Brife notes under The mole concept and stochiometry

Here are brief notes on The Mole Concept and Stoichiometry:

• The Mole: A unit of amount of substance. One mole of any substance contains the same number of particles (atoms, molecules, ions).

  $$1 \text{ mole} = 6.02 \times 10^{23} \text{ particles (Avogadro's Constant, } N_A)$$

• Molar Mass ($M_r$ or $A_r$): The mass of one mole of a substance.

  • For elements, it's the relative atomic mass ($A_r$) in grams. E.g., $A_r(\text{C}) = 12$, so $1 \text{ mole of C} = 12 \text{ g}$.
  • For compounds, it's the relative molecular mass ($M_r$) or formula mass in grams. E.g., $M_r(\text{H}_2\text{O}) = (2 \times 1) + 16 = 18$, so $1 \text{ mole of H}_2\text{O} = 18 \text{ g}$.

• Calculating Moles:

  • From mass: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$
  • From number of particles: $\text{Moles} = \frac{\text{Number of particles}}{N_A}$
  • For gases at room temperature and pressure (r.t.p., $25^\circ\text{C}$, $1 \text{ atm}$): $1 \text{ mole of any gas occupies } 24 \text{ dm}^3$. $$\text{Moles} = \frac{\text{Volume of gas (dm}^3)}{24 \text{ dm}^3/\text{mol}}$$ (Note: At standard temperature and pressure (s.t.p., $0^\circ\text{C}$, $1 \text{ atm}$), $1 \text{ mole of any gas occupies } 22.4 \text{ dm}^3$.)

• Stoichiometry: The study of the quantitative relationships between reactants and products in a chemical reaction.

  • Mole Ratio: Derived from the balanced chemical equation, it shows the ratio of moles of reactants consumed and products formed. Example: $2\text{H}_2(\text{g}) + \text{O}_2(\text{g}) \to 2\text{H}_2\text{O}(\text{l})$ The mole ratio of $\text{H}_2 : \text{O}_2 : \text{H}_2\text{O}$ is $2:1:2$.

• Calculations using Stoichiometry:

  1. Write a balanced chemical equation.
  2. Convert known quantities (mass, volume, particles) to moles.
  3. Use the mole ratio from the balanced equation to find moles of the unknown substance.
  4. Convert moles of the unknown substance back to the required quantity (mass, volume, particles).

• Empirical Formula: The simplest whole-number ratio of atoms in a compound.

  • To find: Convert mass/percentage of each element to moles, divide by the smallest number of moles, and simplify to the simplest whole-number ratio.

• Molecular Formula: The actual number of atoms of each element in a molecule.

  • It is a whole-number multiple of the empirical formula.
  • $\text{Molecular Formula} = (\text{Empirical Formula})_n$
  • $n = \frac{\text{Molar Mass of Molecular Formula}}{\text{Molar Mass of Empirical Formula}}$