Molecular Partition Function

q =

sum over levels

q = Σ

q = Σ g(i)

sum over levels

q = Σ g(i) exp(

sum over levels

q = Σ g(i) exp(-

sum over levels

q = Σ g(i) exp(-β

sum over levels

Boltzmann Distribution

Pi =

not in terms of q, over levels

Pi = g(i)

not in terms of q, over levels

Pi = g(i) exp(

not in terms of q, over levels

Pi = g(i) exp(-

not in terms of q, over levels

Pi = g(i) exp(-β

not in terms of q, over levels

Pi = g(i) exp(-βε(i))

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) /

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) / Σ g(i)

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) / Σ

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) / Σ g(i) exp(

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) / Σ g(i) exp(-

not in terms of q, over levels

Pi = g(i) exp(-βε(i)) / Σ g(i) exp(-β

not in terms of q, over levels

Translational Partition Function

q(tr) =

q(tr) = V

q(tr) = V /

q(tr) = V / Λ

Electronic Partition Function

q(elec) =

kT small compared to Δε

q(elec) = g(0) exp(

kT small compared to Δε

q(elec) = g(0) exp(

kT small compared to Δε

q(elec) = g(0) exp(-

kT small compared to Δε

q(elec) = g(0) exp(-β

kT small compared to Δε

Vibrational Partition Function

q(vib) =

q(vib) = exp(

q(vib) = exp(-

q(vib) = exp(-(1/2)

q(vib) = exp(-(1/2)β

q(vib) = exp(-(1/2)βћ

q(vib) = exp(-(1/2)βћω)

q(vib) = exp(-(1/2)βћω) Σ

q(vib) = exp(-(1/2)βћω) Σ exp(

q(vib) = exp(-(1/2)βћω) Σ exp(-

q(vib) = exp(-(1/2)βћω) Σ exp(-β

q(vib) = exp(-(1/2)βћω) Σ exp(-βћ

q(vib) = exp(-(1/2)βћω) Σ exp(-βћω

Rotational Partition Function

q(rot) =

in terms of θ(rot)

q(rot) = Σ

in terms of θ(rot)

q(rot) = Σ (2J+1)

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(-

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(-θ(rot)

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(-θ(rot) J

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(-θ(rot) J (J+1)

in terms of θ(rot)

q(rot) = Σ (2J+1) exp(-θ(rot) J (J+1)/

in terms of θ(rot)

Where θ(rot) =

Where θ(rot) = B

Where θ(rot) = Bh

Where θ(rot) = Bhc

Where θ(rot) = Bhc/

Homonuclear diatomic: q(rot) =

Homonuclear diatomic: q(rot) = T

Homonuclear diatomic: q(rot) = T /

Homonuclear diatomic: q(rot) =T / σ

Curie's Law

Χ =

Χ = C

Χ = C /

Cononical Partition Function

Distinguishable: Q =

Distinguishable: Q = q

Distinguishable: Q = q^

Indistinguishable: Q =

Indistinguishable: Q = q

Indistinguishable: Q = q^

Indistinguishable: Q = q

Indistinguishable: Q = q /

Indistinguishable: Q = q / N

Energy:

E =

E = k

E = kT

E = kT^2

Arrhenius Free Energy

A =

A = -

A = -k

A = - kT

A = -kT ln(

Entropy S =

In terms of A

Entropy S = -

In terms of A

Therefore S =

Therefore S = k

Therefore S = kT

Therefore S =kT(dlnQ/dT)v

Therefore S =kT(dlnQ/dT)v +

Therefore S =kT(dlnQ/dT)v + k

Therefore S =kT(dlnQ/dT)v + k ln(

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