A mole is 6.022×1023 of anything, chosen so that a mole of a substance weighs its formula mass in grams: 18.02 g of water, 58.44 g of salt, 180.16 g of glucose, 44.01 g of carbon dioxide.
At the same pressure and temperature a mole of any ideal gas fills the same volume: 24.06 litres at 20 °C and 1 atm, 22.41 at 0 °C, 24.79 at 25 °C and 1 bar, whichever gas it is.
The mass of solute for a concentration c in a volume V is cVM: for 250 mL of 0.1 mol/L sodium chloride that is 1.461 g, dissolved and made up to the mark.
Adding water does not change how much solute there is, so c1V1 = c2V2. Concentrated hydrochloric acid is 12.0 mol/L, so 84 mL of it makes a litre of 1 mol/L.
A 1 mol/L solution of sodium chloride has 58.44 g of it in each litre of solution: its molar mass, 58.440 g/mol from 22.990 for sodium and 35.45 for chlorine. A 0.1 mol/L one has a tenth of that.
The tool reads elements (a capital letter, perhaps one small one), the numbers after them, brackets with a number after them, and hydrates after a dot: Ca(OH)2 is one calcium, two oxygens and two hydrogens (74.092 g/mol), Al2(SO4)3 is 2 aluminium, 3 sulfur and 12 oxygen, and CuSO4.5H2O is the blue crystals with five waters, 249.7 g/mol. Case matters: CO is carbon monoxide, Co is cobalt.
Water is two hydrogens to one oxygen by number but only 11.2 percent hydrogen by mass, because an oxygen atom (15.999) is nearly sixteen times as heavy as a hydrogen (1.008). The share of the mass of each element is the number of its atoms times its atomic weight over the molar mass.
Grams divide by the molar mass to give moles; moles multiply by Avogadro’s number to give molecules; and for a gas, moles multiply by the molar volume. So 1 g of water is 0.0555 mol, which is 3.34×1022 molecules, and 18.015 g of it is one mole, 6.022×1023. A mole of carbon dioxide, 44.01 g, fills 24.1 litres at 20 °C and 1 atm.
A mole of any ideal gas fills RT/P: 22.41 litres at 0 °C and 1 atmosphere, 24.06 at 20 °C, 24.79 at 25 °C and 1 bar (the IUPAC standard of 0 °C and 1 bar gives 22.71). Use the one your problem names. The tool treats any substance as an ideal gas on request, even one that is a liquid or a solid at that temperature, so check that it really is a gas.
To make 250 mL of 0.1 mol/L sodium chloride, weigh 1.461 g (0.1 × 0.25 × 58.44), dissolve it in some water in a volumetric flask and add water up to the mark. The final volume is 250 mL, which is not the same as adding 250 mL of water to the salt, because the dissolved salt takes up room.
A concentration of c mol/L is cM g/L, cM/10 percent weight per volume and 1,000 cM parts per million by mass in dilute water solutions: 0.1 mol/L of sodium chloride is 5.84 g/L, 0.58 g per 100 mL and 5,844 mg/L.
Take a volume V1 of a solution of c1 and add water to a total V2: the same moles, c1V1, are in a bigger volume, so c2 = c1V1/V2. To go from 12 mol/L to 1 mol/L, take 1/12 of the final volume: 84 mL of stock for a litre. Always add the stock to the water.
A laboratory acid is sold as a mass percent and a density, not a molarity. A litre of 37 percent hydrochloric acid at 1.18 g/mL weighs 1,180 g, of which 37 percent, 437 g, is hydrogen chloride, which is 12.0 mol: so it is 12.0 mol/L. The same arithmetic gives 18.4 mol/L for 98 percent sulfuric acid and 15.7 for 70 percent nitric acid.
The molar masses use the standard atomic weights to four or five figures (the elements up to uranium), so they are good to about 0.01 percent and are for the natural mixture of isotopes. The tool does not know about ions and charges, does not balance equations (the Reacting Masses tool does), treats concentration as moles per litre of final solution, does not correct for temperature, and takes a stock bottle’s strength as printed: real ones vary by a percent or two.
A mole is the amount of a substance with 6.02214076×1023 particles in it (the number is exact in the SI since 2019). It is a count, like a dozen, chosen so that the mass of a mole in grams is the formula mass: a mole of carbon-12 atoms is 12 g.
Add the atomic weights of all the atoms in the formula: water, H2O, is 2 × 1.008 + 15.999 = 18.015 g/mol. Brackets multiply what is inside, so Ca(OH)2 has two oxygens and two hydrogens, and the water in a hydrate counts: CuSO4·5H2O is 249.7 g/mol.
Divide by the molar mass and multiply by Avogadro’s number: 1 g of water is 0.0555 mol and 3.34×1022 molecules; 1 g of hydrogen gas has 2.99×1023.
About 24 litres at 20 °C and 1 atmosphere, 22.4 litres at 0 °C and 1 atmosphere, whichever gas it is, because the molecules are so far apart that their kind does not matter. It is RT/P.
Molarity is moles of solute per litre of solution (mol/L), and it changes a little with temperature because the volume does; molality is moles per kilogram of solvent, which does not. This tool uses molarity, the one on laboratory labels.
Because the concentration is moles per litre of the whole solution, and the dissolved solute takes up room. Dissolving 1.46 g of salt in 250 mL of water gives more than 250 mL of solution, a little weaker than 0.1 mol/L; dissolving it in less water and making up to the mark in a volumetric flask gives exactly 250 mL.
Use c1V1 = c2V2: the moles do not change when you add water. To make 500 mL of 0.1 mol/L from 1 mol/L, take 50 mL and make it up to 500 mL. Add concentrated acid to water, never the other way round, because the heat of mixing can make it spit.
The label gives a mass percent and a density; the concentration is 10 × percent × density / molar mass. Concentrated hydrochloric acid, 37 percent, is 12.0 mol/L, sulfuric acid at 98 percent 18.4 mol/L, nitric acid at 70 percent 15.7 mol/L.
A crystal that has water built into it: copper(II) sulfate pentahydrate, CuSO4·5H2O, is blue and has five waters to every copper sulfate, so its molar mass is 249.7 g/mol, not the 159.6 of the anhydrous salt. Weighing the hydrate for a solution means using its full molar mass.
Because an element is a natural mixture of isotopes with different masses, and the atomic weight is their weighted average: chlorine is 75 percent chlorine-35 and 25 percent chlorine-37, so its weight is 35.45. Weights here are the standard values for ordinary samples.
This page has changed in 1 archived release, but each of those was a site-wide pass, so none is attributable to this tool on its own and none is listed here. That is not a claim that the tool never changed — a release that reworked many pages at once may well have altered this one too. The changelog has them.