Problem 1 — Moles, Molecules, Atoms from Mass

Q: How many atoms are present in 36 g of water ($H_{2}O$)?

Step 1 — Find moles of $H_{2}O$: $n = \frac{\text{mass}}{\text{molar mass}} = \frac{36 \ \text{g}}{18 \ \text{g/mol}} = 2 \ \text{mol}$

Step 2 — Find number of molecules: $N_{\text{molecules}} = n \times N_A = 2 \ \text{mol} \times 6.022 \times 10^{23} \ \text{mol}^{-1} = 1.2044 \times 10^{24} \ \text{molecules}$

Step 3 — Find number of atoms (each $H_{2}O$ has 3 atoms: 2 H + 1 O): $N_{\text{atoms}} = 3 \times 1.2044 \times 10^{24} = \mathbf{3.613 \times 10^{24} \ \text{atoms}}$

Units check: g ÷ (g/mol) = mol; mol × $mol^{-1}$ = dimensionless count ✓