CHM112 Home Page Reference Materials Homework Assignments Lectures Exams & Quizzes Grades Study Aids URI Home Page


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