CHEM 102: General Chemistry II
An introduction to the principles of chemistry from a molecular perspective
Intro.1 of 2
General Sequence
1.
2.
3.
4.
5.
6.
7.
8.
Chemical Kinetics (Book Chapter 14)
Thermodynamics (Book Chapter 18)
Chemical Equilibrium (Book Chapter 15)
Acids and Bases (Book Chapter 16)
Aqueous Ionic Equilibrium (Book Chapter 17)
Electrochemistry (Book Chapter 19)
Radiochemistry (Book Chapter 20)
Coordination Compounds (Book Chapter 22)
(time permitting)
Intro.2 of 2
Overview of basic SI units
SI units are an international standard (MKS; 1960)
Quantity
length
mass
time
current
temperature
Unit
meter
kilogram
second
ampere
kelvin
Symbol
m
kg
s
A
K
Luminous
intensity
Amount of
substance
candela
cd
mole
mol
Definition
Speed of light
Reference weight
Cs radiative life
Reference current
0 K is the absolute zero
273.16 K water triple pt.
Black-body reference
Avogadro's constant
NA = 6.022x1023 mol-1
Derived SI units
Quantity
force
energy
electric charge
pressure
magnetic field
frequency
power
voltage
resistance
conductivity
Unit
newton
joule
coulomb
pascal
tesla
hertz
watt
volt
ohm
siemens
Symbol
N
J
C
Pa
T
Hz
W
V
W
S
Definition
1 N = 1 kg m s-2
1 J = 1 kg m2 s-2
1 C = 1 As
1 Pa = 1 N m-2
1 T = 1 kg s-2 A-1
1 Hz = 1 s-1
1 W = 1 J s-1
1 V = 1 W A-1
1 W = V A-1
1 S = 1 W-1
These are compatible with the basic SI units
Non­SI units and unit conversions
Non-SI unit
ångström (Å)
inch (in)
foot (ft)
mile (mi)
AMU
eV
cal
torr (Hgmm)
atmospheres (atm)
bar
psi
gauss (G)
SI unit
Conversion factor
meter (m)
1 Å = 10-10 m
meter (m)
1 in = 2.54 cm = 0.0254 m
meter (m)
1 ft = 12 in = 0.3048 m
meter (m)
1 mi = 5280 ft = 1609.344 m
kilogram (kg) 1 AMU = 1.66054 x 10-27 kg
joule (J)
1 eV = 1.602177 x 10-19 J
joule (J)
1 cal = 4.1868 J
pascal (Pa) 1 torr = 1.33322 x 102 Pa
pascal (Pa) 1 atm = 1.01325 x 105 Pa
pascal (Pa) 1 bar = 105 Pa
pascal (Pa) 1 psi = 6.8948 x 103 Pa
tesla (T)
1 G = 10-4 T
These are not compatible with SI units and require conversion.
Common conversion factors
Spectroscopic units
Hz
1
2.99792458x1010
3.289842x1015
2.417988x1014
cm-1
3.335641x10-11
1
1.097373x105
8.065541x103
Ry
3.039660x10-16
9.112671x10-6
1
7.349862x10-2
eV
4.135669x10-15
1.239842x10-4
1.360570x101
1
Energy units
K
1
3.0325x1026
7.24292x1022
1.16045x104
kcal
3.298x10-27
1
2.388x10-4
3.827x10-23
J
1.38066x10-23
4.1868x103
1
1.602177x10-19
eV
8.61739x10-5
2.6132x1022
6.241506x1018
1
Common conversion factors
Pressure
Pa
1
105
1.333x102
1.013x105
bar
10-5
1
1.333x10-3
1.013
torr
7.5006x10-3
7.5006x102
1
760
atm
9.869x10-6
9.869x10-1
1.316x10-3
1
Example. How many pascals is ten atm?
Solution. 1 atm = 1.013x105 Pa (see above) and
therefore 10 atm = 1.013x106 Pa.
Scientific notation of numbers
Often numerical values can be very small or very large.
For example:
1 g of H has 602,200,000,000,000,000,000,000 atoms.
Thus each hydrogen atom has only a mass of
0.00000000000000000000000166 g.
It is convenient to express these in the scientific notation:
6.022x1023 and 1.66x10-24. Most calculators use this notation
as 6.022E23 and 1.66E-24.
Special mathematical functions
Trigonometric functions: sin(x), cos(x), tan(x)
and their inverses: sin-1(x), cos-1(x), tan-1(x)
or: asin(x), acos(x), atan(x) (different notation).
Note: x is usually in radians rather than degrees
(360 degrees = 2p in radians or 180 degrees = p)
Pythagoras' theorem: a2 + b2 = c2
c
a
a
b
sin(a) = a/c, cos(a) = b/c, tan(a) = a/b
sin-1(a/c) = a, cos-1(b/c) = a, tan-1(a/b) = a
Special mathematical functions
Common logarithm (10-base):
log(1) = 0
log(10) = 1
log(100) = 2
100 = 1
101 = 10
102 = 100
etc.
Natural logarithm (e-base; e ≈ 2.7182818....):
ln(1) = 0
e0 = 1
ln(2.7182818...) = 1
e1 = 2.7182818...
ln(7.3890560...) = 2
e2 = 7.3890560... etc.
Rules for logarithms (both log and ln):
log(AB) = log(A) + log(B), log(A/B) = log(A) - log(B)
log(AB) = Blog(A), etc. for more see a math table book.
Conversion: ln(x) = ln(10log(x)) = ln(10)log(x)≈ 2.303log(x)
Quadratic and cubic equations
ax + bx + c = 0:
2
−b±√ b −4 ac
2a
2
(two roots)
x3 + a1x2 + a2x + a3 = 0:
3 a2 −a21
Q=
9
9 a1 a2 −27 a3 −2 a31
R=
54
√
3
S= R + √ Q3+R 2
√
3
T= R−√ Q3 +R2
Solutions in terms of Q, R, S and T are (three roots):
1
x1 =S +T − a 1
3
1
1 1
x2 =− (S+T)− a1 + i √3(S−T)
2
3 2
1
1 1
x3 =− (S+T)− a1 − i √3(S−T)
2
3 2
Note: imaginary unit i
Differentiation and integration
Review differentiation and integration rules.
y
y
x
x
Derivative:
- rate of change
- tangent line
lower
limit
upper
limit
Integral (definite & indefinite):
- area, summation
- “anti-derivative”