Process & Water Chemistry · The mole machine
Two exchange rates
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Two exchange rates

A balance weighs grams. Chemistry reacts in whole numbers of particles. The mole is the bridge, and crossing it costs one multiplication in each direction.

n=mMn = \dfrac{m}{M} — read aloud n equals m over M. nn is the amount of substance in moles, mm is the mass you weighed in grams, and MM is the molar mass in grams per mole, a property of the substance that you look up rather than measure. The unit does the arguing for you: grams divided by grams per mole leaves moles, and nothing else on the page divides that way.

The second rate is N=nNAN = n\,N_AN equals n times N-A. NN is the number of particles, a bare count, and NAN_A is the Avogadro constant, 6.022×10236.022 \times 10^{23} particles per mole, fixed by definition since 2019. Note the direction: NAN_A multiplies a number of moles. It has never multiplied a mass, and a mass fed into it comes back meaningless by a factor of the molar mass.

Scale is the point of this chapter, so get a feel for it. A 25 kg sack of caustic soda is 625 moles, and it is also about 3.8×10263.8 \times 10^{26} formula units. Nobody counts the second number, and every dosing calculation on the plant runs on the first.

The nugget worth carrying: a mole is a count, not a mass. A mole of caustic soda is 40 g and a mole of limestone is 100 g, and they contain exactly the same number of formula units. That is the whole reason stoichiometry works in moles and never in kilograms.