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Cheat Sheet for Final
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Cheat Sheet for Final
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CHEAT SHEET FOR FINAL. Statistical Mechanics and Chemical Dynamics ( Chem 130C). (Dated: June 6, 2008). Boltzmann Constant: kB = 1.381 × 10. −23.
CHEAT SHEET FOR FINAL
Statistical Mechanics and Chemical Dynamics (Chem 130C) (Dated: June 6, 2008)
Boltzmann Constant: kB = 1.381 × 10−23 J · K−1 ; Avogadro Constant: NA = 6.022 × 1023 mol−1 ; Planck Constant: h = 6.626 × 10−34 J · s; Speed of light in vacuum: c = 2.998 × 108 m · s−1 ; Standard Atmosphere: 1 atm = 1.013 × 105 Pa; Atomic Weights: H 1.008; He 4.00; Cl 35.45; Ar 39.95; Br 79.90; Kr 83.80. Z ∞ −∞
e
−ax2
s
dx =
π ; a
Z
N ∂q ∆U = U − U (0) = − q ∂β
!
= N kT
2
hν ; k
θR =
∂ ln q ∂T
!
; V
∂ ln q p = kT ∂V
A = ∆U − T S;
H = ∆U + pV ;
1 , when x < 1; 1−x
xi =
i=0
V
U − U (0) S= + N k ln q; T
θV =
∞ X
1 dx = ln(ax+b)+C; ax + b a
!
; T
G = H − T S;
hcB ; k
B=
h ¯ ; 4πcI
n2 h2 En = , n = 1, 2, 3 · · · for one-dimentional particle in a box; 8mL2 1 hω, n = 0, 1, 2 · · · for one-dimentional harmonic oscillator; En = (n + )¯ 2 EJ = hcBJ(J +1), J = 0, 1, 2 · · · for rigid rotor. Degeneracy for J-th level: 2J + 1; Within 3-D Maxwell-Boltzmann distribution: c¯ =
v u u 8RT t
πM
;
c∗ =
v u u 2RT t
M
;
cRM S =
v u u 3RT t
M
;
λ=
c¯ kT =√ . z 2σp
×
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