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FORMULA SHEETS UNITS
Physical
Quantity
SI Unit CGS Unit Other Unit(s) Conversion
Length meter (m) centimeter(cm) angstrom (A) 1m= 100 cm
1m = 1010
A
Mass kilogram (kg) gram (g) 1kg = 1000g
Temperature Kelvin (K) Celsius (C) Fahrenheit (F)
K = C + 273.15
F = 9/5 C + 32
Volume cubic meter
(m3)
cubic
centimeter (cm3)
liter (L)
milliliter (mL)
1m3 = 10
6 cm
3
1m3 = 1000 L
1L = 1000 cm3
1mL = 1 cm3
Density kg m-3
g cm-3
1kg cm-3
= 10-3
g cm-3
Force Newton
(N =kg m s-2
)
dyne (g cm s
-2)
1 N = 105 dyne
Pressure
pascal (Pa = N m
-2)
dyne cm
-2
atm. torr, mmHg,
bar
1atm = 101,325 Pa 1 atm = 760 torr
1 atm = 760 mmHg 1bar = 10
5 Pa
Energy
Joule
(J=kg m2s
-2)
erg (g cm
2 s
-2)
calorie (cal) electron volt (eV)
Calorie (Cal) : nutritional Calorie
1 J =107 erg
1 cal = 4.184 J 1eV=1.6022x10
-9J
1 Cal = 1kcal = 103 cal
Other useful units: Amperes (A) = C s-1
Watts (W) = J s-1
= kg m2 s
-3 = V A
Volts (V) = J C-1
= J A-1
s-1
for PV work: 1 J = 101.325 L atm (expansion/compression
work)
Prefixes Used with SI Units
Prefix Symbol Meaning
Tera- T 1012
Giga- G 109
Mega- M 106
Kilo- k 103
Deca- dc or dk 101
Deci- d 10-1
Centi- c 10-2
Milli- m 10-3
Micro- 10-6
Nano- n 10-9
Pico- p 10-12
Femto f 10-15
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IDEAL GAS
Kinetic Molecular Theory of Gases
root-mean-square speed: crms = 3
mean speed: c = 8
most probable speed: c* = 2
Van der Waals Equation of State
(P + 2
2)(V nb) = nRT
Pc =
272
Vc = 3b
Tc = 8
27
Pr =8
272 -
3
2
Kinetic Molecular Theory of Gases
Collision frequency:
ZA = d2
AB (8
)1/2 (
)
number of collisions:
ZAB = d2
AB (8
)1/2 (
) (
)
Where: d = :
2
= reduced mass
=
:
For A-A collision,
collision frequency:
ZA = 2d2 c (
)
number of collisions:
ZAA = 2
2d2 c (
)2
mean free path: =
=
1
2 2 (
) Virial Equations of State
PVm = RT (1 +
+
2 + )
PVm = RT ( 1 + BP + CP2 + )
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FIRST LAW OF THERMODYNAMICS
= +
W = -
Heat Capacities
Cp = (
)p
Cv = (
)v
ADIABATIC REVERSIBLE PROCESS
FOR IDEAL GAS
Cv dT = -P dV
Cv,m ln
= -R ln
2
1 = (
1
2) 1
P1V1 = P2V2
Where = ,
,
OR: T1V1c = T2V2
c
2
1
+1 =
1
2
Where c =
,=
EXPERIMENTAL COEFFICIENTS
Coefficient of Thermal Expansion:
=
(
)p
Isothermal Compressibility:
KT = ;1
(
)T
Joule Thomson Coefficient:
JT = (
) H
For ideal gas systems:
Process qrev wrev Isobaric
-P = or =
Isochoric 0
Isothermal nRTln( 2
1) -nRTln(
2
1) 0 0 nRTln(
2
1)
Adiabatic 0 0
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Legendre Transformation
H = U + PV
A = U TS
G = H TS
Combined First and Second Law
dU = TdS PdV (
)S = - (
)V
dH = TdS + VdP (
)S = - (
)P
dA = -SdT PdV (
)T = - (
)V
dG = -SdT + VdP (
)T = - (
)P
dU = Cv dT + (
)T dV
dH = Cp dT + (
)T dP
dS =
+
1
[P + (
)T]dV
dS =
+
1
[ (
)T - V ]dP
Consequences of Maxwell Relations:
(
)T = T(
)V P
(
)T = V T (
)P
Temperature Dependence of Thermodynamic Functions
2 = 1 + 21
2 = 1 + 21
Gibbs-Helmholtz Equation:
(
)P =
;
2
(
)P =
;
2
THERMODYNAMICS OF MIXING OF IDEAL GASES/SOLUTION = ntRT = -ntR =
0 = 0
SOLUTIONS Raoults Law: Pi = Xl Pi Henrys Law: Pi = XI Ki
Where: Ki = Henrys law constant
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DEBYE-HUCKEL LIMITING LAW
log = -0.51 |Z+ Z- |
where: I = 1
2
2
COLLIGATIVE PROPERTIES Vapor Pressure Lowering: P = X2 P1
Psoln = X1 P1 Boiling Point Elevation:
= m where =
21
1000
Freezing Point Depression:
= m where =
21
1000
Osmotic Pressure: = Note: 1- solvent; 2 - solute
Electrochemical Cells Nernst Equation:
= 0
ln
At 25C: = 0 0.0592
log
= Where: n = moles of electron F = Faradays constant = 96485 c
mol-1
CHEMICAL EQUILIBRIUM
= ;0
= ()
Where = moles of gaseous products moles of gaseous reactants
Vant Hoff Equation:
ln 2
1 =
;
(1
2
1
1)
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PHASE EQUILIBRIA Clapeyron Equation:
=
Clausius- Clapeyron Equation:
ln 2
1=
(
1
2
1
1)
Troutons Rule:
= 21
;= 88
;
Gibbs Phase Rule: F = C P + 2 Where: F= variance; degrees of
freedom C= components P= phases
Electrical Quantities
Quantity Units Defining Relationship
Resistance Ohm, V = IR Conductance Siemen (S), -1 G =
1
=
Cell constant m-1 K=
Conductivity S m-1 K=
=
Molar Conductance S m2 mol-1 m =
Kohlrauschs Law: 0 = : :
0 + ;0
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CHEMICAL KINETICS
Order Integrated Rate Equation Half-life Unit of k
0 [A]t = -kt + [A]0 t1/2 = 0
2
Conc time-1
1 ln[A]t = -kt + ln[A]0 t1/2 = 2
time-1
2 1
= kt +
1
0 t1/2 =
1
0
Conc-1 time-1
QUANTUM CHEMISTRY
CHEMICAL KINETICS
Arrhenius Equation: k = A ;
ln (2
1) = -
(1
2 -
1
1)
Collision Theory:
k = p d2 (8
)1/2 NA
;
where : p = steric factor
d = :
2
= reduced mass
=
:
NA = Avogadro's Number
SURFACE TENSION
Capillary Rise: y =
2
SOLID STATE
Bragg Equation: n = 2d sin
De Broglie Equation: =
=
Heisenberg's Uncertainty Principle: xp
4
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SCHRODINGER WAVE EQUATION
- 2
2(2
2 +
2
2 +
2
2) + V(x,y,z) = E
PARTICLE-IN-A-BOX
Particle in a one-dimensional box:
= 2
sin
E = 22
82
Particle is a three-dimensional box: nonchalant
(x,y,w) = 2
sin
][
2
][
2
]
E(x,y,z) = 2
8 (2
+
2
+
2
)
=( + 1)2
2
HARMONIC OSCILLATOR
Ev = (v + 1
2) hv
where: v = 1
2
RIGID ROTOR
2
2 2
2+2
2+ 2
2
2
4 0 =
HYDROGEN AND HYDROGEN-LIKE IONS
Schrdinger Wave Equation:
= 42
2(40)222
= ()()()
