LearnChem · Part IV — What makes a reaction go further, or faster?
No liquid dissolves everything. This module asks what water does to a grain of salt, and how much it will take. Then it asks where the numbers that describe it fail. It ends at a sachet of ORS after a fever.
"Is there a liquid that dissolves everything? If not, why does water dissolve so much and petrol so little?"
No, there is no such liquid, and the reason is the whole module. By the end you can say which way water moves through your own gut wall.
Module 19 said an acid hands a proton over and a base takes one. Module 17 gave every balance a number for where it settles. Module 8 showed a water molecule with a charged end at each side. All three come back here. Module 8's charged ends do the work of this module. Module 17's number gets a new name. And a proton handed over is what makes a Chennai borewell so hard.
This module sits across two school years. Its first four sections belong to the class 11 unit on Equilibrium, where solubility and Ksp are taught. Its last two belong to the class 12 unit on Solutions, where freezing points and osmosis are taught. You are fifteen, so neither half is assumed here. Everything is built from module 17 and module 8. One box in §2 is marked enrichment, because it is in neither year's syllabus.
Is there a liquid that dissolves everything? No. A liquid that dissolved everything would dissolve its own bottle. Every liquid dissolves some things and leaves others alone. Water dissolves salt, sugar and vinegar, and leaves oil alone. Petrol dissolves oil and wax, and leaves salt alone. Module 8 said why water is different. A water molecule has a charged end at each side. So water can grip a charge. Petrol has no charged ends, and it cannot. Table salt is a crystal. Stir a spoon of it into water and it disappears. Before the chemistry, say what you think is in the glass.
A spoon of table salt has disappeared into a glass of water. The water is clear. What is in the water now?
Answer from your gut. The reveal follows.
The salt is gone as salt. What is left is two kinds of ion. An ion is an atom that has lost or gained electrons, so it carries a charge. The sodium ions carry a positive charge. The chloride ions carry a negative charge. In the crystal, every sodium ion sat surrounded by chloride ions, and every chloride ion by sodium ions. In the water, each ion is on its own. Water molecules surround it, with their charged ends turned towards it. Module 8 built those ends. A negative end faces every sodium ion. A positive end faces every chloride ion. Chemists call this hydration. Hydration is water molecules gathering round an ion and holding it. The whole change is one line.
NaCl(s) → Na+(aq) + Cl-(aq)
So two things pull on every ion at the crystal's edge. The crystal grips it from behind. The water pulls it from the front. Which pull wins, and by how much? That is a question about energy. Before the numbers, a picture.
Picture one water molecule arriving at the crystal's edge. It turns a charged end towards a corner ion and pulls. The crystal grips that ion from behind. This is a tug of war over one ion. Chemists call the crystal's regular stack of ions a lattice. One team is the lattice, and its pull is the lattice's grip. The other team is water, and its pull is hydration. The picture holds in one way. Both pulls are real, and both are measured in energy. A tug of war ends when one side wins and the rope stops moving. Whether dissolving ends the same way is a question for §2. Keep it open until then. And a tug of war has two teams and nothing else. Dissolving has a third thing. There are vastly more ways to spread the ions through the water than to stack them in a crystal. Module 13 counted such ways. That count pulls too, and it is on neither team.
Put a sensitive thermometer in the glass. Now stir in the spoon of table salt and let it dissolve. Which way does the reading move?
Commit first. The numbers follow.
The glass gets colder, and only a little. It settles two things. First, dissolving is not a reaction. A reaction makes a new substance, and boiling the water away gives the same salt back. An ion can still react with something later, as §3's carbonate will. That is a second step, after the dissolving. Second, for this salt the two pulls nearly match, and the lattice wins by a little. Pulling the crystal apart into free ions costs energy. Chemists call that cost the lattice enthalpy. Enthalpy is module 12's word for heat at steady pressure. Water pays most of that cost back when it gathers round the ions. It does not pay quite all of it. The shortfall comes out of the water's own heat, so the glass cools. Then why does the salt dissolve at all? The third thing pays, and the arithmetic below prices it.
Pulling one mole of the crystal apart into separate ions costs 786 kJ. That is the lattice enthalpy, and it comes from a chain of other measurements. Dissolving one mole of the salt in plenty of water takes in 3.88 kJ. That number is measured directly, with a thermometer in the water itself. Both numbers are positive, because in both cases heat goes into the salt. Water's pull is not measured directly, because free ions never arrive without a crystal. So water's pull is worked out as the difference between the two measured numbers. Take the lattice's 786 kJ/mol away from the 3.88 kJ/mol that dissolving costs. That is 3.88 minus 786, which comes to −782.12 kJ/mol for the whole salt. The minus sign means this part gives heat out rather than taking it in. So the grip is 786 kJ/mol and the pull is 782.12 kJ/mol. The grip wins, and it wins by only 3.88 kJ/mol out of 786. The readout below adds a second measured route, which agrees within 0.2 kJ/mol.
Now the third thing gets numbers of its own, from the same tables. Module 13 counted the ways a state can be arranged and called the count entropy. Module 14 used entropy as the referee that decides whether a change happens. The CODATA table that gave the enthalpies gives the dissolved ions' entropies too. A dissolved sodium ion has 58.45 and a dissolved chloride ion has 56.60 J/(mol·K). The crystal itself has 72.11 J/(mol·K), from the NIST-JANAF tables. So dissolving gains 58.45 plus 56.60 minus 72.11, which is 42.94 J/(mol·K). Module 14's referee multiplies that gain by the temperature, measured in kelvin. In kelvin, which count from the coldest temperature possible, 25 °C is 298.15 K. So 42.94 J/(mol·K) multiplied by 298.15 K comes to 12.80 kJ/mol of disorder. That is 3.3 times the 3.88 kJ/mol shortfall that the lattice's grip left. Take the 12.80 from the 3.88 and the balance comes to −8.92 kJ/mol. The minus sign is module 14's verdict, and it says the salt dissolves. A second route, through Gibbs energies of formation, gives −8.99 kJ/mol instead. The two routes agree to 0.07 kJ/mol, so the number is solid. Each ion's entropy is counted from an agreed zero, and that zero scales with charge. In a neutral salt the charges cancel, so this sum does not depend on the zero. The per-ion enthalpies have no such cancellation, which is why the source line refuses to split them.
One number above is derived and not measured, and it is water's pull. Textbooks often split that −782 of enthalpy between the two ions. The sodium ion gets one share and the chloride ion the other. No experiment can make that split. Any split rests on a convention, an agreed starting point, and different conventions move the shares by tens of kJ/mol. So this page gives the total and no shares. Anhydrous calcium chloride is the opposite case. Anhydrous means the crystal holds no water of its own. For it, water's pull beats the lattice's grip by 81.2 kJ/mol, so the glass gets warmer. That is how a chemical hand-warmer works. There the energy term decides the outcome on its own, and disorder is not needed to settle it. The readout says anhydrous on purpose. The same salt with water already built into its crystal gives out far less.
Two textbooks print different hydration enthalpies for the sodium ion on its own. Both print the same total for sodium chloride. Which statement is true?
— The crystal comes apart into separate ions, and water holds every one of them.
Keep adding salt to the glass and stirring. For a while every spoon disappears. Then one does not. The grains sink and stay at the bottom, however long you stir. Chemists call the solution saturated. Saturated means the water holds as much of that salt as it will hold at that temperature. The glass now looks finished. Before the reveal, say what is happening at the surface of those grains.
A saturated salt solution stands with a layer of grains at the bottom. Nothing you can see changes for hours. What is happening at the surface of those grains?
Guess before you are shown.
Saturated is not full. It is a standoff. Ions leave the grains all the time, exactly as they did from the first spoon. Ions also rejoin the grains all the time. At saturation the two rates are equal. So the amount dissolved holds still while the exchange at the surface never stops. Module 17 called this a balance. A balance is a change that runs both ways and settles. Here is how anybody knows. Drop a rough, broken crystal into its own saturated solution and leave it. Its mass does not change. Its shape does. Corners go and smooth faces grow. Ions are leaving the corners and landing on the faces. Nothing has stopped. The equation gets a double arrow.
NaCl(s) ⇌ Na+(aq) + Cl-(aq)
Now change one thing. Warm the water. Sugar dissolves faster in hot tea, and more of it dissolves. Module 18 said what heat does to a balance. Heat pushes a balance towards the side that takes heat in. Dissolving table salt takes heat in, as §1 measured. So warming pushes it towards the dissolved side, and a little more salt dissolves. Sugar goes the same way. Now take sodium sulfate, a salt sold as a laxative powder, and predict what heat does to it.
You warm a glass of water step by step, from cold to hot. At each step you dissolve as much sodium sulfate as the water will take. What happens to the amount it takes?
Commit, then read what the measurements say.
This box is enrichment, in neither year's syllabus. Sodium sulfate's solubility climbs steeply as cold water warms. It peaks at 32.374 °C. Above that it falls a little and then goes almost flat. Below the turn, the solid sitting in the solution is a hydrate, Na2SO4·10H2O. A formula unit is the smallest set of ions a formula names. A hydrate is a crystal with water molecules built in, here ten per formula unit. Above the turn, the stable solid is the bare salt, Na2SO4. Chemists call that switch an incongruent phase transition. The solid at the bottom becomes a different solid. The two solids dissolve differently, so the balance follows whichever solid is stable at that temperature. A gas breaks the rule too. Carbon dioxide gets less soluble as water warms, with no turn. Warm cola goes flat for that reason, and tier 2 puts a number on it.
This box carries two flags. Only two of sodium sulfate's numbers are properly sourced, the peak and the temperature of the turn. The peak is 49.7 g of salt per 100 g of water, and the readout gives it as moles too. The values at the cold end and the hot end of the curve come from weaker sources. So the curve is not drawn or tabulated here. And the carbon dioxide figure that tier 2 computes is computed from a measured constant, not measured itself. No measured bottle pressure above 20 °C was found.
A sealed bottle of cola goes into the fridge. Compared with the same bottle at room temperature, what is true once it is cold?
— A saturated solution is a standoff, not a full container.
Chennai runs on borewells. Boil borewell water and a white crust forms in the kettle. The crust is mostly calcium carbonate, the eggshell mineral of module 19. Engineers call such water hard, and report it as milligrams of calcium carbonate per litre.
Chemists call the mineral calcite. Calcite dissolves in water, and what dissolves is a balance like §2's. For a dissolving solid, module 17's balance number has its own name, Ksp. Ksp is the calcium concentration multiplied by the carbonate concentration, once the balance has settled. Concentration means moles per litre. The solid itself does not appear in it, because a solid has no concentration to change. For calcite at 25 °C, Ksp is 3.3 × 10−9.
CaCO3(s) ⇌ Ca2+(aq) + CO32-(aq)
Calcite's Ksp is 3.3 × 10−9. Before any arithmetic, guess how much calcium carbonate one litre of pure water can hold.
Predict before you are told.
Each formula unit that dissolves gives one calcium ion and one carbonate ion. So the two concentrations are equal, and each equals the calcite dissolved per litre. Ksp is that amount multiplied by itself, so the amount is its square root. The square root of 3.3 × 10−9 is 5.7446 × 10−5 mol/L of dissolved calcite. One mole of calcium carbonate weighs 100.0869 g, and engineers want grams, not moles. Multiply 5.7446 × 10−5 mol/L by 100.0869 g/mol, and the moles cancel out. That leaves 5.75 × 10−3 g of calcium carbonate in every litre of water. A gram is a thousand milligrams, so 5.75 × 10−3 g/L is 5.75 mg/L. Pure water, then, holds 5.75 mg of calcite per litre, according to Ksp alone. Now read what a real Chennai borewell actually holds in each litre.
Pure water holds 5.75 mg/L. Chennai District's borewells were sampled in four rounds, and the averages ran from 362.70 to 449.21 mg/L. That is between sixty-three and seventy-eight times what Ksp allows. Every round's average sits above the BIS acceptable limit of 200 mg/L, and none reaches the permissible 600 mg/L. So what fills the gap? Rain falls through air, and air holds carbon dioxide. Dissolved carbon dioxide and water make carbonic acid. Module 19 said what an acid does. It hands a proton to a base. The carbonate ion is a base, and it takes the proton. That makes bicarbonate, HCO3−. This is §1's second step, a reaction after the dissolving. Ksp counts carbonate, not bicarbonate. So the product falls below Ksp, and module 17's balance answers in one way. More calcite dissolves. Calcium fluoride has a different shape of expression, because it gives two fluoride ions for every calcium ion.
CaF2(s) ⇌ Ca2+(aq) + 2 F-(aq)
Now the fluoride appears twice on the right. So in the product it is multiplied in twice, as the fluoride concentration squared. Calcite is a 1:1 salt, one calcium for one carbonate. Calcium fluoride is a 1:2 salt, one calcium for two fluorides. Working the amount back out of a squared factor needs a cube root. Bench 2 in §4 does that sum for you. The values of Ksp are not beyond doubt either. Different reference tables do not agree on it. For calcium fluoride one table says 2.5 × 10−11 and another says 3.45 × 10−11, about a third apart. This module uses 2.5 × 10−11. Calcite's value is better agreed. Small constants for barely soluble salts are hard to measure, because there is so little in the water to measure.
Sodium sulfate, the salt of §2, dissolves in water. Which particles are in the water?
— Ksp describes pure water, and a borewell is not pure water.
The kettle crust and the grey scum in a bucket of soapy borewell water are the same calcium. Washing soda is sodium carbonate, Na2CO3. Dissolve a spoon of it in borewell water that stands over a little calcite. Now the water holds carbonate from two places. One is the calcite. The other is the washing soda. Predict how much calcite the water holds now.
Calcite alone put 5.7446 × 10−5 mol/L of carbonate into the water. The washing soda takes the carbonate to 10−2 mol/L. How far does the amount of dissolved calcite fall?
Predict, then drive the bench.
Read the readout at the starting setting. The product of the two concentrations equals Ksp. Slide the anion up tenfold and read it again. It still equals Ksp. Nothing you do to the slider moves the constant. What moves is the solubility, and it falls every time the anion rises. Chemists call this the common-ion effect. The common-ion effect is one salt dissolving less because another substance has supplied one of its ions. Now count the fall. For calcite, ten times more carbonate divides the solubility by ten. Switch to calcium fluoride. Ten times more fluoride divides its solubility by a hundred, because the fluoride is squared in the product. That is the rule for the slope. It is not a rule for the size of the drop.
Why does it fall? Ksp is a product, and the balance holds the product. When the carbonate rises, calcium times carbonate would rise above Ksp. Module 18 said what a balance does when it is pushed. It gives some of the push back. Here it gives back by moving calcium and carbonate ions out of the water and on to the solid. The calcium falls until the product is back at Ksp. That is the whole mechanism, and it is §3's borewell run backwards. There carbonate was removed and more calcite dissolved. Here carbonate is added and calcite comes out.
This is why washing soda softens water. It puts carbonate in on purpose, the calcium comes out as calcite, and the soft water goes to the wash. It is also why soap scum forms in the first place. Soap is the sodium salt of a long fatty acid. Its sodium salt dissolves. Its calcium salt does not. Hard water hands the soap its calcium, and the calcium salt comes out of the water as scum. It comes out on the bucket, on the cloth and on you. Wash in water that washing soda has treated and there is no calcium left for the soap to meet.
Barium sulfate is a 1:1 salt. Calcium fluoride is a 1:2 salt. Set the bench to each in turn, with the added anion at its highest, 10−2 mol/L. Which salt shows the bigger fold drop from its pure-water value?
— Feed a solution one of its own ions and it gives up the other.
In Himachal and Kashmir, road crews throw salt on icy roads before dawn. In Chennai the closest thing is the kulfi seller's tub, where ice and salt are packed round the moulds. Both use table salt, the salt of §1. Both work. This section asks what the salt actually does to the ice. Commit to an answer before the bench, because the bench draws the answer.
Ice sits on a road, a little below freezing. A crew throws table salt on it, and within the hour the ice is water. What did the salt do?
Commit, then drive the bench yourself.
No. Salt does not eat ice, and salt water does freeze. The sea is salt water, and the Arctic Ocean freezes every winter. What the salt did is drawn on the bench below. Slide the salt up and read the freezing point. Every step drives it lower. Ice on a road sits a little below freezing. That is now above the freezing point of the brine on it, so it melts. How salt does that comes after the bench.
Here is the mechanism. Ice and liquid water sit in a balance, like §2's grains and solution. Water molecules leave the ice and rejoin it at equal rates. That happens at one temperature only, the freezing point. Now dissolve salt in the liquid. The ions take up places in the liquid. So fewer water molecules reach the ice to rejoin it. Molecules still leave the ice at the old rate. So the ice loses. It melts until the liquid is cold enough for leaving to slow and match. The balance now sits at a lower temperature. The salt did not melt the ice. It moved the line. Ice and salt in the kulfi tub sit at that lower balance, colder than plain ice. The number of particles in the liquid did the work, not their being salt. Sugar would do it too.
Chemists write the drop in freezing point as i times Kf times m. Here i is the van't Hoff factor, the particles from one formula unit. Table salt gives one sodium ion and one chloride ion, so i is 2. Kf is a constant for water, 1.853 K·kg/mol, measured on dilute solutions. The K is the kelvin, and one kelvin of drop is one degree Celsius. m is the molality, the moles of salt dissolved in each kilogram of water. Road brine is 23.3 per cent salt by weight, which is 5.198 mol/kg. So the drop is 2 times 1.853 times 5.198, which comes to 19.26 K. Take 19.26 degrees off pure water's freezing point, and the formula predicts −19.26 °C. That brine actually freezes at −21.1 °C, so the formula is 1.84 °C too warm. Now tick the box, and the bench uses the real factor, 2.414, instead. With 2.414 the drop is 23.26 K, and the formula predicts −23.26 °C. That is 2.16 °C too cold, and the miss is now in the other direction. The better factor gives the worse answer, and the readout below shows both misses.
The night will be colder than −21.1 °C, so the crew throws far more salt. The brine goes well past 23.3 per cent. How cold can that liquid now get before it freezes?
Answer it, then push the slider to the end.
The brine at 23.3 per cent holds all the salt the water will take. It freezes at −21.1 °C, and no salt brine freezes lower. Chemists call that point the eutectic. Past it, the extra salt stays solid on the road. The liquid cannot get colder without freezing. So more salt buys nothing.
Two flags on the sources. The real van't Hoff factor is computed from measurements made at 25 °C. It is then used at a freezing point, and that is one reason it still misses. At this strength it is 2.41. It dips to about 1.87 near 1 mol/kg and climbs back to 2.41 where road salt lives. The mid-curve point the bench draws is 12.1 per cent freezing at −8.3 °C. It comes from an industrial brine table with no author or date, so it is flagged secondary. Against that point the formula with a factor of 2 is out by only 0.43 °C. So the formula is good where the solution is dilute and bad near saturation.
Calcium chloride gives three particles when it dissolves, one calcium ion and two chloride ions. You make a calcium chloride solution and a table-salt solution with the same molality, both dilute. How do their freezing points compare?
— Dissolved particles lower the temperature where ice and water balance, and that is all salt does to a road.
After a fever with loose motions, a doctor says drink ORS. ORS is oral rehydration salts, a sachet of salt and sugar for one litre of clean water. Why that recipe, and why not plain water? The answer is about a wall that lets water through far faster than anything dissolved in it. Chemists call such a wall a semipermeable membrane, and they call the dissolved particles the solute. Your gut lining is such a wall, and so is the skin of every cell. Doctors count the solute on each side of it in mOsm/L. One osmole is one mole of separate dissolved particles, whatever they are. A milliosmole is a thousandth of that, and mOsm/L means milliosmoles per litre. Blood plasma holds 291 mOsm/L.
A model cell holds 291 mOsm/L of solute, like blood. You drop it into a bath at 400 mOsm/L. The cell's skin lets water cross and holds the solute back. What happens to the cell?
Predict, then run the model.
Water left the cell and moved to the crowded side. Chemists call this osmosis. Osmosis is water crossing a wall that holds the solute back, towards the side with more solute. Nothing pulled it. Water molecules hit the skin from both sides all the time, and some pass through. On the crowded side, part of every litre is particles, so fewer water molecules reach the skin. More cross from the dilute side than come back. Now drive the bench. Change how fast water crosses. The time changes and the final volume does not, because the endpoint is set by the two concentrations alone. Set the bath to pure water. The cell swells past its limit and bursts. Tick the box and let the particles cross too. The crowding equalises before the water can do any lasting work, and the cell ends close to its normal size.
Osmosis pushes. Osmotic pressure is the pressure you would need on the crowded side to stop the water crossing. The table below gives it for plasma and for two drinks. There is a second unit for counting solute, and it appears once here. Doctors also use osmolality, which counts particles per kilogram of water instead of per litre of solution. Plasma's osmolality is 288 mOsm/kg. The two are close in blood and are not the same quantity, and this module uses mOsm/L throughout. Sweat is salty for the same reason blood is. It is made from fluid drawn out of the blood, and that fluid carries plasma's solute. The gland takes only part of the salt back before the sweat reaches your skin. The sachet comes next. You stir it into a litre and leave the glass on the table overnight. Predict what you find in the morning.
The ORS was stirred into its litre last night, covered, and left on the table. This morning, what is true of the drink?
Commit, then read the table.
Nothing settles and nothing stops. Every ion in that glass is held by water and knocked about by water. So the drink stays the strength you made it. The recipe was changed in 2002, and here is why. Until 2002 the World Health Organization's sachet made a drink of 311 mOsm/L. Plasma is 291. So the drink was the crowded side, hypertonic to plasma. It held water in the gut instead of letting it into the blood. Patients had more stool and more vomiting. The current sachet makes 245 mOsm/L, hypotonic to plasma. Water crosses out of it and into the blood. In trials, that change cut the number of patients who needed a drip by about a third. Nothing else about a drink matters to the direction, because osmosis counts particles and not what they are. The table gives both drinks and plasma side by side.
A hospital drip is salt water matched to plasma, near 291 mOsm/L. A drip far saltier than that would harm the patient. Using bench 1, say what a very salty drip does to the blood cells.
You now hold the one dial that matters. Take any drink, count its dissolved particles in mOsm/L, and set the number beside plasma's 291. Above 291 the drink is the crowded side, and water crosses into the gut. Below it, water crosses into the blood. Now a case this module has not worked. Someone in a hurry stirs a whole sachet into half a litre of water instead of one. All the sachet's particles are there and the water is halved. Work out the strength of that drink in mOsm/L. Compare it with plasma, and with the 311 that was withdrawn. Say which way water crosses the gut wall, and what that does to the patient. Do the sum before you read the box below.
— Water crosses towards the crowded side, and the solute it cannot follow sets how far.
{salt} has Ksp = {ksp} at 25 °C. The water already holds {added} mol/L of {anion}. How much of the salt dissolves, in mg/L? The molar masses in g/mol are calcite 100.0869, barium sulfate 233.390, silver chloride 143.320 and calcium fluoride 78.075. When the anion already present is far above what the salt adds, the sum is short. Divide Ksp by the anion for a 1:1 salt. For the 1:2 salt, divide it by the anion squared. That gives the moles per litre. When it is not far above, the full balance is needed, and bench 2 solves it.
1.
2. A sealed bottle of cola holds carbon dioxide at 4.0 bar above the liquid. Henry's law says the amount of gas dissolved is a constant multiplied by the gas pressure. At 25 °C that constant is 0.034 mol/(L·bar) for carbon dioxide in water. At 35 °C the same law, with its temperature term, gives 0.1047 mol/L dissolved at 4.0 bar, a computed figure. First find the amount dissolved at 25 °C. Then find what percentage of the dissolved gas is lost when the bottle warms from 25 °C to 35 °C.
At 25 °C the dissolved amount is 0.034 mol/(L·bar) multiplied by 4.0 bar. That product is 0.136 mol/L of carbon dioxide in every litre of cold cola. At 35 °C the same pressure dissolves only 0.1047 mol/L, from the same law. The fraction that remains is 0.1047 divided by 0.136, warm amount over cold amount. Take that fraction from one, and the fraction lost comes out at 23 per cent. So ten degrees of warming, at the same pressure, drives out nearly a quarter. That quarter leaves as foam when the warm bottle is opened, and the cola is flat. The readout below gives the same figures in grams per litre. It also gives the constant in the form your textbook writes it.
The lattice grips, water pulls, and disorder settles the difference.
Sources for this module, in the order the page uses them. Lattice enthalpy of sodium chloride, +786 kJ/mol, Born–Haber, experimental. Heat of solution +3.88 kJ/mol from Parker, Thermal Properties of Uni-Univalent Electrolytes, NBS Reference Data Series 2, 1965, at infinite dilution. The CODATA Key Values route gives +3.70. Anhydrous calcium chloride −81.2 kJ/mol from CODATA ion values and the NIST Chemistry WebBook. Solubility products from Plummer and Busenberg, Geochimica et Cosmochimica Acta 46, 1982, and the WATEQ4F database via aqion.de. Hardness limits from BIS IS 10500:2012, Table 2. Chennai District groundwater from the South African Journal of Chemical Engineering, 2024, doi:10.1016/j.sajce.2024.08.006, Table 3. Kf from Aylward and Findlay, SI Chemical Data, 5th edition. The eutectic from Maine DOT, 2023, and the Western Transportation Institute, 2022. The real van't Hoff factor is computed from the 25 °C parameters of Pitzer and Mayorga, Journal of Physical Chemistry 77, 1973. The 12.1 per cent point is from an uncredited industrial brine table and is flagged secondary. Plasma osmolarity from Zander, Ziegenfuß and Sümpelmann, European Journal of Medical Research 30, 2025. ORS compositions from Pulungsih and others, Journal of Health, Population and Nutrition 24, 2006, Table 1. The reason for the change is from WHO, The Treatment of Diarrhoea, 2005. Henry's constant from Sander, Atmospheric Chemistry and Physics 23, 2023, cross-checked against the NCERT class 12 value. Sodium sulfate's transition temperature from Magin and others, Journal of Research of the National Bureau of Standards 86, 1981. Its peak from Bharmoria and others, Journal of Physical Chemistry B 118, 2014. The beliefs the gates test come from Naah and Sanger, 2012, and from Fisher, Williams and Lineback, 2011. One comes from Riddle and Lo-Fan-Hin, 2023. Verified 26 September 2026.