Formulas

Chemistry

Stoichiometry

Density
D = m / V
D Density
m Mass
V Volume

Molar Mass
M = m / n
M Molar Mass
m Mass
n Number of Moles

Number of Moles
n = m / M
n Number of Moles
m Mass
M Molar Mass

Molarity
M = n / V
M Molarity
n Number of Moles of Solute
V Volume of Solution in Liters

Molality
m = n / m_solvent
m Molality
n Number of Moles of Solute
m_solvent Mass of Solvent in Kilograms

Mass Percent
Mass Percent = (mass solute / mass solution) * 100%
mass solute Mass of the Solute
mass solution Total Mass of the Solution

Mole Fraction
X_A = n_A / n_total
X_A Mole Fraction of Component A
n_A Number of Moles of Component A
n_total Total Number of Moles in the Mixture

Dilution Formula
M1 V1 = M2 V2
M1 Initial Molarity
V1 Initial Volume
M2 Final Molarity
V2 Final Volume

Gases

Ideal Gas Law
P V = n R T
P Pressure
V Volume
n Number of Moles
R Ideal Gas Constant
T Temperature

Boyles Law
P1 V1 = P2 V2
P1 Initial Pressure
V1 Initial Volume
P2 Final Pressure
V2 Final Volume

Charless Law
V1 / T1 = V2 / T2
V1 Initial Volume
T1 Initial Temperature
V2 Final Volume
T2 Final Temperature

Gay Lussacs Law
P1 / T1 = P2 / T2
P1 Initial Pressure
T1 Initial Temperature
P2 Final Pressure
T2 Final Temperature

Combined Gas Law
P1 V1 / T1 = P2 V2 / T2
P1 Initial Pressure
V1 Initial Volume
T1 Initial Temperature
P2 Final Pressure
V2 Final Volume
T2 Final Temperature

Avogadros Law
V1 / n1 = V2 / n2
V1 Initial Volume
n1 Initial Number of Moles
V2 Final Volume
n2 Final Number of Moles

Daltons Law of Partial Pressures
P_total = P_A + P_B + P_C +
P_total Total Pressure of the Mixture
P_A Partial Pressure of Gas A
P_B Partial Pressure of Gas B
P_C Partial Pressure of Gas C

Mole Fraction from Partial Pressure
P_A = X_A * P_total
P_A Partial Pressure of Gas A
X_A Mole Fraction of Gas A
P_total Total Pressure

Root Mean Square Velocity
u_rms = sqrt(3RT / M)
u_rms Root Mean Square Velocity
R Gas Constant
T Temperature
M Molar Mass

Average Kinetic Energy
KE_avg = (3/2)RT
KE_avg Average Kinetic Energy per Mole
R Gas Constant
T Temperature

Van der Waals Equation
(P + a(n/V)²) (V – nb) = nRT
P Pressure
V Volume
n Number of Moles
R Gas Constant
T Temperature
a Constant for Intermolecular Forces
b Constant for Molecular Volume

Thermochemistry

Heat Transfer
q = m * c * ΔT
q Heat Transferred
m Mass
c Specific Heat Capacity
ΔT Change in Temperature

Enthalpy Change
ΔH = q_p
ΔH Change in Enthalpy
q_p Heat Transferred at Constant Pressure

Standard Enthalpy of Reaction
ΔH°_rxn = Σ n ΔH°_f products – Σ n ΔH°_f reactants
ΔH°_rxn Standard Enthalpy Change of Reaction
Σ n ΔH°_f products Sum of Standard Enthalpies of Formation of Products
Σ n ΔH°_f reactants Sum of Standard Enthalpies of Formation of Reactants

Hesss Law
ΔH_total = ΔH1 + ΔH2 + ΔH3 +
ΔH_total Total Enthalpy Change for the Reaction
ΔH1 Enthalpy Change of Step One
ΔH2 Enthalpy Change of Step Two
ΔH3 Enthalpy Change of Step Three

Heat of Fusion
q = n * ΔH_fus
q Heat Absorbed during Melting
n Number of Moles
ΔH_fus Molar Heat of Fusion

Heat of Vaporization
q = n * ΔH_vap
q Heat Absorbed during Vaporization
n Number of Moles
ΔH_vap Molar Heat of Vaporization

Heat of Reaction from Calorimetry
q_rxn = – C_cal * ΔT
q_rxn Heat of Reaction
C_cal Heat Capacity of the Calorimeter
ΔT Change in Temperature

Heat Capacity
C = q / ΔT
C Heat Capacity
q Heat Absorbed
ΔT Change in Temperature

Specific Heat
c = q / (m * ΔT)
c Specific Heat Capacity
q Heat Transferred
m Mass
ΔT Change in Temperature

Molar Heat Capacity
C_m = q / (n * ΔT)
C_m Molar Heat Capacity
q Heat Transferred
n Number of Moles
ΔT Change in Temperature

Standard Enthalpy of Formation
ΔH°_f
ΔH°_f Standard Enthalpy of Formation

Thermodynamics

Entropy Change
ΔS = q_rev / T
ΔS Change in Entropy
q_rev Heat Transferred Reversibly
T Temperature

Gibbs Free Energy
ΔG = ΔH – T ΔS
ΔG Change in Gibbs Free Energy
ΔH Change in Enthalpy
T Temperature
ΔS Change in Entropy

Gibbs Free Energy & Equilibrium
ΔG = ΔG° + RT ln Q
ΔG Change in Gibbs Free Energy
ΔG° Standard Change in Gibbs Free Energy
R Gas Constant
T Temperature
Q Reaction Quotient

Standard Gibbs Free Energy
ΔG° = – RT ln K
ΔG° Standard Change in Gibbs Free Energy
R Gas Constant
T Temperature
K Equilibrium Constant

Standard Gibbs Free Energy of Formation
ΔG°_f
ΔG°_f Standard Gibbs Free Energy of Formation

Standard Entropy
S°
S° Standard Entropy

Change in Entropy for a Reaction
ΔS°_rxn = Σ n S°_products – Σ n S°_reactants
ΔS°_rxn Standard Entropy Change of Reaction
Σ n S°_products Sum of Standard Entropies of Products
Σ n S°_reactants Sum of Standard Entropies of Reactants

First Law of Thermodynamics
ΔU = q + w
ΔU Change in Internal Energy
q Heat Added to the System
w Work Done on the System

Work of Expansion
w = – P ΔV
w Work Done by the System
P Pressure
ΔV Change in Volume

Kinetics

Rate Law
Rate = k [A]^m [B]^n
Rate Reaction Rate
k Rate Constant
[A] Concentration of Reactant A
[B] Concentration of Reactant B
m Order with Respect to A
n Order with Respect to B

Integrated Rate Law Zero Order
[A]_t = [A]_0 – kt
[A]_t Concentration at Time t
[A]_0 Initial Concentration
k Rate Constant
t Time

Integrated Rate Law First Order
ln [A]_t = ln [A]_0 – kt
[A]_t Concentration at Time t
[A]_0 Initial Concentration
k Rate Constant
t Time

Integrated Rate Law Second Order
1 / [A]_t = 1 / [A]_0 + kt
[A]_t Concentration at Time t
[A]_0 Initial Concentration
k Rate Constant
t Time

Half Life Zero Order
t_1/2 = [A]_0 / 2k
t_1/2 Half Life
[A]_0 Initial Concentration
k Rate Constant

Half Life First Order
t_1/2 = 0.693 / k
t_1/2 Half Life
k Rate Constant

Half Life Second Order
t_1/2 = 1 / (k [A]_0)
t_1/2 Half Life
k Rate Constant
[A]_0 Initial Concentration

Arrhenius Equation
k = A e^(- E_a / RT)
k Rate Constant
A Pre Exponential Factor
E_a Activation Energy
R Gas Constant
T Temperature

Linear Form of Arrhenius Equation
ln k = ln A – (E_a / R) (1 / T)
ln k Natural Log of the Rate Constant
ln A Natural Log of the Pre Exponential Factor
E_a Activation Energy
R Gas Constant
T Temperature

Rate Constant & Half Life First Order
k = 0.693 / t_1/2
k Rate Constant
t_1/2 Half Life

Equilibrium

Reaction Quotient
Q = [C]^c [D]^d / [A]^a [B]^b
Q Reaction Quotient
[C] Concentration of Product C
[D] Concentration of Product D
[A] Concentration of Reactant A
[B] Concentration of Reactant B
a Stoichiometric Coefficient of A
b Stoichiometric Coefficient of B
c Stoichiometric Coefficient of C
d Stoichiometric Coefficient of D

Equilibrium Constant Kc
K_c = [C]^c [D]^d / [A]^a [B]^b
K_c Equilibrium Constant for Concentrations
[C] Equilibrium Concentration of Product C
[D] Equilibrium Concentration of Product D
[A] Equilibrium Concentration of Reactant A
[B] Equilibrium Concentration of Reactant B
a Stoichiometric Coefficient of A
b Stoichiometric Coefficient of B
c Stoichiometric Coefficient of C
d Stoichiometric Coefficient of D

Equilibrium Constant Kp
K_p = (P_C)^c (P_D)^d / (P_A)^a (P_B)^b
K_p Equilibrium Constant for Partial Pressures
P_C Equilibrium Partial Pressure of Product C
P_D Equilibrium Partial Pressure of Product D
P_A Equilibrium Partial Pressure of Reactant A
P_B Equilibrium Partial Pressure of Reactant B
a Stoichiometric Coefficient of A
b Stoichiometric Coefficient of B
c Stoichiometric Coefficient of C
d Stoichiometric Coefficient of D

Relationship between Kp & Kc
K_p = K_c (RT)^Δn
K_p Equilibrium Constant for Partial Pressures
K_c Equilibrium Constant for Concentrations
R Gas Constant
T Temperature
Δn Change in Number of Moles of Gas

Acids & Bases

pH
pH = – log [H⁺]
pH pH
[H⁺] Concentration of Hydrogen Ions

pOH
pOH = – log [OH⁻]
pOH pOH
[OH⁻] Concentration of Hydroxide Ions

Ion Product of Water
K_w = [H⁺] [OH⁻] = 1.0 x 10^-14
K_w Ion Product Constant for Water
[H⁺] Hydrogen Ion Concentration
[OH⁻] Hydroxide Ion Concentration

pH & pOH Relationship
pH + pOH = 14
pH pH
pOH pOH

Strong Acid pH
pH = – log [HA]
pH pH
[HA] Initial Concentration of the Strong Acid

Strong Base pOH
pOH = – log [MOH]
pOH pOH
[MOH] Initial Concentration of the Strong Base

Ka Acid Dissociation Constant
K_a = [H⁺] [A⁻] / [HA]
K_a Acid Dissociation Constant
[H⁺] Hydrogen Ion Concentration
[A⁻] Conjugate Base Concentration
[HA] Weak Acid Concentration

Kb Base Dissociation Constant
K_b = [BH⁺] [OH⁻] / [B]
K_b Base Dissociation Constant
[BH⁺] Conjugate Acid Concentration
[OH⁻] Hydroxide Ion Concentration
[B] Weak Base Concentration

pKa
pK_a = – log K_a
pK_a pKa
K_a Acid Dissociation Constant

pKb
pK_b = – log K_b
pK_b pKb
K_b Base Dissociation Constant

Relationship between Ka & Kb
K_a * K_b = K_w
K_a Acid Dissociation Constant
K_b Base Dissociation Constant for its Conjugate Base
K_w Ion Product Constant for Water

Henderson Hasselbalch Equation for Acids
pH = pK_a + log ([A⁻] / [HA])
pH pH
pK_a Negative Log of Ka
[A⁻] Concentration of Conjugate Base
[HA] Concentration of Weak Acid

Henderson Hasselbalch Equation for Bases
pOH = pK_b + log ([BH⁺] / [B])
pOH pOH
pK_b Negative Log of Kb
[BH⁺] Concentration of Conjugate Acid
[B] Concentration of Weak Base

pH of a Weak Acid Approximation
[H⁺] = sqrt(K_a * [HA]_0)
[H⁺] Hydrogen Ion Concentration
K_a Acid Dissociation Constant
[HA]_0 Initial Weak Acid Concentration

pOH of a Weak Base Approximation
[OH⁻] = sqrt(K_b * [B]_0)
[OH⁻] Hydroxide Ion Concentration
K_b Base Dissociation Constant
[B]_0 Initial Weak Base Concentration

Solutions & Colligative Properties

Osmotic Pressure
Π = i M R T
Π Osmotic Pressure
i Van t Hoff Factor
M Molarity
R Gas Constant
T Temperature

Freezing Point Depression
ΔT_f = i K_f m
ΔT_f Freezing Point Depression
i Van t Hoff Factor
K_f Molal Freezing Point Depression Constant
m Molality

Boiling Point Elevation
ΔT_b = i K_b m
ΔT_b Boiling Point Elevation
i Van t Hoff Factor
K_b Molal Boiling Point Elevation Constant
m Molality

Raoults Law
P_A = X_A * P°_A
P_A Vapor Pressure of Component A in the Mixture
X_A Mole Fraction of Component A in the Mixture
P°_A Vapor Pressure of Pure A

Raoults Law for Total Vapor Pressure
P_total = P_A + P_B = X_A P°_A + X_B P°_B
P_total Total Vapor Pressure of the Solution
X_A Mole Fraction of Component A
P°_A Vapor Pressure of Pure A
X_B Mole Fraction of Component B
P°_B Vapor Pressure of Pure B

Electrochemistry

Standard Cell Potential
E°_cell = E°_cathode – E°_anode
E°_cell Standard Cell Potential
E°_cathode Standard Reduction Potential of the Cathode
E°_anode Standard Reduction Potential of the Anode

Nernst Equation
E = E° – (RT / nF) ln Q
E Cell Potential under Nonstandard Conditions
E° Standard Cell Potential
R Gas Constant
T Temperature
n Number of Moles of Electrons Transferred
F Faradays Constant
Q Reaction Quotient

Relationship between ΔG° & E°_cell
ΔG° = – n F E°_cell
ΔG° Standard Change in Gibbs Free Energy
n Number of Moles of Electrons Transferred
F Faradays Constant
E°_cell Standard Cell Potential

Faradays Law for Mass
m = (Q * M) / (n * F)
m Mass of Substance Deposited or Dissolved
Q Total Electric Charge
M Molar Mass of the Substance
n Number of Electrons Transferred per Ion
F Faradays Constant

Charge
Q = I * t
Q Total Electric Charge
I Current
t Time

Cell Potential & Equilibrium Constant
E°_cell = (RT / nF) ln K
E°_cell Standard Cell Potential
R Gas Constant
T Temperature
n Number of Moles of Electrons Transferred
F Faradays Constant
K Equilibrium Constant

Atomic & Quantum Chemistry

Energy of a Photon
E = h ν
E Energy of a Photon
h Plancks Constant
ν Frequency

Speed of Light
c = λ ν
c Speed of Light
λ Wavelength
ν Frequency

Energy from Wavelength
E = h c / λ
E Energy of a Photon
h Plancks Constant
c Speed of Light
λ Wavelength

De Broglie Wavelength
λ = h / (m v)
λ Wavelength
h Plancks Constant
m Mass
v Velocity

Heisenberg Uncertainty Principle
Δx * Δp ≥ h / (4π)
Δx Uncertainty in Position
Δp Uncertainty in Momentum
h Plancks Constant

Rydberg Formula for Hydrogen
1/λ = R_H (1/n1² – 1/n2²)
λ Wavelength
R_H Rydberg Constant for Hydrogen
n1 Lower Energy Level
n2 Higher Energy Level

Energy of an Electron in Hydrogen
E_n = – R_H / n²
E_n Energy of the Electron in the nth Level
R_H Rydberg Constant in Energy Units
n Principal Quantum Number

Effective Nuclear Charge
Z_eff = Z – S
Z_eff Effective Nuclear Charge
Z Atomic Number
S Shielding Constant

Coulombs Law for Energy
E = k (q1 q2) / r
E Potential Energy
k Coulombs Constant
q1 Charge of Particle One
q2 Charge of Particle Two
r Distance between Charges

Schrödinger Equation
Ĥψ = Eψ
Ĥ Hamiltonian Operator
ψ Wavefunction
E Energy

Constants

Ideal Gas Constant R
R = 0.0821 L atm mol⁻¹ K⁻¹
R Ideal Gas Constant
L Liters
atm Atmospheres
mol Moles
K Kelvin

Ideal Gas Constant R in SI
R = 8.314 J mol⁻¹ K⁻¹
R Ideal Gas Constant
J Joules
mol Moles
K Kelvin

Faradays Constant
F = 96485 C / mol
F Faradays Constant
C Coulombs
mol Mole of Electrons

Plancks Constant
h = 6.626 x 10^-34 J s
h Plancks Constant
J Joules
s Seconds

Speed of Light
c = 3.00 x 10^8 m / s
c Speed of Light
m Meters
s Seconds

Avogadros Number
N_A = 6.022 x 10^23 particles / mol
N_A Avogadros Number
particles Atoms Molecules Ions etc
mol Mole

Analytical Chemistry

Beer Lambert Law
A = ε b c
A Absorbance
ε Molar Absorptivity
b Path Length
c Concentration

Percent Yield
Percent Yield = (Actual Yield / Theoretical Yield) * 100%
Actual Yield Amount of Product Actually Obtained
Theoretical Yield Amount of Product Predicted by Stoichiometry

Percent Error
Percent Error = |(Theoretical – Experimental)| / Theoretical * 100%
Theoretical Accepted or Theoretical Value
Experimental Measured Value

Empirical Formula from Percent Composition
Assume 100g sample convert mass to moles find simplest whole number ratio
mass Mass of Each Element in a 100g Sample
mole Number of Moles of Each Element
ratio Simplest Whole Number Ratio of Moles

Molecular Formula from Empirical Formula
Molecular Formula = (Empirical Formula)_n
n = Molar Mass / Empirical Formula Mass
n Multiplying Integer
Molar Mass Mass of One Mole of the Compound
Empirical Formula Mass Mass of One Mole of the Empirical Formula

Dipole Moment
μ = Q * r
μ Dipole Moment
Q Magnitude of Charge
r Distance between Charges