Mole

Amount of substance

• The amount of substance (n) of a sample of matter is the number of entities (atoms, molecules, ions, etc.) in the sample.
  • the SI unit: mole (mol)
    • The Avogadro number is $N_0=6.02214076\times 10^{23}$.
    • $1\mathsf{mol}$ of a substance contains exactly $N_0$ entities.
    • The Avogadro constant $N_{\text{A}}=6.02214076\times 10^{23}{\text{mol}}^{-1}$
    • Approximately one mole is based on the number of atoms in 12 grams of carbon-12.
  • other unit: equivalent (symbol: $\mathrm{equiv}$ or $\mathrm{Eq}$)
    • $1\mathrm{Eq}$ is the amount of a substance that reacts with (or is equivalent to) an arbitrary amount (typically $1\mathrm{mol}$) of another substance in a given chemical reaction

Molar mass

• molar mass ($M$) (unit: $g/mol$)
  • The molar mass of an element is the mass per mole of its atoms.
  • The molar mass of a molecular compound (or ionic compound) is the mass per mole of its molecules (or its formula units)
    • $M={\sum }_i\left(a_i\times M_i\right)$, where:
      • $M$ is the molar mass of the compound (in $g/mol$)
      • $a_i$ is the subscript of the $i$-th element in the compound’s chemical formula (which is the number of atoms of that element in one molecule of the compound).
      • $M_i$ is the molar mass of the $i$-th element (in $g/mol$)
    • Examples:
      • The molar mass of $\mathrm{H}{}_2\mathrm{O}$ is $2\times 1.008g/mol+15.999g/mol=18.015g/mol$.
      • The molar mass of $\mathrm{CO}{}_2$ is $12.011g/mol+2\times 15.999g/mol=44.01g/mol$.
  • $M=\frac{m}{N_A}$, where:
    • $m$ is the mass of the substance (in $\mathrm{g}$)
    • $N_0$ is Avogadro’s number
  • $M=\frac{m}{n}$, where:
    • $m$ is the mass of the substance (in $\mathrm{g}$)
    • $n$ is the number of moles of the substance (in $\mathrm{mol}$)

Concentration

• concentration (ריכוז)
  • molar concentration (or molarity) (ריכוז מולרי, מולריות)
    • $c=\frac{n}{V}$ (also denoted $M$)
    • $[\mathrm{A}]$ is the molarity of $\mathrm{A}$
    • SI unit: $mol/{\mathrm{m}}^3$
    • other units: $mol/L=\mathrm{M}$ (molar)
    • equivalent concentration (or normality) $\mathrm{N}=\frac{\mathrm{eq}}{\mathrm{L}}$
      • $\text{eq/L}=\text{molarity}\times \text{valence}$
  • mass concentration (ריכוז מסה)
    • ${\rho }_i=\frac{m_i}{V}$
  • volume concentration ${\sigma }_i=\frac{V_i}{V}$
  • number concentration

Related quantities

• mole fraction (or molar fraction) ${\chi }_i=\frac{n_i}{n_{\text{total}}}$
  • (see also Dalton’s law)
• mass fraction $w_i=\frac{m_i}{m_{\mathrm{total}}}.$
• volume fraction ${\phi }_i=\frac{V_i}{V_{\text{total}}}$
  • for ideal gases: ${\varphi }_i=x_i$
• molality $m$ (or $b$)
  • $b=\frac{n_{\mathrm{solute}}}{m_{\mathrm{solvent}}}$
  • unit: $mol/kg=\mathrm{m}$ (molal)

Yield

• yield (or reaction yield or chemical yield)
  • $\text{percent yield}=\frac{\text{actual yield}}{\text{theoretical yield}}\times 100\%$
• limiting reagent (or limiting reactant or limiting agent)