Mole Calculator

Quick mole reference

Mole Calculator: All Three Pathways

The mole is the SI unit of amount of substance. One mole contains exactly 6.02214076 x 10^23 elementary entities (atoms, molecules, ions or formula units). The mole calculator converts between moles and three different quantities: mass (n = m/M), concentration and volume (n = cV), and number of particles (n = N/NA).

Moles from mass: n = m/M

The most used pathway in chemistry: n = mass / molar mass. For 18.0 g H2O: n = 18.0/18.015 = 0.9992 mol. For 1.000 kg NaCl: n = 1000/58.443 = 17.11 mol. For 2.00 g He: n = 2.00/4.003 = 0.4996 mol (approximately 0.5 mol). The key step is always getting the molar mass right -- use the periodic table or the LazyTools molar mass calculator. Type the formula in the mole calculator and the molar mass is filled automatically from 72 elements in the database.

Moles from concentration and volume: n = cV

n = c x V where c is in mol/L and V is in litres. For 250 mL of 0.200 M NaOH: n = 0.200 x 0.250 = 0.0500 mol. For 50.0 mL of 2.00 M HCl: n = 2.00 x 0.0500 = 0.100 mol. For 1.00 L of 0.0500 M KMnO4: n = 0.0500 x 1.00 = 0.0500 mol. This pathway is essential for titrations and all volumetric analysis. Always remember to convert mL to L before multiplying.

Moles from number of particles: n = N/NA

n = N / NA where NA = 6.02214076 x 10^23 mol^-1. For 3.011 x 10^23 molecules: n = 3.011e23 / 6.022e23 = 0.5000 mol. For 1.204 x 10^24 atoms of carbon: n = 1.204e24 / 6.022e23 = 2.00 mol, which has a mass of 2.00 x 12.011 = 24.02 g. This pathway appears in exam questions about Avogadro's number and atomic/molecular scale chemistry.

The mole map: connecting all quantities

The mole map shows the central role of moles in connecting all quantitative chemistry calculations. Mass (g) converts to moles via molar mass (divide by M). Concentration (mol/L) and volume (L) convert to moles via multiplication (n = cV). Number of particles converts to moles via Avogadro's number (divide by NA). At the centre, the balanced equation stoichiometric ratio converts between moles of different species (multiply by the ratio from the equation). Gas volume at STP converts to moles via the molar volume (22.414 L/mol at 273 K and 1 atm; 24.465 L/mol at 298 K and 1 atm). Every quantitative chemistry problem can be mapped onto this diagram.

History and definition of the mole

The mole was originally defined as the amount of substance containing the same number of particles as there are atoms in exactly 12 grams of carbon-12. Since 2019, the mole is defined by fixing Avogadro's number to exactly 6.02214076 x 10^23 mol^-1, an exact number by definition. This means the mass of one mole of C-12 is no longer exactly 12 g (it is 11.9999999958... g) but the difference is negligible for all practical purposes. The name comes from the German word "Molekulargewicht" (molecular weight). The concept was developed in the late 19th century by Avogadro, Loschmidt and others, and the name "mole" was first used by Wilhelm Ostwald around 1900.

Using this calculator in lab reports and coursework

All LazyTools chemistry calculators run in your browser with no data sent to any server. Results can be copied with one click for use in lab reports, assignments and problem sets. The formula is displayed with every result for easy verification. For effective exam preparation, attempt calculations by hand first and use this tool to check your answer -- this builds fluency alongside error-checking skill. The LazyTools stoichiometry suite covers all major quantitative chemistry calculations; see the related tools section for the calculators used most often alongside this one.

Stoichiometry: the central skill in quantitative chemistry

Stoichiometry is the quantitative study of the relationships between reactants and products in chemical reactions. Every stoichiometry calculation ultimately involves converting between mass (grams), amount of substance (moles), number of particles (atoms, molecules, ions) and concentration (mol/L or mol/kg). The mole is the central unit that connects these quantities: moles = mass / molar mass; moles = volume x concentration; particles = moles x Avogadro's number (6.022 x 10^23). Mastering these interconversions -- and the stoichiometric ratios from balanced equations -- is the single most important quantitative skill in A-level, IB and undergraduate general chemistry.

The mole in reaction stoichiometry: complete worked example

The mole connects all parts of a stoichiometry calculation. Full worked example: what mass of water is produced when 2.50 g of hydrogen burns in excess oxygen? Balanced equation: 2H2 + O2 -> 2H2O. Step 1 (grams to moles): n(H2) = 2.50/2.016 = 1.240 mol. Step 2 (stoichiometric ratio): from the equation, 2 mol H2 produces 2 mol H2O, so the ratio is 1:1. n(H2O) = 1.240 mol. Step 3 (moles to grams): m(H2O) = 1.240 x 18.015 = 22.34 g. This grams-moles-ratio-moles-grams sequence is the universal stoichiometry algorithm. For solution-based reactions: n from c x V, then ratio, then V = n/c or m = n x M at the end. For gas reactions: n from PV/RT, then ratio, then P = nRT/V. The mole is the common currency that makes all these conversions possible.

Mole fractions and concentration expressions

The mole is also used in composition calculations beyond molarity. Mole fraction (x) = moles of component / total moles in mixture. Mole percent = mole fraction x 100. For a mixture of 2 mol N2, 0.5 mol O2 and 0.1 mol Ar: total = 2.6 mol. x(N2) = 2/2.6 = 0.769; x(O2) = 0.5/2.6 = 0.192; x(Ar) = 0.1/2.6 = 0.038. Sum = 1.000. Molality (b) = moles solute / kg solvent (note: per kg solvent, not solution). Molarity (c) = moles solute / L solution. For colligative properties (boiling point elevation, freezing point depression, osmotic pressure), molality is used because it is temperature-independent. For most other concentration calculations, molarity is standard. The LazyTools suite includes dedicated calculators for molality, mole fraction, and molarity.

Moles at standard temperature and pressure (STP)

At STP (273.15 K, 101.325 kPa by IUPAC 1982 definition), one mole of any ideal gas occupies 22.414 L -- the molar volume of an ideal gas at STP. At SATP (25 degrees C, 100 kPa, the more modern standard), the molar volume is 24.465 L/mol. For gas volumes: n = V/22.414 (at STP) or n = V/24.465 (at SATP). Example: what mass of CO2 is in 11.2 L at STP? n = 11.2/22.414 = 0.4997 mol. m = 0.4997 x 44.010 = 22.00 g. This molar volume approach is a quick alternative to the full PV = nRT calculation for problems specifically at STP or SATP conditions.

Mole calculations in examinations: common question patterns

The most frequent mole calculation patterns in A-level, IB and AP Chemistry examinations are: (1) mass of reactant to mass of product via moles and stoichiometric ratio; (2) volume of gas at STP to moles via molar volume 22.414 L/mol; (3) concentration and volume of solution to moles via n = cV, then to mass of product via molar mass; (4) moles of limiting reagent to moles of product; (5) percent yield: actual yield / theoretical yield x 100. Use the LazyTools mole calculator for the core moles step in any of these patterns, then apply the stoichiometric ratio and the relevant molar mass or concentration conversion. Building fluency with these five patterns through practise problems covering a range of contexts is the most efficient preparation for quantitative chemistry examinations.

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