Solutions and lab maths
Make up solutions by weight, convert between molarity, % w/v, % w/w, ppm, molality and normality, plan dilutions and serial dilutions, calculate pH, design buffers, solve the ideal gas law and limiting-reagent problems, work out osmolarity and tonicity (van 't Hoff factor, permeant solutes), and do the available-chlorine arithmetic for disinfectant tablets.
Added · updated 14 October 2026
How to use it
Prepare. Mass = concentration × volume × molar mass. Give the solute as a formula (looked up with the chemistry tool) or a molar mass. If the bottle is a hydrate the formula does not show, enter its waters of hydration and the mass includes them.
Concentration units. Everything is converted through mol/L and grams of solute per litre. % w/w and molality need the solution’s density; normality needs the equivalents per mole for the reaction you care about. ppm assumes a dilute aqueous solution where 1 ppm = 1 mg/L.
Dilute and mix. C1·V1 = C2·V2 — leave one of the four blank. Serial dilutions transfer V/F into V − V/F of diluent at each step. Mixing two stocks solves for the volumes that give a target concentration (volumes assumed additive).
pH. pH, pOH, [H⁺] and [OH⁻] interconvert with pKw at the chosen temperature (14.94 at 0 °C, 14.00 at 25 °C, 13.62 at 37 °C). Weak acids and bases are solved exactly from the charge balance, including water’s ions; strong acids and bases include water too, so very dilute solutions correctly stay near neutral. Activities are not modelled.
Buffers. Henderson–Hasselbalch, pH = pKa + log([A⁻]/[HA]), with pKa values at 25 °C and their temperature coefficients (Tris falls by about 0.028 per °C). The recipe gives the amounts of the acid and base forms to weigh. Always check the final pH with a calibrated meter.
Ideal gas. PV = nRT with R = 8.314 462 618 J/(mol·K); leave one of P, V, n, T blank. Give the gas formula to get its mass and density.
Stoichiometry. The equation is balanced automatically; enter amounts of the reactants to find the limiting reagent, the theoretical yield of every product, what is left over, and the percent yield from an actual mass.
Osmolarity and tonicity
Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. The Osmolarity tab is solution arithmetic, not a fluid prescription.
Add solutes (or pick a preset) with a concentration in mmol/L, mol/L, g/L or % w/v. Each one is converted to mmol/L and multiplied by its van 't Hoff factor i — the particles each formula unit gives when it dissolves (NaCl → Na⁺ + Cl⁻, i = 2; CaCl₂, i = 3; glucose, i = 1). The sum is the theoretical osmolarity: 0.9 % w/v NaCl is 9 g/L ÷ 58.44 g/mol = 154 mmol/L × 2 ≈ 308 mOsm/L, the book’s worked example.
Tonicity is what a cell feels. Solutes that cross the membrane (urea, glycerol — marked permeant) count towards osmolarity but pull no water once they have equilibrated, so they are left out of the effective osmolarity. Measured osmolality is a little lower than the theoretical figure because ions do not behave fully independently; the tool estimates it with an osmotic coefficient φ applied to electrolytes (default 0.93, NaCl’s value near 0.15 mol/kg — Robinson & Stokes, Electrolyte Solutions, 1959; φ = 1 gives the ideal figure). The estimate is then called hypotonic, isotonic or hypertonic against a comparison band you can edit, which defaults to the book’s plasma osmolality of ~275–295 mOsm/kg. That figure is orientation only (Appendix C), and the words describe the solution relative to the band — which way water would tend to move — not anybody’s state. Glucose is treated as an effective solute, as it is in the bag; in the body it is taken up by cells, which the arithmetic does not model.
Companion to Chapter 2, Basic chemistry (saline and osmolarity) and Chapter 1, Reading the body (tonicity) of Human Biology for the Medical Maker; the 5 % glucose and saline figures are in its Appendix C.
Available chlorine from tablets
Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. The Chlorine tablets tab shows the arithmetic of the book’s worked example; it does not tell you what strength to use. Strength, contact time and when to discard a made-up solution come from the product’s instructions and your local infection-prevention policy.
Enter the available chlorine each tablet releases (from its label — not the tablet’s weight), the number of tablets, the volume of water and the strength in ppm, and leave one blank to solve it. In dilute water solutions 1 ppm ≈ 1 mg/L, so 1,000 ppm is 1 g/L and a tablet releasing 1.5 g needs 1.5 L of water — the book’s example, whose figures are invented for teaching. The volume error shows how much a vaguely measured fill changes the strength: a jug 20 % out makes the solution 25 % too strong or 17 % too weak, which is why the book’s answer is an unambiguous fill mark.
Companion to Chapter 2, Basic chemistry ("can you make us a dispenser for the chlorine tablets?") of Human Biology for the Medical Maker.
Related: chemistry (molar masses and electrochemistry), lab calculations.
| For learning and planning. Check critical work against authoritative references and your lab’s validated procedures. |
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