Equation Sheet.pdf

F   S S   G G   C C      D

E m V  

D  =

Density  Converting C to K 

  + 273.15 K  = C  +

Converting F to C

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C  = ( F  − 32) ×

Converting C to F 

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F  = C  ×  + 32

Number of moles

n  =

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Percent Percent composition

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5 9

9 5

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m M 

n × molar mass of element

× 100% molar mass of compound  where n =  the number of moles of the element in one mole of the compound

Percent Percent yield

actual yield theoretical yield

Molarity 

M  =

Dilution of Solution

M i V  i  =  M f  f V   f 

Ideal gas equation

P V   =  nRT 

Charles’ Law 

V  1 V  2 = T 1 T 2

Boyle’s Law 

P 1 V  1  =  P 2 V  2

Combined gas law 

P 1 V  1 P 2 V  2 = T 1 T 2

 Avogadro’  Avogadro’s Law  L aw 

n ∝ V  

Density of ideal gas

d  =

×

100%

 moles of solute liters of solution

P M  RT 

continued on next page 

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D Mole fraction of A

E moles A X A  = total moles

Partial pressure of a gas

P A  =  P total X A

 Total gas pressure

P total  =  P A + P B  + P C  + . . .

Kinetic energy

1 KE  = mv2 2

Kinetic energy of ideal gas

KE 3 = RT n mole 2

Root mean square velocity  Graham’s Law of Effusion Van der Waals equation

√  √  √  � � 3kT 

urms  = r1 = r2

m

3RT 

=

M 

M 2 M 1

an2 P  + 2 V  

Energy of photon

E  =  hν 

Electromagnetic radiation

c  =  λν 

de Broglie Wavelength

λ  =

Linear momentum

p  =  mv

(V   − bn) =  nRT 

h mv

�

1

1

Bohr equation

∆E  =  B

Formal charge on an atom in a Lewis structure

F C  = # valence e

Molality 

m  =

Freezing point depression

∆T f  =  iK f m

n2i

−

n2f  −

�

−

#lone e

−

−

moles of solute kilograms of solvent

continued on next page 

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#bonds

D

E

Boiling point elevation

∆T b  =  iK b m

Osmotic pressure

π  =  iMRT 

Henry’s law 

c  =  kP 

Raoult’s Law 

P 1  =  X 1 P 1

Equilibrium constant

[C ]ceq [D]deq  where K  = [A]aeq [B ]beq

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aA + bB

Reaction quotient

[C ]c [D]d  where [A]a [B ]b

Q  =

aA + bB K  p  from  K c

cC  + dD

→

cC  + dD

→

∆n

K  p  =  K c (RT )

� � K 2 K 1

∆H 

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=−

 van’t Hoff equation

ln

 pH   denition

pH  =

 pOH   denition

pOH  =

 pH  and pOH  relationship

pH  +  pOH  = 14

−

R

�

1

−

T 2

1 T 1

�

log[H + ]

−

log[OH + ]

Ion product constant for wa- K w = [OH  ][H + ] ter =  K a × K b  = 1.0 × 10 −

14

−

 Acid Ionization constant

[H + ][A ] K a  = [HA]

Base Ionization constant

[OH  ][HB ] K b  = [B ]

 pK a  denition

pK a  =

at 25 C 

−

−

−

−

log K a continued on next page 

3

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D  pK b  denition

E pK b  =

−

log K b

Henderson-Hasselback equa-  pH  =  pK a  +  log tion  Arrhenius equation

k  =  Ae

First-order rate law

ln

Second-order rate law 

 [conjugate base] [acid]

E  /RT 

−

a

 [ A]0 =  kt [A]

1 [A]

=

1 + kt [A]0

Heat Equation

q  =  mc ∆T 

Heat capacity 

C  p  =

First law of thermodynamics

∆U  =  Q + W 

∆H  ∆T 

 Work done in gas expansion W  = −P ∆V   or compression Enthalpy (or energy) change ∆H  = ∆U  + P ∆V   for a constant pressure process  e second law of thermody- ∆S universe  = ∆S system + ∆ S surroundings > 0 namics (spontaneous process)  e second law of thermody- ∆S universe  = ∆S system + ∆ S surroundings  = 0 namics (reversible process) Enthalpy Change

∆H  = ΣH f   products − ΣH f   reactants

Enthalpy change of a reaction from bond energies

∆H  = ΣBE reactants − ΣBE  products

Entropy Change

∆S  = ΣS products − ΣS reactants

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q 

Entropy change of heat ow  ∆S  = T  at constant temperature continued on next page 

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D

E

Gibb’s Free Energy Change

∆G = ΣGf   products − ΣGf   reactants

Gibb’s Free Energy Change

∆G = ∆H 

Gibb’s Free Energy Change

∆G = −RT  ln K 

Gibb’s Free Energy Change

∆G = −nF E 

Non-standard free energy 

∆G  = ∆G + RT  ln Q

∆H  vap, vapor pressure, or boiling point of a liquid

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T ∆S 

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−

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∆H  vap  P 1 ln = P 2 R

�

1 T 1

−

1 T 2

�

 Charge q  = t  Time

Electric Current

I  =

Standard emf 

E cell  =  E ox − E red  =  E cathode − E anode

Cell Voltage

E cell  =  E cell −

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©Dhrubajyoti Das and Justin Weinberg. All rights reserved

5

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RT  ln Q nF 

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C

V

 Avogadro’s Number, N A

6.022 × 1023 mol−1

 Atomic mass,  1  amu

1.661 × 10−27 kg

Mass of proton/neutron

1.67 × 10−27 kg

Mass of electron

9.11 × 10−31 kg

Ideal gas constants,  R

0.0821(L · atm) / (mol · K ) = 8.314 J/ (mol · K )

Standard pressure

1.00 atm  = 101.3 kPa  = 760 mmHg = 760 Torr

Standard temperature

0 °C = 273  K 

Volume of  1  mole of any ideal gas at STP

22.4 L

Boltzmann’s constant, k B

1.381 × 10−23 m2 kg · s−2 K −1

Planck’s constant,  h

6.626 × 10−34  J · s

Speed of light in vacuum,  c

2.998 × 108 m/s

Bohr’s constant

2.117 × 10−18  J

Faraday’s constant,  F 

9.649 × 104 C/mol

Electron charge,  e

−

Electronvolt, 1  eV 

1.602 × 10−19  J

Specic heat capacity of H2 O (liquid)

4.18 J/g · K  = 1 cal /g · K 

1.602 × 10−19 C

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