Solutions
The purest water that can be produced measures 18.2 MΩ·cm, and that number is not a purification goal but a physical limit: water ionizes itself, and those intrinsic ions set the floor.
01How much of what
A solution is a homogeneous mixture: the solute is dispersed in the solvent at the molecular scale, with no separating surface. The only thing to decide is how to report how much there is, and there half a dozen units coexist that are not interchangeable.
| Unit | Definition | When it is convenient |
|---|---|---|
| Molarity \( M \) | Moles of solute per liter of solution | For reacting: it is the one that goes into the calculations |
| Molality \( m \) | Moles per kilogram of solvent | When the temperature changes: it does not depend on volume |
| Mole fraction \( x \) | Moles of the component over total moles | Vapor pressures, gas laws |
| % by mass | Grams of solute per 100 g of solution | Commercial reagents: HF comes at 49 % |
| ppm, ppb | Parts per million or per billion | Impurities: process water is specified this way |
Molarity is calculated over the volume of the solution, which expands with temperature; molality, over the mass of solvent, which does not. In dilute aqueous solutions the numbers almost coincide and that is why they get confused, but in a concentrated electrolyte the difference is large. If the calculation involves heating, use molality.
02What dissolves what
The old rule —like dissolves like— is a direct consequence of chemical bonding. A polar solvent such as water surrounds ions with its dipoles and pulls them apart; a nonpolar one has nothing to do it with, and that is why it does not dissolve salts. Solubility is the maximum concentration that the solvent admits at a given temperature, and once it is reached the solution is saturated.
| Solvent | Dissolves | In electronics it is used for |
|---|---|---|
| Deionized water | Salts, acids, bases | Rinsing wafers and circuit boards after fluxing |
| Isopropyl alcohol | Polar residues and some grease | Cleaning boards and contacts; it evaporates without leaving a residue |
| Acetone | Resins, polymers, photoresist | Removing photoresist; it attacks many plastics |
| Hydrocarbons | Oils and waxes | Preliminary degreasing, before the aqueous rinse |
Temperature almost always helps to dissolve solids, and almost always hinders with gases: the oxygen dissolved in water falls by half between 0 and 30 °C. That matters in process water, where dissolved oxygen oxidizes freshly etched surfaces.
03Electrolytes, and the water that does not conduct
An electrolyte is a solute that separates into ions when it dissolves, and those ions are what carry charge. The conductivity of the solution directly measures how many ions there are and how fast they move:
And on the other side is ultrapure water, which is the closest thing to a liquid insulator that can be had in industry: 18.2 MΩ·cm at 25 °C. That number is not chosen, it is a physical limit. Water autoionizes —\( \mathrm{H_2O \rightleftharpoons H^+ + OH^-} \)— and those intrinsic ions set a floor of conductivity that no purification can lower.
Choose the solute and move the concentration. The resistivity is compared against process ultrapure water, drinking water and seawater. Note the difference between a strong and a weak electrolyte at the same concentration.
A 0.01 M solution of potassium chloride has 1413 µS/cm at 25 °C, and that value is tabulated to four digits. KCl serves as a standard because its two ions have nearly equal mobilities, the salt is easy to obtain pure and it is not altered by air. The lab above reproduces that number.
04Colligative properties
Four properties of a solution depend only on how many solute particles there are, not on which ones: vapor pressure lowering, boiling-point elevation, freezing-point depression and osmotic pressure.
The most direct application in electronics is the coolant: ethylene glycol in water lowers the freezing point of a liquid cooling circuit and raises the boiling point, both at the same time. And osmotic pressure is the principle of reverse osmosis, the first stage of every deionized water plant: a pressure greater than \( \pi \) is applied to push the water through the membrane against its natural tendency.
05In the lab
Prepare a 0.01 M KCl solution by weighing, measure its conductivity and compare with the tabulated 1413 µS/cm. Calculate the error and discuss whether it comes from the weighing, the volume or the temperature.
Measure the conductivity of HCl and of acetic acid, both 0.01 M. Explain why they differ by more than an order of magnitude even though the concentration is the same, and estimate the degree of dissociation of acetic acid from the measurement.
Measure the conductivity of mains water, of pharmacy-grade distilled water and of deionized water if it can be found. Convert to resistivity and to equivalent ppm of NaCl, and compare with the process-water specification of the electronics industry.
06Common mistakes
- Calculating molarity over the volume of solvent. It goes over the volume of solution, which is not the sum of the volumes.
- Adding water to concentrated acid. It always goes the other way: acid into water, a little at a time. Dilution releases a lot of heat.
- Assuming that every electrolyte dissociates completely. Weak ones reach an equilibrium, and that is why they conduct much less.
- Forgetting the factor \( i \) in colligative properties. A salt contributes two or three particles per formula.
- Confusing conductivity with concentration. The relationship is not linear: beyond a certain concentration the ions hinder each other.
07Self-assessment
What is the resistivity of ultrapure water at 25 °C?
18.2 MΩ·cm. It is a physical limit imposed by the autoionization of water, not a purification goal.
What does Kohlrausch's law say?
That the molar conductivity falls with the square root of the concentration, because as the solution becomes concentrated the ions hinder each other.
Why is 0.01 M KCl the calibration standard?
Because its two ions have nearly equal mobilities, the salt can be obtained pure and its conductivity is tabulated: 1413 µS/cm.
What is the van 't Hoff factor?
The number of particles each formula separates into when dissolved: 1 for sugar, 2 for NaCl, 3 for CaCl₂.
Why does reverse osmosis need pressure?
Because it pushes water through the membrane against the natural tendency, and for that the osmotic pressure has to be exceeded.
Molarity or molality for a calculation with a change in temperature?
Molality: it is defined over the mass of solvent, which does not expand.
08Further reading
- Raymond Chang and Kenneth A. Goldsby. Chemistry. 12th ed. (Spanish edition, “Química”), McGraw-Hill, 2017. All of chapter 12: concentration units, solubility and colligative properties.
- Peter Atkins and Julio de Paula. Physical Chemistry. 10th ed. (Spanish edition, “Química física”), Editorial Médica Panamericana, 2018. Conductivity of electrolytes, Kohlrausch's law and ionic mobility, with the derivation of the term in the square root of c.
- Werner Kern (ed.). Handbook of Semiconductor Wafer Cleaning Technology. Noyes Publications, 1993. Wafer cleaning solutions and the specifications of process ultrapure water.