The Mole Concept & Stoichiometry – Quick Revision

Sub-Atomic Particles

• Atom: smallest part of an element; molecule: smallest part of element/compound that can exist alone.
• Proton $({}^{1}<em>{1}p)$: $+1$ charge, $1$ amu, nucleus. Neutron $({}^{1}</em>{0}n)$: $0$ charge, $1$ amu, nucleus. Electron $({}^{0}_{-1}e^-)$: $-1$ charge, $1/1840$ amu, outside nucleus.
• Atomic (proton) number $Z$ = no. of protons; Mass (nucleon) number $A$ = protons + neutrons.
• Isotopes: same $Z$, different $A$ → identical chemical, different physical properties.

Relative Masses

• Carbon-12 scale: $^{12}C$ defined as $12$.
• Relative isotopic mass $=\dfrac{\text{mass of isotope atom}}{\tfrac{1}{12}\text{mass of }^{12}C}$ (unitless).
• Relative atomic mass $A_r=\sum (\text{isotopic mass})(\text{abundance fraction})$.
• Relative molecular/formula mass $M<em>r$ = sum of $A</em>r$ of atoms in molecule/formula unit.

The Mole & Avogadro Constant

• $1\text{ mol}$ contains $L=6.02\times10^{23}$ entities.
• Molar mass $M$ (g mol$^{-1}$) numerically = $A<em>r$ or $M</em>r$.
• Key equations:
  • $n=\dfrac{m}{M}$ • $n=\dfrac{N}{L}$.

Empirical & Molecular Formulae

• Empirical: simplest whole-number ratio. Molecular: actual numbers; $\text{Molecular}=k\times\text{Empirical}$.
• Steps: convert masses/percentages → moles → divide by smallest → adjust (multiply by $2,3,4,5$ if ratios $1.5,1.33,1.25,1.20$ etc.).
• Molecular formula: $k=\dfrac{M<em>r}{M</em>{\text{emp}}}$.

Stoichiometry

• Balanced equation gives mole, mass and (for gases at same $T,P$) volume ratios.
• Limiting reagent: completely consumed; determines theoretical yield.
• Percentage yield $=\dfrac{\text{actual}}{\text{theoretical}}\times100\%$.

Reacting Volumes of Gases

• Avogadro’s law: equal volumes at same $T,P$ have equal molecules.
• Molar volume: $V_m=22.7\,\text{dm}^3\,\text{mol}^{-1}$ (s.t.p. $273\,\text{K},10^5\,\text{Pa}$); $24.0\,\text{dm}^3\,\text{mol}^{-1}$ (r.t.p. $293\,\text{K},1\,\text{atm}$).
• $n=\dfrac{V}{V_m}$.
• Complete combustion of hydrocarbon:
  $C<em>xH</em>y+\left(x+\frac{y}{4}\right)O<em>2 \rightarrow x\,CO</em>2+\tfrac{y}{2}H_2O$; gaseous volume ratios follow coefficients.

Solution Concentration

• Molar: $[X]=\dfrac{n<em>X}{V}$ (mol dm$^{-3}$). Mass: $c</em>{g\,dm^{-3}}=[X]M$.
• Dilution: $c<em>1V</em>1=c<em>2V</em>2$.
• Preparation: weigh solute, dissolve, make up to calibration mark in volumetric flask.

Acid-Base Titrations

• Volumetric analysis uses known standard to find unknown concentration via titration; endpoint detected by indicator.
• Basicity: mono- ($1H^+$), di- ($2H^+$), tri- ($3H^+$) acids.
• Calculation shortcut: $\dfrac{M<em>aV</em>a}{n<em>a}=\dfrac{M</em>bV<em>b}{n</em>b}$ where $n$ = stoichiometric coefficients.

Back Titrations

• Add known excess reagent to sample, titrate leftover with second standard; difference gives amount reacting with sample – useful for solids, volatile or weakly soluble substances.

Quick Reference Equations

• $n=\dfrac{m}{M}=\dfrac{N}{L}=\dfrac{V<em>{\text{gas}}}{V</em>m}=\dfrac{cV}{1000}$ (if $V$ in cm$^3$).
• $\text{Percentage mass of element}=\dfrac{A<em>r\times\text{number of atoms}}{M</em>r}\times100\%$.
• $\text{Percentage yield}=\dfrac{\text{actual yield}}{\text{theoretical yield}}\times100\%$.
• $\text{Atom economy}=\dfrac{\text{desired Mr}}{\text{total Mr of products}}\times100\%$ (for synthesis efficiency questions).