AP Chemistry

## Counting particles by weighing Atoms, molecules and ions are far too small to count one at a time, yet every laboratory measurement of a chemical change has to connect the mass of a sample to the number of particles that react. The link is the **mole**, a fixed count of particles. One mole of any substance contains the **Avogadro constant** of particles: $$N_A = 6.022 \times 10^{23}\ \mathrm{mol^{-1}}$$ The particles may be atoms, molecules, ions or formula units, so you have to say which you mean. A mole of $\ce{H2O}$ holds $6.022 \times 10^{23}$ molecules, and a mole of $\ce{NaCl}$ holds $6.022 \times 10^{23}$ formula units, which is the same number of $\ce{Na+}$ ions and the same number of $\ce{Cl-}$ ions. ### Atomic mass units and molar mass The mass of a single atom or molecule is expressed in **atomic mass units** (amu). The useful fact about this unit is that the average mass of one particle in amu is numerically equal to the **molar mass** of the substance in grams per mole. A water molecule has an average mass of 18.02 amu, so one mole of water has a mass of 18.02 g. This one-to-one correspondence is what turns a balance reading into a count of particles. The molar mass of a compound is the sum of the molar masses of its atoms, each multiplied by the number of times it appears in the formula. For calcium nitrate, $\ce{Ca(NO3)2}$, the subscript outside the bracket multiplies everything inside it: $$ \begin{aligned} M &= 40.08 + 2\,(14.01 + 3 \times 16.00) \\ &=…