left, and what is needed: the scissors that close on a fixer

• Free thiosulfate still available: T − 2x
• Free thiosulfate the equilibrium requires: x ÷ 4.9

Show the numbers behind this plot

Two lines against the amount of silver already dissolved, for a fixer that started with one mole of thiosulfate per litre. The first line, labelled free thiosulfate still available, starts at 1.0 and falls steeply and straight, reaching zero when 0.5 moles of silver have been dissolved, because each silver takes two thiosulfate ions with it. The second line, labelled free thiosulfate the equilibrium requires, starts at zero and rises gently and straight, reaching only 0.10 at the right-hand edge, because the required amount is the silver dissolved divided by 4.9. The two lines cross at 0.454 moles of silver dissolved, where both are 0.093. To the left of that crossing there is more free thiosulfate available than the equilibrium requires and the fixer keeps working; at the crossing the fixer stops. The important feature is the shape of the approach: for most of the range the available line is far above the required line, so the fixer works briskly and gives little warning, and the two lines converge only in the last tenth of the journey, which is why clearing time is nearly constant for most of a bath's life and then lengthens sharply.

Series	Silver halide already dissolved, mol per litre	Free thiosulfate, mol per litre
Free thiosulfate still available: T − 2x	0.00	1.00
Free thiosulfate still available: T − 2x	0.10	0.80
Free thiosulfate still available: T − 2x	0.20	0.60
Free thiosulfate still available: T − 2x	0.30	0.40
Free thiosulfate still available: T − 2x	0.40	0.20
Free thiosulfate still available: T − 2x	0.45	0.09
Free thiosulfate still available: T − 2x	0.50	0.00
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.00	0.00
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.10	0.02
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.20	0.04
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.30	0.06
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.40	0.08
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.45	0.09
Free thiosulfate the equilibrium requires: x ÷ 4.9	0.50	0.10

Arithmetic rather than measurement: both lines are computed from the combined constant K = 24 and the stoichiometry, for an illustrative fixer of 1 mol/L total thiosulfate. Real fixers are ammonium thiosulfate at a concentration the maker sets, and carry sulfite and an acid as well, so the numbers on the axes are illustrative and the shape is the lesson. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

Three consequences fall straight out of that picture, and all three are confirmed by what Ilford publishes.

Capacity is proportional to concentration, and has a hard ceiling. The crossing sits at x = 0.454 × T, just under the stoichiometric limit of one silver per two thiosulfate. Halve the fixer strength and you halve the capacity, exactly. No amount of extra time recovers it, because the limit is a stoichiometric one and not a kinetic one.

A dilute fixer fixes worse, not merely more slowly. This is the counter-intuitive one, and Ilford states the practical version: “if the solution concentration of a fixer bath is too high or too low efficiency is reduced and poor fixing can be experienced.” Under-dilution reduces the free thiosulfate that drives the reaction and the capacity that ends it, so a bath mixed at half strength does not take twice as long — it clears fewer films and leaves more behind in the ones it does clear.

The warning comes late. For most of a bath’s life the available line sits far above the required line, so clearing time barely changes; the two converge only near the end. That is precisely why Ilford defines the test the way it does: find the clearing time in fresh fixer, fix for twice the clearing time, and discard the bath when the clearing time in used fixer exceeds twice the fresh clearing time. It is a test that watches the last tenth of the curve.

📷The permanence consequence, which is the one that matters

Ilford’s silver-concentration limits are the sharpest published statement of what an exhausted fixer costs. A film bath may run to 8–10 g of silver per litre “without serious effect”. A bath fixing fibre-base prints for commercial permanence must stay below 2 g/L, which is about forty 8 × 10 prints; and for maximum stability in long-term storage, below 0.5 g/L, which is about ten prints. Above those levels, Ilford says, “compounds may remain in the paper base after washing and over time possibly contribute to print staining.”

The mechanism is the one this page has been building. In an exhausted bath the free thiosulfate has gone, so the silver in the paper is held in the lower complexes rather than converted cleanly to the soluble one — and those species are not removed by washing. The Image Permanence Institute’s account of historical processes makes the same point from the conservator’s end: the wash step exists “to eliminate the silver thiosulfate complexes formed during the fixing of the image”. Fix badly and you have not saved time; you have built the decay into the print. Part XI turns this into a fixing method and Part XII into a washing one.

Two-bath fixing follows from the same picture, and both makers recommend it. Kodak’s 1928 primer calls it “the best way of insuring complete fixing”; Ilford describes it as “an extremely efficient method” and gives the sequence: fix for half the time in the first bath and half in the second, work until the first bath reaches capacity, discard it, promote the second to first and make a fresh second. The reason is on the plot. The first bath does the bulk of the work in the region where the scissors are wide open; the second bath is always near the left-hand edge, so the print’s final contact is always with a fixer that has plenty of free thiosulfate. Part XI is where this becomes practice.

The other ligands in this course

Ligand	Binds	Where it appears	Note
Thiosulfate, S₂O₃²⁻	silver	every fixer	the reason the course exists in its present form
Sulfite, SO₃²⁻	silver, weakly	fine-grain developers	the solvent action below
Halide (Cl⁻, Br⁻, I⁻)	its own silver	emulsions, chloride papers	[AgCl₂]⁻ at 1.8 × 10⁵ is far too weak to fix with
Thiocyanate, SCN⁻	silver, gold	some fixers and toners	[Ag(SCN)₄]³⁻ at 1.2 × 10¹⁰
Ammonia, NH₃	silver	historical processes	restricted by this course; see below
Oxalate, C₂O₄²⁻	iron(III)	platinum, palladium, kallitype	[Fe(C₂O₄)₃]³⁻ at 2.0 × 10²⁰, a bidentate chelate
Citrate	iron(III)	cyanotype sensitiser	ammonium iron(III) citrate
Cyanide, CN⁻	silver, iron	historical fixer; ferricyanide salts	[Ag(CN)₂]⁻ at 1 × 10²¹; Part XXVI
EDTA, hexametaphosphate	calcium, magnesium, iron	clearing baths, some formulas	sequestrants, below

The silver-sulfite complex, and why D-76 has fine grain

Kodak’s 1928 primer explains D-76’s characteristic grain in one sentence that is pure complex chemistry: the formula carries “a high concentration of sulphite which is a solvent for silver bromide and iodide”, so that as development proceeds “the sulphite actually dissolves a small quantity of each grain and thereby minimizes greatly the tendency for clump formation which would increase the graininess.”

That is a silver-sulfite complex doing on a small scale what thiosulfate does on a large one. The course has no formation constant for it from a source it has read, and so gives none; what is sourced is the effect and the manufacturer’s own explanation of it. It also explains why a change to a developer’s sulfite is never only a change to its keeping, which is the point the aerial oxidation page made from the other side.

Ammonia, and the course’s restriction

Ammonia forms [Ag(NH₃)₂]⁺ with a formation constant of 1.7 × 10⁷ — strong enough that ammonia dissolves silver chloride readily, and the reason ammoniacal silver appears throughout the nineteenth-century literature. The course teaches the chemistry and restricts the practice, for a reason set out in full on the silver nitrate page: an ammoniacal silver solution can deposit silver nitride on standing or drying, and that compound is a highly sensitive contact explosive. No ammoniacal silver solution is stored, and none is allowed to dry out. Where a later part uses such a step, it is made immediately before use and quenched immediately afterwards. The complex is on the table above because you will meet it in historical texts and because it makes the point about coordination number cleanly; it is not an invitation.

Sodium thiosulfate and ammonium thiosulfate are not the same fixer

The course keeps these two apart, and this is the page where the reason belongs. Both supply the same ligand — the thiosulfate ion — and both form the same silver complexes; the counter-ion is the difference. Ilford is explicit about what is in its own bottles: the fixing agent in Rapid Fixer and in Hypam “is ammonium thiosulphate, it contains no sodium thiosulphate (hypo)”. The Image Permanence Institute dates the change in its process history: “ammonium thiosulfate (i.e., rapid fix) started being used as a fixer in addition to sodium thiosulfate.”

Ammonium thiosulfate fixers are the ones sold as rapid fixers, and the practical difference is speed. What this page will not do is explain the speed difference, because the mechanism belongs to the ammonium ion’s own behaviour in the emulsion and the course has no source it has read that establishes it. What it can say with confidence is what does not differ: the ligand, the complexes, the stoichiometric ceiling of one silver per two thiosulfate, and the consequence that an exhausted bath of either kind leaves species behind that washing will not take out. Part XI compares them as products.

The related pair is anhydrous against hydrated. A formula calling for sodium thiosulfate almost always means the pentahydrate, whose molar mass PubChem gives as 248.19 against 158.11 for the anhydrous salt — a difference of more than half as much again in the weighed mass for the same amount of ligand. Naming which one, every time, is the discipline Part II established.

Colour from complexes and from mixed valence

Complexes are often intensely coloured, because the ligands change the energies available to the metal’s electrons. Prussian blue is the case this course cares about, and it is a step further: Mike Ware’s monograph identifies it as ferric ferrocyanide, an iron cyanide complex “quite unusual in containing the element combined in two different states of oxidation”, with the deep blue attributed directly to electrons hopping from the iron(II) to the iron(III) and absorbing red light in the process. Ware gives the insoluble form as Fe₄[Fe(CN)₆]₃, a 4:3 ratio of iron(III) to iron(II). Part XXI is where that becomes a print.

Sequestrants and the water you mix with

A sequestrant is a chelating ligand added to grab metal ions that would otherwise cause trouble — calcium and magnesium from hard water, iron from pipework. Two appear in published photographic formulas: Foma’s own published reversal bath for Fomapan R100 calls for either Calgon, sodium hexametaphosphate, at 1.5 g/L or Chelaton III, an EDTA salt, at 5.0 g/L, and Kodak Ltd listed Calgon among its tested chemicals in 1949. So the practice is real and sourced.

What is not well supported is the folklore around it. Kodak’s own 1928 chapter on water supply is notably unimpressed: impurities in water “are not responsible for as many troubles as is usually supposed”, the presence of calcium and other salts “is sometimes beneficial as they tend to retard the swelling of the gelatin coating” during washing, and the only impurities the primer says are “liable to cause serious trouble with developers” are hydrogen sulfide and soluble metallic sulfides. The course’s position is therefore: use a sequestrant where a published formula calls for one, use distilled water where a source recommends it, and treat a general claim that your tap water is ruining your negatives as something to test rather than to assume.

The lesson to carry forward

Solubility is not a property of a compound. It is a property of a compound in a particular solution.

Silver bromide is insoluble in water and readily soluble in thiosulfate, and both statements are true without contradiction because “insoluble” was never an absolute. The solubility page left this paradox standing on purpose; the resolution is that adding a ligand does not break the solubility product, it simply arranges that the ion product never reaches it.

The same reasoning will come back with different metals, and three of them are worth naming now so that the pattern is recognisable when it arrives.

Iron(III) with oxalate, [Fe(C₂O₄)₃]³⁻, has a formation constant of 2.0 × 10²⁰ and is a chelate: each oxalate binds through two oxygen atoms, so three of them fill a coordination number of six. That complex is the light-sensitive species of the platinum, palladium and kallitype processes, and its photochemistry belongs to Parts XXIV and XXV.

Gold and selenium in toning reach a silver image as complexes rather than as free ions, which is what allows a metal that would otherwise be quite insoluble to be delivered evenly through a gelatin layer. Part XX.

Cyanide with silver, [Ag(CN)₂]⁻ at 1 × 10²¹, is the strongest silver complex in the table and was used as a fixer in the collodion era, faster than hypo. The course studies it and does not reproduce it; Part XXVI explains why in the terms the hazard deserves.

Whenever a later part says a substance “dissolves in” something it does not dissolve in alone, look for the ligand.

Recap

A complex is a metal ion with ligands attached, the ligand donating both electrons of the bond; the coordination number counts the donor atoms, and silver’s is two in the complexes that matter here. A complex is a distinct chemical species with its own solubility, colour and redox potential — silver’s standard potential falls from +0.80 V free to +0.02 V in the thiosulfate complex. Formation constants measure stability and are enormous: 4.7 × 10¹³ for [Ag(S₂O₃)₂]³⁻ by OpenStax’s value, 2.9 × 10¹³ by Lange’s. Multiply that by silver bromide’s solubility product of 5.0 × 10⁻¹³ and you get a net constant of about 24 for fixing: an ordinary, workable equilibrium assembled from two impossible ones, which is what coupling equilibria does. From that constant alone, a fixer’s capacity is proportional to its concentration and capped just under one silver per two thiosulfate; a dilute fixer therefore fixes worse rather than slower; and the clearing time gives almost no warning until the very end, which is why Ilford’s test is a doubling of the clearing time and its permanence limits are stated as grams of silver per litre. Two-bath fixing works because the last contact is always with a fresh bath. Sulfite is a weak enough silver ligand to dissolve a little of each grain, which is D-76’s fine grain; ammonia is a strong enough one to be historically important and is restricted here for a hazard reason; oxalate, citrate, thiocyanate and cyanide each hold their own metal in later parts. And the general lesson is that solubility belongs to a compound in a solution, never to a compound alone.

Next: how any of this reaches the silver in the first place. Fixer, developer and wash water all have to travel into and out of a swollen gelatin layer, and that journey decides agitation, edge effects and wash times.

Check your understanding

Question 1. Write the equation for dissolving silver bromide in sodium thiosulfate, name the ligand and its coordination number, and name the equilibrium that drives it.

• AgBr + Na₂S₂O₃ → AgNa + BrS₂O₃; the ligand is sodium, coordination number 1; driven by precipitation
• AgBr + 2 S₂O₃²⁻ ⇌ [Ag(S₂O₃)₂]³⁻ + Br⁻; the ligand is thiosulfate, coordination number 2; driven by complex formation, whose constant of 4.7 × 10¹³ multiplies the tiny solubility product to give a workable net constant of 24
• AgBr + 2 S₂O₃²⁻ ⇌ Ag + Br₂ + 2 S₂O₃²⁻; driven by oxidation
• AgBr + H₂O ⇌ Ag⁺ + Br⁻; driven by dilution

Show the answer and why

Answer: AgBr + 2 S₂O₃²⁻ ⇌ [Ag(S₂O₃)₂]³⁻ + Br⁻; the ligand is thiosulfate, coordination number 2; driven by complex formation, whose constant of 4.7 × 10¹³ multiplies the tiny solubility product to give a workable net constant of 24

Two thiosulfate ions coordinate to one silver ion, giving the coordination number of two that OpenStax states for silver in this kind of complex, and a net charge of 3−. The equilibrium that drives it is the complex formation: on its own the dissolution has a constant of 5.0 × 10⁻¹³ and goes nowhere, and multiplying by the formation constant gives 24. The answer that turns it into silver metal and bromine is the classic misreading — fixing is not a redox reaction, and nothing is oxidised or reduced in it, which is what distinguishes it from every other bath in the sequence.

Question 2. A student dilutes fixer to half the recommended strength to save money. Predict the effect on clearing time, on capacity and on the permanence of the print, and say which is noticed first and which matters most.

• Clearing time doubles, capacity is unchanged, permanence is unaffected
• Capacity doubles because the bath is bigger
• Nothing changes as long as the fixing time is doubled
• Clearing time lengthens, capacity is halved exactly, and permanence suffers because a weak or loaded bath leaves lower silver-thiosulfate complexes in the paper that washing does not remove; the clearing time is noticed first and the permanence matters most

Show the answer and why

Answer: Clearing time lengthens, capacity is halved exactly, and permanence suffers because a weak or loaded bath leaves lower silver-thiosulfate complexes in the paper that washing does not remove; the clearing time is noticed first and the permanence matters most

Capacity is stoichiometric: the ceiling is a fraction under one silver per two thiosulfate, so half the thiosulfate is half the silver, exactly, and no extra time recovers it. Ilford states the practical version — efficiency is reduced and poor fixing experienced when the concentration is too low. The clearing time is what a student notices, because it happens in front of them; the permanence consequence is invisible for years and is the one that ends the print. Ilford puts numbers on it: for maximum stability the silver in the bath is kept below 0.5 g per litre, which is about ten 8 × 10 fibre-base prints.

Question 3. Explain in three sentences why silver bromide is called insoluble even though a fixer dissolves it completely.

• "Insoluble" is wrong; it is soluble and the textbooks are mistaken
• The fixer chemically destroys the silver bromide, so it is not dissolution at all
• Insoluble describes its behaviour in water, where the solubility product of 5.0 × 10⁻¹³ limits it to 0.13 mg per litre; a fixer does not repeal that product but consumes the silver ion as fast as it appears, so the ion product never reaches it; solubility therefore belongs to a compound in a particular solution rather than to the compound alone
• The fixer raises the temperature enough to dissolve it

Show the answer and why

Answer: Insoluble describes its behaviour in water, where the solubility product of 5.0 × 10⁻¹³ limits it to 0.13 mg per litre; a fixer does not repeal that product but consumes the silver ion as fast as it appears, so the ion product never reaches it; solubility therefore belongs to a compound in a particular solution rather than to the compound alone

This is the sentence the page exists to make you able to write. Note the middle clause especially: the solubility product is not violated, suspended or exceeded at any point. It is simply never reached, because a second equilibrium keeps removing one of its products. That is what a coupled equilibrium is, and it is the same reasoning by which an acid dissolves a carbonate or an alkali dissolves aluminium hydroxide.

Question 4. A fixer bath contains 0.40 mol of thiosulfate per litre. Using the net constant of 24 and the stoichiometry, roughly how many moles of silver halide per litre can it dissolve before it stops?

• About 0.18 mol, which is 0.454 × 0.40 — a little under the stoichiometric ceiling of one silver per two thiosulfate
• About 0.40 mol, one silver per thiosulfate
• About 0.80 mol, since each thiosulfate handles two silvers
• Unlimited, provided you allow enough time

Show the answer and why

Answer: About 0.18 mol, which is 0.454 × 0.40 — a little under the stoichiometric ceiling of one silver per two thiosulfate

Set the free thiosulfate remaining, T − 2x, equal to the free thiosulfate the equilibrium requires, x ÷ √24 = x ÷ 4.9. That gives T = 2.204x, so x = 0.454 T, which for T = 0.40 is 0.18 mol/L. Two things to take away. The ceiling of 0.5 T is stoichiometric and cannot be beaten by time or agitation. And the answer is proportional to T, which is why a fixer's published capacity scales with its dilution and why mixing it weak is a false economy rather than a slow one.

Question 5. Ilford says to fix for twice the clearing time and to discard the bath when the clearing time in used fixer exceeds twice the clearing time in fresh fixer. Why is a doubling of clearing time the right trigger rather than, say, a ten per cent increase?

• Because ten per cent is too small to measure with a stopwatch
• Because the free thiosulfate stays far above what the equilibrium requires for most of the bath's life, so clearing time barely moves until the very end; a doubling is the first change large enough to be a reliable signal that the bath is close to its stoichiometric limit
• Because the clearing time doubles as soon as the first film goes through
• Because doubling is a convention with no chemical basis

Show the answer and why

Answer: Because the free thiosulfate stays far above what the equilibrium requires for most of the bath's life, so clearing time barely moves until the very end; a doubling is the first change large enough to be a reliable signal that the bath is close to its stoichiometric limit

Look at the shape of the two lines. The available free thiosulfate falls steeply and the required amount rises gently, so the gap between them — which is what drives the reaction — stays wide for most of the journey and closes only in the last tenth. A test based on a small change would fire on ordinary variation; a test based on a doubling fires when the gap is genuinely closing. The corollary is a warning: a bath that has just passed the test was already deteriorating before it did, which is the reason for the second bath and for the separate, stricter silver-concentration limits where permanence matters.

Question 6. Kodak explains D-76's fine grain by saying its high sulfite concentration is a solvent for silver bromide. What is happening, and what does it imply about changing the sulfite in a formula?

• The sulfite reduces the silver, so raising it makes the developer more active only
• The sulfite precipitates silver sulfite, which is what gives fine grain
• The sulfite raises the pH, which dissolves the grain
• Sulfite is acting as a weak silver ligand, dissolving a little of each grain during development so that grains clump less; raising or lowering it therefore changes grain and effective speed as well as keeping, so it is never a single-purpose ingredient

Show the answer and why

Answer: Sulfite is acting as a weak silver ligand, dissolving a little of each grain during development so that grains clump less; raising or lowering it therefore changes grain and effective speed as well as keeping, so it is never a single-purpose ingredient

It is the same mechanism as fixing, weaker by many orders of magnitude — a ligand taking silver ion into solution and so shifting the dissolution equilibrium. The 1928 primer's wording is that the sulfite "actually dissolves a small quantity of each grain and thereby minimizes greatly the tendency for clump formation". The practical lesson is the general one for reading formulas: an ingredient usually does more than one job, and the quantity in a published formula is a compromise between those jobs rather than a maximum or a minimum for any one of them.

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