Useful Equations
Density
!!""
!
! =!
!( )
!!"#$% !"
Frequency and Wavelength
!
!=
!
Dipole Moment
! = !×!
Energy of a photon
ℎ!
! = ℎ! =
!
Henry’s Law
!!"# = !! !!"#
Molarity
!"#!!"#$%&
!=
!!!"#$!"#$
Molality
!"#!!"#$%&
!=
!"!!"#$%&'
de Broglie Relation
ℎ
!=
!"
Solution Dilution
!! !! = !! !!
Energy of Hydrogen Atom Levels
!!"!#$
1
[!]! = −!" + !
ln !
!
½ Life
!
= −!" + ln![!]!
1
1
= !" +
[!]!
[!]!
2
!!
!
=
[!]!
2!
!!
!
=
0.693
!
!!
!
=
1
![!]!
Arrhenius Equation
!!"
!"
Van der Waals Equation
!
! + !( )! × ! − !" = !"#
!
Freezing Point Depression
Δ!! = !!×!!!
Boiling Point Elevation
Δ!! = !!×!!!
Kc and Kp
!! = !! (!")!!
Osmotic Pressure
Π = !"#
Entropy
! = !!!"#
pH Scale
!" = −log![!! !! ]
Average Kinetic Energy
3
!"!"# = !"
2
Δ in Entropy of Surroundings
−Δ!!"!
Δ!!"## =
!
Henderson-Hasselbalch Equation
[!"#$%&'()!!"#$]
!" = !!! + log!
[!"#$]
ΔGibb’s Free Energy
Δ! = Δ! − !Δ!
Temp Dependence of K
°
°
Δ!!"#
1
Δ!!"#
!"# = ! −
+
!
!
!
3!"
ℳ
!"#$!!
=
!!"#!!
ℳ!
ℳ!
Δ in Free Energy Nonstandard Conditions
!! Δ!!° (!"#$%#&%')
°
Δ!!"# = Δ!!"#
+ !"#$%
Internal Energy
Δ! = ! + !
Heat Capacity
! = !×!! ×Δ!
ΔG°rxn and K
°
Δ!!"#
= −!!!!!"#
Pressure-Volume work
! = −!Δ!
Change in Enthalpy
Δ! = Δ! + !Δ!
!! Δ!!° !"#$%&'( −
! = !!
!"!!"# =
Effusion
Standard Enthalpy of Reaction
°
Δ!!"#
=
Integrated
0
Two-point Arrhenius Equation
!!"
Coulomb’s Law
1 !! !!
!=
4!!! !
Mole Fraction
!!
!! =
!!"!#$
Kinetic Energy
1
!" = !! !
2
Root Mean Square Velocity
!!"# =
Clausius-Clapeyron Equation
Integrated Rate Laws & Half-life
Order
−Δ!!"#
+ !"#
!"
!! −Δ!!"# 1
1
!"
=
( − )
!!
!
!! !!
!! = −2.18×10
Ideal Gas Law
!" = !"#
Dalton’s Law
= !! + !! + !! + ⋯ + !!
1
! ! (! = 1,2,3 … )
!
Raoult’s Law
°
!!"#$%&"' = !!"#$%&' !!"#$%&'
The Rate Law
!"#$ = ! ! ! (single reactant)
!"#$ = ! ! ! [!]! (mult reactants)
!!"##
Nernst Equation
0.0592!
°
= !!"##
−
!"#$
!
!!
!2
!1
=
!" 1
1
( − )
! !1 !2
E°cell and K
0.0592!
°
!!"##
=
!"#$
!
ΔG° and E°cell
°
Δ! ° = −!!!!!!"##
°
°
°
!!"##
= !!"#!!"#
− !!"#$%
!!"## = !!"#!!"# − !!"#$%