ROYAL SOCIETY OF CHEMISTRY DATA BOOK EQUATIONS AND FORMULAE: PHYSICS, CHEMISTRY & MATHEMATICS Recommended symbols are used, with a minimum of explanation. The list is intended only to refresh the memory. It is necessary to consult textbooks to find out the meaning of the formulae and the assumptions made in deriving them. GAS LAWS Ideal gas (molecular formula X) pV = nRT pV = nLkT pV = Nmc 2 Gas constant R, amount of X n. Avogadro constant L, Boltzmann constant k. Number of molecules N, mass of molecule m, mean square speed c 2 . Dalton's law of partial pressure p = pA + pB + … Pressures of gases existing on own pA, pB … Raoult's law p = p o N/(n+N) Vapour pressure of solution p, of pure solvent p o ; amount of solvent N, of involatile solute n. ENTROPY, ENERGY, ENTHALPY Entropy S = k ln W Boltzmann constant k, number of molecular arrangements W. S = Qreversible/T System at equilibrium Trouton's rule For any process involving a single isothermal. Stotal = 0 S system + S surroundings = 0 S surroundings = Hsystem/T Hb/Tb 82 J mol 1 K 1 For normal non­associated liquids. Ideal gases S = Lkln(p2/p1) When a system changes at constant temperature Stotal = S surroundings + Ssystem G = H T S Gibbs free energy change G = zFEcell e.m.f. of cell Ecell. ideal systems G = RTlnK c/c Standard Gibbs free energy change at concentration c , G Standard Gibbs free energy change at pressure p , G G = RTlnK p/p Change of pressure from p1 to p2. Boltzmann equation (factor) In x = E/kT Ratio of number of molecules in one state to number in another state (lower in energy by E) x, Boltzman constant k (1.38 x 10 23 J K 1 ). Average energy of molecule Eaverage is of the order kT Detailed dependence of Eaverage upon T depends on molecules concerned. Specific heat capacity c = Q/m T Heat exchanged Q, mass m, temperature change T.
ROYAL SOCIETY OF CHEMISTRY DATA BOOK Page 1 of 2 www.chemsoc.org/networks/learnnet/data.htm PHYSICAL CHEMISTRY Equilibrium law Kc = [C] eqm p [D] eqm q [A] eqm m [B] eqm n For mA + nB pC + qD. Kc/c = Kc/(c ) p+q m n Gas phase equilibrium Kp = Kc(RT) p+q m n Kp/p = Kp/(p ) p+q m n pH of a solution pH = lg([H + ] /mol dm ­3 ) pH of a buffer solution pH = pKa + lg([base]eqm/[acid] eqm) Nernst equation Electrode and standard electrode potential E RT [oxidized form] and E , number of electrons transferred in the E = E + In zF [reduced form] reaction involving H2 and H + z, gas constant R (8.314 J K 1 mol 1 ), Faraday constant F (9.648 x 10 4 C mol 1 ). Reaction rates Arrhenius equation d[A]/dt = ko or kot = [A]o [A]t Zero order. d[A]/dt = k1[A] or k1t = ln([A]o /[A]) and t½ = ln2/k1 = 0.69/k1 First order. d[A]/dt = k2 [A] 2 or k2t = 1/[A] 1/[A]o and t½ = 1/[A]ok2 Second order. k = Ae Ea/RT Activation energy Ea, pre­exponential factor A, gas constant R (8.314 J K 1 mol 1 ), any unit of k u. ln(k/u) = ln(A/u) Ea /RT
ROYAL SOCIETY OF CHEMISTRY DATA BOOK Page 2 of 2 www.chemsoc.org/networks/learnnet/data.htm