## Useful equations used throughout the course

Kinetics
 Zero order reaction Rate = –k [A] = –kt + [A]o t½ = [A]o/2k Rate is the reaction velocity in units of ML–1 t is time in units of s k is the rate constant in units of ML–1s–1 [A]o is the initial concentration of the reactant in units of M [A] is the concentration of reactant at any time t t½ is the half-life, the time for the initial concentration to decrease by 50% First order reaction Rate = –k[A] ln[A] = –kt + ln[A]o t½ = 0.693/k Rate is the reaction velocity in units of ML–1 t is time in units of s k is the rate constant in units of s–1 [A]o is the initial concentration of the reactant in units of M [A] is the concentration of reactant at any time t t½ is the half-life, the time for the initial concentration to decrease by 50% Second order reaction Rate = –k[A]2 1/[A] = kt + 1/[A]o t½ = 1/[A]ok Rate is the reaction velocity in units of ML–1 t is time in units of s k is the rate constant in units of M–1Ls–1 [A]o is the initial concentration of the reactant in units of M [A] is the concentration of reactant at any time t t½ is the half-life, the time for the initial concentration to decrease by 50% Arrhenius equation k is the rate constant, in any appropriate units Ea is the activation energy in units of J/mol or kJ/mol R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 A is the pre-exponential factor in the same units as the rate constant

Equilibrium
 Quadratic equation For the equation Kp - Kc relationship Kp is the equilibrium constant written in terms of partial pressures (atm) Kc is the equilibrium constant written in terms of concentrations (M) R is the gas constant, = 0.0821 L•atm/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 n is the change in moles of gas phase materials, the total number of moles of gas phase products minus the total number of moles of gas phase reactants Law of Multiple Equilibria: When chemical equations are added, equilbrium constants are multiplied Reaction 1: A(aq) + B(aq) C(aq) + D(aq)   Kc1 Reaction 2: C(aq) + E(aq) F(aq) + B(aq)   Kc2 Net reaction: A(aq) + E(aq) D(aq) + F(aq)   Kcnet = Kc1×Kc2

Acid - Base Chemistry
 definition of pH pH = –log[H3O+] [H3O+] is the hydronium ion concentration in units of M definition of pOH pOH = –log[OH–] [OH–] is the hydroxide ion concentration in units of M definition of pKa pKa = –logKa Ka is the acid ionization equilibrium constant definition of % ionization is the % ionization [H3O+]e is the equilibrium concentration of hydronium ion in units of M [A–]e is the equilibrium concentration of the conjugate base anion in units of M [HA]init is the initial concentration of the weak acid in units of M Ka - Kb relationship Kw = KaKb for conjugate acid/base pairs Kw is the equilibrium constant for the autoionization of water Ka is the acid ionization equilibrium constant Kb is the base ionization equilibrium constant Equilibrium constant for acid-base reactions Kc = KaKb/Kw Kw is the equilibrium constant for the autoionization of water Ka is the acid ionization equilibrium constant Kb is the base ionization equilibrium constant

Thermodynamics
 First Law U = q + w U is the internal energy in units of J/mol or kJ/mol q Is the heat transferred in units of J/mol or kJ/mol w is the work in units of J/mol or kJ/mol Pressure-volume work w = –PV w is the work in units of L-atm P is the constant external pressure in units of atm V is the volume change in units of L Enthalpy of reaction Ho is the enthalpy of reaction in units of kJ Hof is the enthalpy of formation in units of kJ/mol mi is the stoichiometric coefficient for each product mj is the stoichiometric coefficient for each reactant Entropy of reaction So is the entropy of reaction in units of J/K So is the absolute entropy in units of J/mol•K mi is the stoichiometric coefficient for each product mj is the stoichiometric coefficient for each reactant Second Law for a spontaneous process S is the change in entropy in units of J/mol•K q is the heat transferred in units of J/mol T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 Third Law S = RlnW S is the absolute entropy R is the gas constant, 8.314 J/mol•K W is the degeneracy of the system (unitless) Trouton's equation Sovap is the entropy change for vaporization in units of J/K Hovap is the enthalpy change for vaporization in units of J Tbp is the boiling point in units of Kelvins T(K) = T(oC) + 273.15 Gibb's Free Energy G = H – TS G is the Gibb's Free Energy change in units of kJ H is the enthalpy change in units of kJ S is the entropy change in units of kJ/K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 Gibb's Free Energy - work relationship G = wmax G is the Gibb's Free Energy change in units of kJ wmax is the maximum work available from a system in units of kJ Gibb's Free Energy at nonstandard conditions G = Go + RTlnQ G is the Gibb's Free Energy change in units of kJ Go is the Gibb's Free Energy change at standard conditions in units of kJ R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 Q is the reaction quotient expressed with gases in units of atm and concentration in units of M Gibb's Free Energy - Equilibrium constant relationship Go =–RTln Keq Go is the Gibb's Free Energy change at standard conditions in units of kJ R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 Keq is the thermodynamic equilibrium constant expressed with gases in units of atm and concentration in units of M van't Hoff equation Keq is the thermodynamic equilibrium constant expressed with gases in units of atm and concentration in units of M R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 Ho is the enthalpy change at standard conditions in units of J So is the entropy change at standard conditions in units of J/K

Electrochemistry
 Standard cell potential Eocell = Eored + Eoox Eocell is the standard cell potential in units of V Eored is the potential for the reduction half-reaction in units of V Eoox is the potential for the oxidation half-reaction in units of V Nernst Equation - Cell potential at nonstandard conditions Ecell is the cell potential in units of V Eocell is the standard cell potential in units of V R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 n is the number of electrons transferred in the balanced chemical equation F is Faraday's constant, 96485 C/mol Q is the reaction quotient expressed with gases in units of atm and concentration in units of M Relationship of cell potential to equilibrium constant Eocell is the standard cell potential in units of V R is the gas constant, 8.314 J/mol•K T is the absolute temperature in units of Kelvins, T(K) = T(oC) + 273.15 n is the number of electrons transferred in the balanced chemical equation F is Faraday's constant, 96485 C/mol Keq is the thermodynamic equilibrium constant expressed with gases in units of atm and concentration in units of M Relationship of Gibb's Free Energy to cell potential Go =–nFEocell Go is the Gibb's Free Energy change at standard conditions in units of J n is the number of electrons transferred in the balanced chemical equation F is Faraday's constant, 96485 C/mol Eocell is the standard cell potential in units of V Relationship of cell potential to work wmax = –nFEcell wmax is the maximum work available from a system in units of J n is the number of electrons transferred in the balanced chemical equation F is Faraday's constant, 96485 C/mol Ecell is the cell potential in units of V Electrolysis nF = At n is the number of electrons transferred F is Faraday's constant, 96485 C/mol A is the current passed in units of amps t is the time in units of s