thermochemistry
Enthalpy & calorimetry, Hess & Born–Haber cycles, fuels & fuel cells, entropy & Gibbs energy.
enthalpy & calorimetry · Hess cycles · Born–Haber & lattice · fuels & fuel cells · entropy & Gibbs
Enthalpy & calorimetry
System & surroundings. Energy is conserved between system and surroundings. Exothermic: heat released to surroundings, \(\Delta H\lt 0\), products at lower enthalpy. Endothermic: heat absorbed from surroundings, \(\Delta H\gt 0\), products at higher enthalpy.
Enthalpy profiles. Exothermic profile: products sit below reactants, \(\Delta H\lt 0\); endothermic: the opposite, products above reactants, \(\Delta H\gt 0\).
Standard state. Pure substance at 100 kPa and a specified \(T\), usually 298 K; solutions at \(1\,\mathrm{mol\,dm^{-3}}\).
Calorimetry. \(q_{\text{solution}}=mc\Delta T\); \(q_{\text{rxn}}=-q_{\text{surr}}\); \(\Delta H=q_{\text{rxn}}/n_{\text{limiting}}\). Error sources: heat loss, incomplete combustion, evaporation, apparatus heat capacity.
Hess cycles
Hess's law. \(\Delta H\) is independent of path. Reversing an equation flips the sign; multiplying an equation multiplies \(\Delta H\).
Bond enthalpy estimate. \(\Delta H\approx\sum E(\text{bonds broken})-\sum E(\text{bonds formed})\).
Formation & combustion. Formation: from elements in their standard states; \(\Delta H\std=\sum\Delta H_f\std(\text{products})-\sum\Delta H_f\std(\text{reactants})\). Combustion: complete combustion in \(\ce{O2}\) — hydrocarbons give \(\ce{CO2 + H2O}\); \(\Delta H\std=\sum\Delta H_c\std(\text{reactants})-\sum\Delta H_c\std(\text{products})\).
Born–Haber & lattice
Lattice enthalpy. Usually defined as the endothermic dissociation \(\ce{MX(s) -> M+(g) + X-(g)}\); the exothermic lattice-formation direction has opposite sign.
Born–Haber terms.
| Step | Process |
|---|---|
| sublimation / atomization | \(\ce{M(s) -> M(g)}\) |
| dissociation / atomization | \(\ce{1/2X2(g) -> X(g)}\) |
| ionization energy | \(\ce{M(g) -> M+(g) + e-}\) |
| electron affinity | \(\ce{X(g) + e- -> X-(g)}\) |
| lattice formation | \(\ce{M+(g) + X-(g) -> MX(s)}\) |
| formation | \(\ce{M(s) + 1/2X2(g) -> MX(s)}\) |
Covalent character. Deviation of the theoretical from the experimental lattice enthalpy indicates covalent character.
Fuels & fuel cells
Combustion. Complete combustion needs excess \(\ce{O2}\); incomplete combustion (limited \(\ce{O2}\)) gives \(\ce{CO}\) or \(\ce{C}\). CO binds hemoglobin; particulates are a further hazard.
Fossil fuels & biofuels. Fossil fuels: finite, high energy density, \(\ce{CO2}\) and pollutants; processed by fractional distillation and cracking. Biofuels: short carbon cycle, but land/water/fertilizer issues.
Fuel cells. Convert chemical to electrical energy continuously. \(\ce{H2}\)–\(\ce{O2}\) PEM: anode \(\ce{H2 -> 2H+ + 2e-}\); cathode \(\ce{1/2O2 + 2H+ + 2e- -> H2O}\); overall \(\ce{H2 + 1/2O2 -> H2O}\). Alkaline cathode: \(\ce{O2 + 2H2O + 4e- -> 4OH-}\). High efficiency, water as product; hydrogen storage and production are the issues.
Entropy & Gibbs
Entropy. \(S\) = dispersal of energy/matter. \(S\) increases for solid → liquid → gas, dissolution of a solid into more particles, more gas moles, mixing, higher \(T\), larger/more complex molecules. \(\Delta S\std=\sum S\std(\text{products})-\sum S\std(\text{reactants})\).
Gibbs energy. \(\Delta G\std=\Delta H\std-T\Delta S\std\). Spontaneous at constant \(T,P\) when \(\Delta G\lt 0\); equilibrium at \(\Delta G=0\); non-spontaneous when \(\Delta G\gt 0\). Switch temperature \(T=\Delta H/\Delta S\) where \(\Delta G=0\). Trap: \(\Delta S\) comes in \(\mathrm{J\,K^{-1}\,mol^{-1}}\) but \(\Delta H\) in \(\mathrm{kJ\,mol^{-1}}\) — convert \(\Delta S\) to kJ before combining with \(\Delta H\).
| \(\Delta H\) | \(\Delta S\) | Spontaneity |
|---|---|---|
| \(\lt 0\) | \(\gt 0\) | always spontaneous |
| \(\gt 0\) | \(\lt 0\) | never spontaneous |
| \(\lt 0\) | \(\lt 0\) | spontaneous at low \(T\) |
| \(\gt 0\) | \(\gt 0\) | spontaneous at high \(T\) |
Link to K. \(\Delta G\std=-RT\ln K\): \(K\gt 1\Rightarrow\Delta G\std\lt 0\), products favored; \(K\lt 1\Rightarrow\Delta G\std\gt 0\), reactants favored. \(\Delta G=\Delta G\std+RT\ln Q\); \(Q\lt K\) forward spontaneous, \(Q\gt K\) reverse.