Chemistry

What this page covers, and which tool fits your task

This page handles the calculation that comes up most often at the bench: you already own a stock solution at a known concentration and need a weaker working solution at a set volume. Enter any three of the four quantities and the solver at the top of the page produces the fourth, along with the dilution factor and the amount of solute involved.

Different starting points call for different tools. If you are weighing out a dry chemical to build a solution from scratch, the molarity calculator converts mass through moles into a target concentration. If you only need grams to moles, the grams-to-moles calculator does that single step. Household products such as bleach or rubbing alcohol are covered by the cleaning dilution pages, which work in volume ratios rather than moles. The table below sorts it out.

Moles: the counting unit that makes reactions predictable

Chemists count atoms and molecules the way paper mills count sheets: in fixed bundles. One mole is exactly 6.02214076 x 10 to the 23 particles, a value fixed by international agreement when the SI was redefined in 2019, as recorded in the NIST SI units page. The bundle is chosen so that the mass of one mole in grams matches the molecular weight in daltons, which is what makes the unit useful for weighing.

Molar mass comes straight off the periodic table. Sodium chloride is one sodium (22.99 g/mol) plus one chlorine (35.45 g/mol), so 22.99 + 35.45 = 58.44 grams per mole. Weigh out 5.844 grams of table salt and you have 5.844 / 58.44 = 0.1 moles, or one tenth of Avogadro's number of formula units.

Glucose shows how the sum extends to bigger molecules: six carbons, twelve hydrogens and six oxygens contribute 72.066 + 12.096 + 95.994 = 180.156 grams per mole, usually rounded to 180.16. Every stoichiometry calculation on this page rests on that one conversion between a mass you can weigh and a count of particles.

Molarity: concentration you can pipette against

Molarity divides moles by liters of solution and gets the unit chemists abbreviate as M. Dissolve 0.1 moles of sodium chloride and bring the volume up to 500 milliliters (0.5 liters), and the concentration is 0.1 / 0.5 = 0.2 mol per liter, written 0.2 M. The final volume is the volume of the whole solution, solvent included, not the volume of water you added.

A laboratory shortcut saves unit juggling: moles per liter times milliliters equals millimoles. Pouring 41.7 mL of 6 mol per liter stock therefore transfers 6 x 41.7 = 250.2 mmol, about a quarter mole. The dilution solver reports this number so you can sanity-check two recipes against each other.

Check one row end to end: 9.008 / 180.16 = 0.05 moles of glucose, and 0.05 / 0.25 = 0.2 mol per liter in a final 250 mL. Same target as the salt row, entirely different chemistry.

The dilution equation: C1 V1 = C2 V2

Dilution adds solvent, never solute. The moles you started with are the moles you end with, so concentration times volume must match on both sides: C1 V1 = C2 V2. In moles per liter and milliliters, each side evaluates in millimoles, which keeps the arithmetic in comfortable ranges.

The worked example from the top of the page: make 500 mL of 0.5 mol per liter solution from 6 mol per liter stock. The stock volume is V1 = 0.5 x 500 / 6 = 41.67 mL. Measure 41.67 mL of stock, add solvent to the 500 mL mark (500 - 41.67 = 458.33 mL of water), and mix. The dilution factor is 500 / 41.67 = 12.0, so this is a twelve-fold dilution.

When a recipe names the dilution instead, work the other way: a 1x working buffer from 10x stock is a ten-fold dilution, so one part stock takes nine parts water.

Worked examples: buffers and serial dilutions

Buffers show the equation at its most routine. To make 500 mL of 1x TAE electrophoresis buffer from 10x concentrate, use V1 = 1 x 500 / 10 = 50 mL of concentrate and dilute to volume: 50 + 450 = 500 mL total. The same one-to-nine split works for any 10x concentrate at any final volume.

Serial dilutions chain the single step. Transfer one part of 100 mg per mL stock into nine parts of solvent and you have 10 mg per mL; repeat into fresh solvent and each tube drops another factor of ten. After four transfers the concentration is 10 x 10 x 10 x 10 = 10,000 times weaker than the stock, which is 0.01 mg per mL. Serial dilutions are the standard route when a working range spans orders of magnitude, as in plate counts and ELISA standard curves.

For the solver, run each tube as its own dilution step rather than entering a chain, and carry the computed concentration forward as the next step's stock.

Where C1 V1 = C2 V2 breaks down

The equation leans on one physical claim: volumes add. Most dilute aqueous work obeys that closely enough for any pipette to measure, but the edges of the map are worth knowing.

Alcohol and water contract. Mix 50 mL of ethanol with 50 mL of water and the total lands near 97 mL, not 100, because the molecules pack together. Proof spirits and lab reagents made with high ethanol fractions need volume-by-weight tables instead of a straight dilution factor.

Concentrated acids are not 100 percent solute. Commercial concentrated hydrochloric acid is about 37 percent HCl by weight with a density near 1.19 g per mL, so its molarity comes from a weight percent calculation, not from the bottle percentage alone. Use the supplier's stated molarity as C1 and the equation holds.

Highly concentrated stocks stack activity on top of concentration. At high ionic strength, effective concentration (activity) drifts from the analytical value printed on the bottle. Dilutions of several fold are fine; predicting the pH of a barely diluted concentrated acid is a different problem.

Finally, keep units consistent. Concentrations on both sides must be the same kind (both molar or both percent), and volumes on both sides the same unit. The solver assumes mol/L and mL and reports the moles balance so a unit slip shows up as a mismatch.

Safety basics the formulas will not tell you

Calculation is the easy half of making a solution. The other half is handling the chemicals, and the rules there come from practice, not algebra.

• Add acid to water, never water to acid. Concentrated acid releases enough heat on dilution to boil a splash of water back out of the vessel; adding the acid slowly to a larger water volume keeps that heat spread out.
• Wear splash goggles and gloves rated for the chemical, and work with volatile or irritating solvents in a fume hood.
• Label every prepared solution with contents, concentration, date and initials. An unlabeled 6 mol per liter acid is a hazard; the same bottle labeled is a reagent.
• Check the safety data sheet before first use of any chemical, and follow your institution's chemical hygiene plan.

Employers in the United States follow the OSHA laboratory safety guidance, which covers the labeling, training and documentation that keep a lab audit-ready. Home and school labs should hold themselves to the same standard in miniature: small quantities, eye protection, and dilution directions worked out before anything is poured.