Thermochemistry

• thermochemistry
  • related topics:
    • Thermodynamics
      • first law of thermodynamics
      • second law of thermodynamics
      • heat: $Q=mc\Delta T$
    • chemical thermodynamics
• in this page, the IUPAC convention of work is used

Internal energy

• $\Delta U_{\text{reaction}}=\sum U_{\text{products}}-\sum U_{\text{reactants}}$

Enthalpy

The enthalpy change here is molar enthalpy change (i.e. per one mole) (unit: $kJ/mol$)

Hess’s law

• Hess’s law of constant heat summation (or Hess’s law)
  • $\Delta H(\mathrm{A}\to \mathrm{B})=-\Delta H(\mathrm{B}\to \mathrm{A})$
  • $\Delta H(\mathrm{A}\to \mathrm{B})=c\Delta H(c\mathrm{A}\to c\mathrm{B})$
  • $\Delta H(\mathrm{A}\to \mathrm{C})=\Delta H(\mathrm{A}\to \mathrm{B})+\Delta H(\mathrm{B}\to \mathrm{C})$
• todo Lavoisier and Laplace’s law

Enthalpy of reaction

• exothermic reaction: $\Delta H<0$
• endothermic reaction: $\Delta H>0$
• The enthalpy of reaction ($\Delta H_{\text{rxn}}$) (or heat of reaction) is the enthalpy change of a reaction. (i.e. $\Delta H_{\text{rxn}}=H_{\text{products}}-H_{\text{reactants}}$).
• There are two methods to calculate the enthalpy of reaction:
  • using average bond enthalpies:
    • $\Delta H_{\text{rxn}}=\sum \Delta H_{\text{(bonds broken)}}-\sum \Delta H_{\text{(bonds formed)}}$
      • $\sum \Delta H_{\text{(bonds broken)}}$ is the total energy to break bonds
        • $\Delta H$ are the average bond enthalpies of the bonds in reactants
      • $\sum \Delta H_{\text{(bonds formed)}}$ is the total energy to form bonds
        • $\Delta H$ are the average bond enthalpies of the bonds in products
  • using standard enthalpy of formation:
    • The standard enthalpy of reaction ($\Delta H_{\text{rxn}}^{\circ }$)
      • enthalpy change for a reaction under standard-state conditions
      • $\Delta H_{\text{rxn}}^{\circ }=\sum {\nu }_p\Delta H_f^{\circ }(p)-\sum {\nu }_r\Delta H_f^{\circ }(r)$
      • $\nu$ are the stoichiometric coefficients of the reactants and products

Enthalpy of formation

• The standard enthalpy of formation (or standard heat of formation) ($\Delta H_f^{\circ }$)
  • The enthalpy change when exactly 1 mole of a compound is formed from its elements in their standard states (typically: 1 atm, 298 K)
  • examples:
    • $\Delta H_f^{\circ }(\mathrm{H}{}_2\mathrm{O}\text{(g)})=-241.8\text{ kJ/mol}$
      • $\mathrm{H}{}_2\text{(g)}+\frac{1}{2}\mathrm{O}{}_2\text{(g)}\to \mathrm{H}{}_2\mathrm{O}\text{(g)}$
    • $\Delta H_f^{\circ }(\mathrm{CO}{}_2\text{(g)})=-393.5\text{ kJ/mol}$
      • $\mathrm{C}\text{(s, graphite)}+\mathrm{O}{}_2\text{(g)}\to \mathrm{CO}{}_2\text{(g)}$
    • $\Delta H_f^{\circ }(\mathrm{O}{}_3\text{(g)})=+142.7\text{ kJ/mol}$
    • for any element in its most stable state: $\Delta H_f^{\circ }=0$
  • reference table: https://en.wikipedia.org/wiki/Standard_enthalpy_of_formation#Examples:_standard_enthalpies_of_formation_at_25_%C2%B0C

Enthalpy of solution

see Solutions

Latent heat

• latent heat (or latent energy, heat of transformation) (חום כמוס)
  • $Q=mL$
    • $L$ is the specific latent heat of the substance
• enthalpy of fusion (or (latent) heat of fusion)
• enthalpy of sublimation (or (latent) heat of sublimation)
• enthalpy of vaporization (or (latent) heat of vaporization)

Lattice enthalpy

• $\Delta H_{\text{lattice}}=\Delta U_{\text{lattice}}+P\Delta V_m$
  • $\Delta V_m$ is the change of molar volume due to the formation of the lattice
  • (notice: IUPAC convention is used)
• lattice energy ($\Delta U_{\text{lattice}}$)
  • “the energy change (released) upon formation of one mole of a crystalline compound from its infinitely separated constituents, which are assumed to initially be in the gaseous state at 0 K” (Wikipedia)
• lattice enthalpy ($\Delta H_{\text{lattice}}$)
  • “the heat required to vaporize the solid to widely separated gaseous ions at constant pressure.” (Jones, 2016)
    • $\Delta H_{\text{lattice}}=H_{\text{m}}(\text{ions},\text{g})-H_{\text{m}}(\text{solid})$
• example:
  • $\mathrm{Na}{}^{+}(\mathrm{g})+\mathrm{Cl}{}^{-}(\mathrm{g})\to \mathrm{NaCl}(\mathrm{s})$: $\Delta H_{\text{lattice}}=-788kJ/mol$
• “The difference between lattice energy and enthalpy is very small and the two terms are often interchanged freely.” (Wikipedia)
• both lattice enthalpy and lattice energy values are negative during lattice formation, become identical at 0 K, and their minor difference is typically disregarded at standard temperatures.
• Born–Haber cycle

Heating value

• heating value (ערך-היסק) (or energy value, calorific value (ערך קלורי), heat of combustion (חום-בערה))
  • “the amount of heat released during the combustion of a specified amount of it” (Wikipedia)
  • The enthalpy of combustion is the heating value expressed as an enthalpy
  • the “amount” of fuel may be either: amount of substance, mass or volume, and the quantities and units are:
    • energy/mole:
    • energy/mass: $J/kg$, $Cal/kg$
    • energy/volume:
  • fuel value
    • ”The energy released when 1 g of any substance is combusted” (Brown, 2012)
    • “the amount of energy per g of food” (Denniston, 2022)
  • higher heating value (HHV)
  • lower heating value (LHV)
• specific energy (or massic energy, gravimetric energy density)

Chemical energy

• chemical energy
  • ”the energy of chemical substances that is released when the substances undergo a chemical reaction and transform into other substances” (Wikipedia)
  • “The energy available from a chemical reaction” (Jones, 2016)
• breaking bonds requires energy (endothermic)
• forming bonds releases energy (exothermic)
  • when reactants with weaker covalent bonds form products with stronger bonds, net energy is released
• chemical potential ($\mu$)
• activity

Bond energy

• https://en.wikipedia.org/wiki/Bond_energy

• bond dissociation energy (BDE)

• bond energy (BE) (or bond enthalpy, bond strength) (אנרגיית קשר)

  • “The enthalpy change accompanying the dissociation of a bond” (Jones, 2016)
  • notations: $D$, and $\Delta H_{\text{B}}$
  • average bond enthalpy (or mean bond) (of a bond)
    • reference table: https://owl.oit.umass.edu/departments/Chemistry/appendix/bond.html
    • examples:
      • $\Delta H_{\text{B}}(\mathrm{H}-\mathrm{H})=+436kJ/mol$ is the enthalpy change of $\mathrm{H}{}_2(\mathrm{g})\to 2\mathrm{H}(\mathrm{g})$.
      • $D(\mathrm{C}-\mathrm{C})=413kJ/mol$
  • $D(\mathrm{C}-\mathrm{C})<D(\mathrm{C}=\mathrm{C})<D(\mathrm{C}\equiv \mathrm{C})$

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References

• Jones, Loretta (2016). Chemical Principles. W. H. Freeman.
• Brown, Theodore L. (2012). Chemistry. Prentice Hall.
• Denniston (2022). General, Organic, and Biochemistry. McGraw-Hill Education.