Physical Chem Final

Weight (W)
W=N!/(n0! n1! n2!)
Most probable distribution
d(lnW) = (dlnW/dni)dni
meaning of q
number of thermally accessible states
average energy E
= E/N = -1/q dq/d?
Internal Energy (U)
N/q dq/d? (3/2nRT for ideal gases)
molar entropy
S/mol = Rlnq + ?U/T
for two energy levels, q=
(n0 and n1)
q=e^(0/KbT) + e^(-E1/KbT)
for equally spaced ladder of energy levels, q=
q= 1/(1-e^(-?E)
for particle in 1-d box, q=
a/? = [(2?m/h^2?)^1/2] x a
for particle in 3-d box, q=
v/?^3 = [(2?m/h^2?)^3/2] x a^3
for translation partition function, q=
qt=v/?^3
Boltzman entropy
S=KblnW
x

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