Cheat Sheet for Final

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