Quantitative Chemistry: Formulae, Moles, and Stoichiometry

Chemical Formulae

• Covalent Chemical Formulae     * Covalent compounds contain molecules.     * Molecules are formed when non-metal atoms are covalently bonded together.     * All molecules are neutral in charge.     * Formulae for covalent compounds generally need to be committed to memory. Examples include:         * Carbon dioxide: $CO_2$         * Carbon monoxide: $CO$         * Ammonia: $NH_3$         * Water: $H_2O$         * Nitrogen dioxide: $NO_2$         * Nitrogen monoxide: $NO$         * Sulphur dioxide: $SO_2$         * Hydrogen sulphide: $H_2S$         * Hydrogen chloride: $HCl$         * Hydrogen fluoride: $HF$

• Diatomic Molecules     * The prefix "di-" means two. Diatomic molecules consist of two atoms covalently bonded together.     * These two atoms can be from the same or different elements.     * Common diatomic molecules involving different elements include: Hydrogen fluoride ($HF$), Carbon monoxide ($CO$), Hydrogen chloride ($HCl$), Nitrogen monoxide ($NO$), and Hydrogen bromide ($HBr$).     * Seven elements exist in nature as diatomic molecules of the same element:         * Hydrogen ($H_2$) - Gas at room temperature.         * Nitrogen ($N_2$) - Gas at room temperature.         * Oxygen ($O_2$) - Gas at room temperature.         * Fluorine ($F_2$) - Gas at room temperature.         * Chlorine ($Cl_2$) - Gas at room temperature.         * Bromine ($Br_2$) - Liquid at room temperature.         * Iodine ($I_2$) - Solid at room temperature.

• Ionic Chemical Formulae     * Ionic compounds form as a result of ionic bonding and contain cations (positive ions) and anions (negative ions).     * There are two types: Simple ionic formulae and polyatomic ionic formulae.     * Examples of simple ionic formulae:         * Sodium chloride: $NaCl$         * Magnesium fluoride: $MgF_2$         * Aluminum oxide: $Al_2O_3$     * Examples of polyatomic ionic formulae:         * Calcium sulphate: $CaSO_4$         * Silver (I) nitrate: $AgNO_3$         * Ammonium phosphate: $(NH_4)_3PO_4$     * Naming Conventions: When atoms in groups V, VI, and VII form anions, the name ending changes to "-ide."         * Chlorine becomes chloride (e.g., magnesium chloride, $MgCl_2$).         * Sulphur becomes sulphide (e.g., lithium sulphide, $Li_2S$).         * Nitrogen becomes nitride (e.g., sodium nitride, $Na_3N$).         * Phosphorus becomes phosphide (e.g., calcium phosphide, $Ca_3P_2$).         * Oxygen becomes oxide (e.g., aluminium oxide, $Al_2O_3$).     * Valency: The valency of an atom is equal to the number of electrons it will gain, loss, or share to become stable.

Writing Chemical Formulae

• Writing Simple Chemical Formulae     * Rule: The sum of the positive charges (from cations) and negative charges (from anions) must equal zero.     * Example 1: Write the chemical formula for calcium chloride.     * Example 2: Write the chemical formula for aluminium sulphide.     * Alternative Method: Swop the valencies of each species in the formula.

• Writing Complex Chemical Formulae (Polyatomic Ions)     * Polyatomic ions must be learned with their specific charges and formulae:         * Valency 1 (Charge 1+): Ammonium ($NH_4^+$).         * Valency 1 (Charge 1-): Hydroxide ($OH^-$), Chlorate ($ClO_3^-$), Ethanoate ($CH_3COO^-$), Nitrate ($NO_3^-$), Nitrite ($NO_2^-$), Permanganate ($MnO_4^-$), Hydrogen carbonate ($HCO_3^-$), Hydrogen sulphate ($HSO_4^-$).         * Valency 2 (Charge 2-): Carbonate ($CO_3^{2-}$), Sulphate ($SO_4^{2-}$), Sulphite ($SO_3^{2-}$), Dichromate ($Cr_2O_7^{2-}$).         * Valency 3 (Charge 3-): Phosphate ($PO_4^{3-}$).     * Rule: The sum of positive and negative charges must equal zero. Swopping valencies also works for complex ions.     * Example 3: Formula for sodium carbonate.     * Example 4: Formula for ammonium phosphate.

• Stock Notation     * Metal atoms in groups I, II, and III have fixed valencies.     * Transition metals (d-block) have multiple possible valency states.     * Developed by Professor Robert Stock in 1950, Stock Notation uses Roman numerals in brackets to denote the valency of the metal in the compound name.     * Examples: silver(I) bromide, copper(II) chloride, iron(III) nitrate, lead(IV) carbonate.     * Example 5: Formula for copper (II) chloride.     * Example 6: Formula for chromium (V) oxide.

Balancing Chemical Equations

• Law of Conservation of Matter     * The total number of atoms in the reactants must equal the total number of atoms in the products.     * Matter cannot be changed or destroyed in a chemical reaction.     * Equations use phase subscripts:         * $(s)$ = solid.         * $(l)$ = liquid phase.         * $(g)$ = gas.         * $(aq)$ = aqueous (dissolved in water).     * Example 7: $CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$

Relative Masses

• Atomic Definitions     * Atomic number (Z): Number of protons in the nucleus.     * Mass number (A): Number of protons and neutrons in the nucleus.     * Isotopes: Atoms of the same element with different numbers of neutrons.

• Relative Atomic Mass ($A_r$)     * This is the average mass based on the percentage abundance of each isotope as they occur in nature.     * The Carbon-12 isotope is the standard, assigned a mass of precisely $12\,a.m.u$ (atomic mass units).     * Relative atomic mass is a number indicating the average mass of an atom compared to one-twelfth the mass of a Carbon-12 atom.     * Example 8 comparison calculation:         * Actual mass of C-12 = $1.992 \times 10^{-26}\,kg$.         * Actual mass of a Copper isotope = $1.055 \times 10^{-25}\,kg$.         * $\text{Ratio} = \frac{1.055 \times 10^{-25}}{1.9926 \times 10^{-26}} = \frac{5.295}{1}$.         * $A_r(\text{Cu}) = 12 \times 5.295 = 63.54\,a.m.u$.

• Relative Formula Mass ($M_r$)     * Calculated by adding the relative atomic masses of all atoms in the formula.     * Example 9: $M_r(H_2O) = 2(1) + 16 = 18$.     * Example 10: $M_r(K_2SO_4) = 2(39) + 32 + 4(16) = 174$.

The Mole Concept

• Foundations of the Mole     * To make measurement practical, the unit "gram" ($g$) is used instead of $a.m.u$.     * Molar Mass (M): The relative atomic mass expressed in grams. Unit: $g\,mol^{-1}$.     * The Mole (n): The amount of substance, expressed in grams, containing as many elementary particles as there are in $12\,g$ of Carbon-12.     * $12\,g$ of Carbon = $1\,mol$ of Carbon ($n = 1\,mol$).

• Elementary Particles     * For elements, particles are atoms. For molecular compounds, they are molecules. For ionic compounds, they are ions or formula units.     * $1\,mol$ of different substances contains the same number of particles, though the mass differs:         * $7\,g\,Li = 1\,mol\,Li$.         * $32\,g\,S = 1\,mol\,S$.     * Calculations of mole from mass: $n = \frac{m}{M}$.         * $40\,g\,Ca = 1\,mol\,Ca$, so $20\,g = 0.5\,mol$.         * $27\,g\,Al = 1\,mol\,Al$, so $54\,g = 2\,mol$.

• Avogadro’s Number ($N_A$)     * Amadeo Avogadro (1811) proposed that $1\,mol$ of any substance contains $6.02 \times 10^{23}$ elementary particles.     * $N_A = 6.02 \times 10^{23}\,mol^{-1}$.     * Relationship: $n = \frac{N}{N_A}$.

• Molar Volume ($V_m$)     * $1\,mol$ of any gas occupies $22.4\,dm^3$ at Standard Temperature and Pressure (S.T.P).     * S.T.P Conditions:         * Standard Temperature ($T^\circ$) = $0\,^\circ C$.         * Standard Pressure ($p^\circ$) = $1\,atm = 101325\,Pa = 1.013 \times 10^{5}\,Pa$.     * Formula: $n = \frac{V}{V_m}$.     * Conversion: Always convert $cm^3$ to $dm^3$ by dividing by $1,000$.

Concentration of Solutions

• Definitions     * Solute: Substance dissolved in the solvent; usually the smaller proportion.     * Solvent: Substance in which the solute is dissolved.     * Aqueous Solution: A solution where water is the solvent.     * Standard Solution: A solution of known concentration.

• Dissociation vs. Ionisation     * Dissociation: Occurs when ionic substances dissolve. Cations and anions are removed from the ionic lattice. Ions already exist; they are simply separated. Ion-dipole forces exist between ions and water molecules.         * Example: $NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)$.     * Ionisation: Occurs when covalent compounds dissolve. Molecules break up and react with water to form ions that did not exist previously.         * Example: $HCl(g) + H_2O(l) \rightarrow H_3O^+(aq) + Cl^-(aq)$.

• Calculating Concentration     * Concentration (c): The number of moles of solute per unit volume of solution.     * Formula: $c = \frac{n}{V}$.     * Units: $mol\,dm^{-3}$.

Stoichiometric Calculations

• General Calculation Template     1. Balance the chemical equation.     2. Convert all given values to number of moles ($n$).     3. Determine the theoretical molar ratio using balancing coefficients.     4. Use the actual moles available to calculate moles of needed/produced substances.     5. Convert the calculated moles back to the required unit (mass, volume, or particles).

• Limiting Reagents     * In many reactions, one reactant is in excess while another is limited.     * The limiting reagent is used up first and determines the amount of product formed.

• Yield and Purity     * Theoretical Yield: The maximum amount of product possible from a reaction.     * Actual Yield: The amount actually produced in practice (often lower due to impurities or incomplete reactions).     * Percentage Yield: $\%\,\text{yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100$.     * Percentage Purity: $\%\,\text{purity} = \frac{\text{Mass of pure compound}}{\text{Total mass of impure sample}} \times 100$.