Physical foundations of chemistry — statistical-mechanical derivation of reaction rates, molecular spectroscopy, and thermodynamic control of equilibria. Arrhenius 1889 (Z. Phys. Chem. 4:226) — the temperature dependence of reaction rate…
chemical-physics
Arrhenius 1889: k(T) = A·exp(−E_a/(k_B T))
Svante Arrhenius 1889 (Z. Phys. Chem. 4:226) formulated the temperature-dependence of chemical reaction rate constants as k(T) =…
Eyring 1935: k(T) = (k_B T/h)·exp(−ΔG‡/RT)
Henry Eyring 1935 (J. Chem. Phys. 3:107; also Evans-Polanyi 1935) transition-state theory — reactants pass through an activated complex X‡…
Beer-Lambert: A = εcL, T_trans = 10^(−A)
Pierre Bouguer 1729, Johann Lambert 1760, August Beer 1852 law of attenuation: in a homogeneous, linearly-absorbing medium, the…
Arrhenius slope: d(ln k)/d(1/T) = −E_a/k_B (exact)
Closed-form symbolic derivative of the Arrhenius law. ln k(T) = ln A − E_a/(k_B·T); let u = 1/T, ln k(u) = ln A − (E_a/k_B)·u; hence d(ln…
Eyring: k = T·k_B·exp(−ΔG/(R·T))/h (canonical form)
Closed-form evaluation of the Eyring transition-state rate expression. Sympy canonical form: k = T·k_B·exp(−Delta_G/(R·T))/h (printer…
Beer-Lambert: T_trans·10^A − 1 ≡ 0 (exact identity)
Closed-form polynomial identity of the Beer-Lambert law. Setting T_trans = 10^(−A) and evaluating T_trans·10^A yields exactly 1; residual…