Stoichiometry: Detailed Summary & Formulae

1. Atomic and Mass Numbers

• Atomic Symbol Notation ($^A_Z X$):
  X: Atomic symbol of the element.
  A (Mass Number): $A = Z + N$ (protons + neutrons).
  Z (Atomic Number): Number of protons. In a neutral atom, $Z = \text{number of electrons}$.

• Ions: Electrons = $Z - (\text{charge})$. For example, $Mg^{2+}$ has 12 protons and 10 electrons ($12 - 2 = 10$).

2. Isotopes and Abundance

• Definition: Atoms with the same $Z$ but different $A$.

• Chemical Properties: Identical because they have the same electron configuration.

3. Relative Atomic Mass (RAM)

• Carbon-12 Reference: $1 \text{ amu} = 1/12 \text{ the mass of one atom of } ^{12}C$.

• RAM Formula:
  $$\text{RAM} = \frac{\text{Average mass of one atom of element}}{1/12 \text{ mass of one atom of } ^{12}C}$$

4. Calculating RAM from Isotopic Abundance

• Weighted Average Formula:
  $$\text{RAM} = \frac{\sum (\text{Isotopic Mass} \times \% \text{ Abundance})}{100}$$

5. Molecular and Formula Mass

• Relative Molecular Mass ($M_r$): Sum of all $A_r$ (relative atomic masses) in a covalent molecule.

• Relative Formula Mass: Sum of all $A_r$ in an ionic compound.

6. The Mole and Avogadro's Constant

• Avogadro’s Constant ($N_A$): $6.022 \times 10^{23} \text{ entities per mole}$.

• Molar Mass ($M$): The mass of one mole of substance (units: $g \text{ mol}^{-1}$). Numerically equal to $M_r$ or $A_r$.

7. Key Calculations (The Mole Map)

• Moles from Mass:
  $$n = \frac{m}{M}$$
  Where $n = \text{moles}$, $m = \text{mass (g)}$, and $M = \text{molar mass (g/mol)}$.

• Number of Particles ($N$):
  $$N = n \times N_A$$
  Where $N = \text{number of atoms/molecules/ions}$.

CH 1.1_STOICHIOMETRY.pdf