The Mole: Counting Atoms by Weighing Them

Welcome to the bench — goggles on first, always. Here is the puzzle: atoms are far too small and far too numerous to count one by one, yet chemical reactions happen atom by atom. So chemists invented a counting unit called the mole. One mole is defined as exactly 6.022 x 10^23 mol^-1, a value called Avogadro's constant, just as 'a dozen' always means 12. The bridge to the balance is molar mass. The molar mass of a substance (in g/mol) equals its atomic or formula mass from the periodic table. The carbon-12 isotope is defined as exactly 12 u per atom, so one mole of pure C-12 has a mass of exactly 12 g. For the element carbon as it naturally occurs (a mix of isotopes), the standard atomic weight is 12.011 g/mol — close to 12, because C-12 dominates. Weighing 12.011 g of carbon gives you one mole, which is 6.022 x 10^23 atoms. Here is a quick worked example: How many moles are in 36.0 g of water (H2O, molar mass 18.0 g/mol)? Write the unit fraction — 36.0 g × (1 mol / 18.0 g) — the grams cancel and you get 2.0 mol. That unit-cancellation trick is your first hint: write the units under each number and cancel them; the surviving units tell you whether to divide or multiply. Now the payoff. In 2 H2 + O2 → 2 H2O, the coefficients are mole ratios: 2 mol H2 reacts with 1 mol O2 to form 2 mol H2O. Your second hint for finding a mole ratio: read the coefficient of the unknown substance and the coefficient of the known substance directly from the balanced equation, then write them as a fraction (unknown on top). That fraction is your conversion factor. Apply it between the two moles values, then convert back to grams.