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Zero order reaction 
Rate = –k 
[A] = –kt + [A]_{o} 
t_{½} = [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^{–1}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 t_{½} is the halflife, the time for the initial concentration to decrease by 50%


First order reaction 
Rate = –k[A] 
ln[A] = –kt + ln[A]_{o} 
t_{½} = 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 t_{½} is the halflife, the time for the initial concentration to decrease by 50%


Second order reaction 
Rate = –k[A]^{2} 
1/[A] = kt + 1/[A]_{o} 
t_{½} = 1/[A]_{o}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 M^{–1}Ls^{–1} [A]_{o} is the initial concentration of the reactant in units of M [A] is the concentration of reactant at any time t t_{½} is the halflife, the time for the initial concentration to decrease by 50%


Arrhenius equation 

k is the rate constant, in any appropriate units E_{a} 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, A is the preexponential factor in the same units as the rate constant 
Quadratic equation 
For the equation 

K_{p}  K_{c} relationship 

K_{p} is the equilibrium constant written in terms of partial pressures (atm) K_{c} 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(^{o}C) + 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) K_{c1} Reaction 2: C(aq) + E(aq) F(aq) + B(aq) K_{c2} Net reaction: A(aq) + E(aq) D(aq) + F(aq) K_{cnet} = K_{c1}×K_{c2} 

definition of pH 
pH = –log[H_{3}O^{+}] 

[H_{3}O^{+}] 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 pK_{a} 
pK_{a} = –logK_{a} 

K_{a} is the acid ionization equilibrium constant 

definition of % ionization 

is the % ionization [H_{3}O^{+}]_{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 

K_{a}  K_{b} relationship 
K_{w} = K_{a}K_{b} for conjugate acid/base pairs 

K_{w} is the equilibrium constant for the autoionization of water K_{a} is the acid ionization equilibrium constant K_{b} is the base ionization equilibrium constant


Equilibrium constant for acidbase reactions 
K_{c} = K_{a}K_{b}/K_{w} 

K_{w} is the equilibrium constant for the autoionization of water K_{a} is the acid ionization equilibrium constant K_{b} is the base ionization equilibrium constant 
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 

Pressurevolume work 
w = –PV 

w is the work in units of Latm P is the constant external pressure in units of atm V is the volume change in units of L 

Enthalpy of reaction 

H^{o} is the enthalpy of reaction in units of kJ H^{o}_{f} is the enthalpy of formation in units of kJ/mol m_{i} is the stoichiometric coefficient for each product m_{j} is the stoichiometric coefficient for each reactant 

Entropy of reaction 

S^{o} is the entropy of reaction in units of J/K S^{o} is the absolute entropy in units of J/mol•K m_{i} is the stoichiometric coefficient for each product m_{j} 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(^{o}C) + 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 

S^{o}_{vap} is the entropy change for vaporization in units of J/K H^{o}_{vap} is the enthalpy change for vaporization in units of J T_{bp} is the boiling point in units of Kelvins T(K) = T(^{o}C) + 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(^{o}C) + 273.15 

Gibb's Free Energy  work relationship 
G = w_{max} 

G is the Gibb's Free Energy change in units of kJ w_{max} is the maximum work available from a system in units of kJ 

Gibb's Free Energy at nonstandard conditions 
G = G^{o} + RTlnQ 

G is the Gibb's Free Energy change in units of kJ G^{o} 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(^{o}C) + 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 
G^{o} =–RTln K_{eq} 

G^{o} 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(^{o}C) + 273.15 K_{eq} is the thermodynamic equilibrium constant expressed with gases in units of atm and concentration in units of M 

van't Hoff equation 

K_{eq} 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(^{o}C) + 273.15 H^{o} is the enthalpy change at standard conditions in units of J S^{o} is the entropy change at standard conditions in units of J/K 
Standard cell potential 
E^{o}_{cell} = E^{o}_{red} + E^{o}_{ox} 

E^{o}_{cell} is the standard cell potential in units of V E^{o}_{red} is the potential for the reduction halfreaction in units of V E^{o}_{ox} is the potential for the oxidation halfreaction in units of V 

Nernst Equation  Cell potential at nonstandard conditions 

E_{cell} is the cell potential in units of V E^{o}_{cell} 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(^{o}C) + 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 

E^{o}_{cell} 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(^{o}C) + 273.15 n is the number of electrons transferred in the balanced chemical equation F is Faraday's constant, 96485 C/mol K_{eq} 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 
G^{o} =–nFE^{o}_{cell} 

G^{o} 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 E^{o}_{cell} is the standard cell potential in units of V 

Relationship of cell potential to work 
w_{max} = –nFE_{cell} 

w_{max} 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 E_{cell} 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 
