Mole conversions (grams ↔ moles ↔ particles)

The mole is the bridge between the invisible world of molecules and the readable gram readings of a lab. Molar mass is the exchange rate: 18.0 g per mole for water. To go from grams to moles, divide. There are 36.0 g of water, so 36.0 divided by 18.0 is 2.00 mol. The division is small; deciding to divide is the actual skill.

The common mistake is flipping the operation. 18.0 divided by 36.0 gives 0.5, and some call that the answer. Check yourself with units: grams divided by grams per mole leaves moles, and that is the direction this question wants. The operation is chosen by which unit must cancel, so write the units next to the numbers. Writing the units is the fastest way to catch a flipped ratio.

To go the other way, from moles to grams, multiply. Two moles of CO2: 2.00 x 44.0 = 88.0 g. Moles times grams per mole gives grams. The same thinking handles particles: divide a particle count by 6.02 x 10^23 per mole to get moles, and work in groups of Avogadro's number. Each direction uses one conversion factor, and the factor is chosen by the units you need to cancel.

Draw the path before you calculate. Grams to moles uses molar mass; moles to particles uses Avogadro's number. Every route between grams, moles, and particles passes through the mole, which is why the mole sits at the center of the conversion map and why one checked answer protects the whole path. You never go straight from grams to particles without passing through the mole.