Final Exam Equation Sheet
𝑛𝑛 =
𝑚𝑚
𝑀𝑀
−1
𝑤𝑤𝑤𝑤𝑤𝑤
∗ 100%
𝑤𝑤𝑤𝑤𝑤𝑤 + 𝑤𝑤𝑤𝑤𝑤𝑤
𝑊𝑊𝐴𝐴 =
𝑋𝑋 % =
𝑦𝑦
∗ 100%
𝑥𝑥 + 𝑦𝑦
𝑋𝑋𝐴𝐴 =
𝑛𝑛𝐴𝐴
∗ 100%
𝑛𝑛𝐴𝐴 + 𝑛𝑛𝐵𝐵
∆𝐺𝐺 ≅
∆𝐻𝐻
(𝑇𝑇 − 𝑇𝑇)
𝑇𝑇𝑚𝑚 𝑚𝑚
𝑊𝑊𝑓𝑓 = −∆𝐺𝐺
𝑣𝑣 ≈
𝑑𝑑 −𝑞𝑞 ∆𝐻𝐻(𝑇𝑇𝑚𝑚 − 𝑇𝑇)
𝑒𝑒 𝑘𝑘𝑘𝑘
6ℎ
𝑇𝑇𝑚𝑚
2𝛾𝛾𝑆𝑆𝑆𝑆 𝑇𝑇𝑚𝑚
|∆𝐻𝐻|(𝑇𝑇𝑚𝑚 − 𝑇𝑇)
𝑟𝑟 ∗ =
𝑑𝑑 −𝑞𝑞 ∆𝐻𝐻(𝑇𝑇𝑒𝑒 − 𝑇𝑇)
𝑣𝑣 ≈
𝑒𝑒 𝑘𝑘𝑘𝑘
6ℎ
𝑇𝑇𝑒𝑒
𝜎𝜎𝑓𝑓 =
𝐾𝐾𝐼𝐼𝐼𝐼
𝑌𝑌√𝜋𝜋𝜋𝜋
𝜎𝜎 𝑚𝑚
𝑃𝑃𝑠𝑠 (𝑉𝑉0 ) = 𝑒𝑒𝑒𝑒𝑒𝑒 �− � � �
𝜎𝜎0
𝜎𝜎 𝑚𝑚
𝑙𝑙𝑙𝑙𝑃𝑃𝑠𝑠 (𝑉𝑉0 ) = − � �
𝜎𝜎0
𝐸𝐸 =
𝜎𝜎
𝜀𝜀
Standard Numbers:
𝑁𝑁𝑎𝑎 = 6.022 × 1023
𝑅𝑅 = 8.3145 Jmol−1 K −1
𝑓𝑓 (1 − 𝑓𝑓)
𝐸𝐸 = � +
�
𝐸𝐸1
𝐸𝐸2
𝐸𝐸𝑐𝑐∥ = 𝑣𝑣𝑓𝑓 𝐸𝐸𝑓𝑓 + �1 − 𝑣𝑣𝑓𝑓 �𝐸𝐸𝑚𝑚
𝐸𝐸𝑐𝑐⊥ =
𝐸𝐸𝑓𝑓 𝐸𝐸𝑚𝑚
�1 − 𝑣𝑣𝑓𝑓 �𝐸𝐸𝑓𝑓 + 𝑣𝑣𝑓𝑓 𝐸𝐸𝑚𝑚
𝜎𝜎𝑇𝑇𝑇𝑇 = 𝑣𝑣𝑓𝑓 𝜎𝜎𝑣𝑣 + �1 − 𝑣𝑣𝑓𝑓 �𝜎𝜎𝑦𝑦𝑚𝑚
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 𝑂𝑂2 + 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 ⇒ 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂
∆𝑚𝑚 = 𝐾𝐾𝐿𝐿 𝑡𝑡
(∆𝑚𝑚)2 = 𝐾𝐾𝑝𝑝 𝑡𝑡
−𝑄𝑄𝐿𝐿
𝐾𝐾𝐿𝐿 = 𝐴𝐴𝐿𝐿 𝑒𝑒 𝑅𝑅𝑅𝑅
𝐾𝐾𝑃𝑃 = 𝐴𝐴𝑃𝑃 𝑒𝑒
𝑑𝑑𝑑𝑑
𝐶𝐶
∝ 𝐷𝐷
𝑑𝑑𝑑𝑑
𝑥𝑥
−𝑄𝑄𝑃𝑃
𝑅𝑅𝑅𝑅
𝑥𝑥 2 = 𝐾𝐾𝑝𝑝 𝑡𝑡
𝐾𝐾𝑐𝑐 =
𝐾𝐾 ′ =
[𝐶𝐶]𝑐𝑐 [𝐷𝐷]𝑑𝑑
[𝐴𝐴]𝑎𝑎 [𝐵𝐵]𝑏𝑏
1
= 𝐾𝐾 −1
𝐾𝐾
𝑝𝑝𝐾𝐾𝑤𝑤 = 𝑝𝑝𝑝𝑝 + 𝑝𝑝𝑝𝑝𝑝𝑝 = 14
𝑝𝑝𝑝𝑝 = −𝑙𝑙𝑙𝑙𝑙𝑙(𝐻𝐻3 𝑂𝑂+ )
𝑝𝑝𝑝𝑝 = −log (𝑋𝑋)
H
Lithium
6.941
K
Fr
Francium
223.020
87
Cesium
132.905
Cs
55
Rubidium
85.468
Rb
37
Potassium
39.098
19
Sodium
22.990
Na
Li
Hydrogen
1.008
11
3
1
1
IA
1A
Y
Actinide
Series
Ti
4
IVB
4B
Zr
Actinium
227.028
Ac
89
Lanthanum
138.905
Thorium
232.038
Th
W
Pr
7
VIIB
7B
Protactinium
231.036
Pa
91
U
Uranium
238.029
92
Neptunium
237.048
Np
93
Promethium
144.913
Ir
Ni
Pt
Ds
110
Platinum
195.085
78
Palladium
106.42
Pd
46
Nickel
58.693
28
10
Rg
111
Gold
196.967
Au
79
Silver
107.868
Ag
47
Copper
63.546
Cu
29
11
IB
1B
Cn
112
Mercury
200.592
Hg
80
Cadmium
112.414
Cd
48
Zinc
65.38
Zn
30
12
IIB
2B
Plutonium
244.064
Americium
243.061
Curium
247.070
96
Gadolinium
157.25
Gd
64
Am Cm
95
Europium
151.964
Eu
63
Berkelium
247.070
Bk
97
Terbium
158.925
Tb
65
In
Tl
Cf
Californium
251.080
98
Dysprosium
162.500
Einsteinium
[254]
Es
99
Holmium
164.930
I
At
Fermium
257.095
Fm
Mendelevium
258.1
Md
101
Thulium
168.934
Tm
69
Nobelium
259.101
No
102
Ytterbium
173.055
Yb
70
© 2014 Todd Helmenstine
sciencenotes.org
Lawrencium
[262]
Lr
103
Lutetium
174.967
Lu
71
Ununoctium
unknown
118
Radon
222.018
Rn
86
Xenon
131.294
Xe
54
Krypton
83.798
Kr
36
Argon
39.948
Ar
18
Neon
20.180
Ne
Helium
4.003
He
10
2
Uus Uuo
117
Astatine
209.987
85
Iodine
126.904
53
Bromine
79.904
Br
35
Chlorine
35.453
Cl
F
Fluorine
18.998
17
9
17
VIIA
7A
Ununpentium Livermorium Ununseptium
unknown
[298]
unknown
116
Polonium
[208.982]
Po
84
Tellurium
127.6
Te
52
Selenium
78.971
Se
34
Sulfur
32.066
S
O
Oxygen
15.999
16
8
16
VIA
6A
Uup Lv
115
Er
100
Bi
Bismuth
208.980
83
Antimony
121.760
Sb
51
Arsenic
74.922
As
33
Phosphorus
30.974
P
N
15
VA
5A
Nitrogen
14.007
15
7
Erbium
167.259
68
Flerovium
[289]
Fl
114
Lead
207.2
Pb
82
Tin
118.711
Sn
50
Germanium
72.631
Ge
32
Silicon
28.086
Si
C
14
IVA
4A
Carbon
12.011
14
6
Ho
67
Ununtrium
unknown
Uut
113
Thallium
204.383
81
Indium
114.818
49
Gallium
69.723
Ga
31
Aluminum
26.982
Al
B
13
IIIA
3A
Boron
10.811
13
5
Dy
66
Meitnerium Darmstadtium Roentgenium Copernicium
[268]
[269]
[272]
[277]
Mt
109
Iridium
192.217
77
Rhodium
102.906
Rh
45
Cobalt
58.933
Pu
94
9
VIII
8
Co
27
Samarium
150.36
62
Hassium
[269]
Hs
108
Osmium
190.23
Os
76
Ruthenium
101.07
Ru
44
Iron
55.845
Fe
26
8
Pm Sm
61
Bohrium
[264]
Bh
107
Rhenium
186.207
Re
75
Technetium
98.907
Tc
43
Manganese
54.938
Mn
25
Nd
60
Seaborgium
[266]
Sg
106
Tungsten
183.84
74
Molybdenum
95.95
Mo
42
Chromium
51.996
Cr
24
6
VIB
6B
Praseodymium Neodymium
140.908
144.243
59
Dubnium
[262]
Db
105
Tantalum
180.948
Ta
73
Niobium
92.906
Nb
41
Cerium
140.116
90
V
5
VB
5B
Vanadium
50.942
23
Ce
58
Rutherfordium
[261]
Rf
104
Hafnium
178.49
Hf
72
Zirconium
91.224
40
Titanium
47.867
22
La
57
89-103
57-71
Yttrium
88.906
39
Scandium
44.956
Sc
21
3
IIIB
3B
Lanthanide
Series
Radium
226.025
Ra
88
Barium
137.328
Ba
56
Strontium
87.62
Sr
38
Calcium
40.078
Ca
20
Magnesium
24.305
Mg
Beryllium
9.012
Be
12
4
2
IIA
2A
Periodic Table of the Elements
18
VIIIA
8A