Equation for Entropy in Statistics

S = k ln(W)

Change of state of Internal Energy

∆U = q + w = q - w*

Ideal Gas Equation

pV = nRT

Change of Universal Entropy due to a Process in a System

∆S_{Univ} = ∆S_{sys} - q_{sys/T}

Entropy Thermodynamically

dS = ∂q_{rev} / T = dH/T

Definition of C_{V}

C_{V} = ∂U/∂T

Definition of C_{P}

C_{P} = ∂H/∂T

Relationship between S and G

∂G/∂T = -S

Gibbs - Helmholtz Equation

∂/∂T ( G/T ) = - H / T^{2}

Chemical Potential, µ

µ = µº + RT ln(a)

activity approximated by p/pº or c/cº, or 1 for solids, liquids

∆_{r}G in terms of Chemical Potentials

∆_{r}G = ∑_{a} v_{a} µ_{a}

∆_{r}Gº = ∑_{a} v_{a} µº_{a}

Relationship between Equilibrium Constant and G

∆_{r}Gº = -RT lnK

can be derived from G in terms of µ and definition of K

Relationship between G and Cell Potential

∆_{r}G_{cell} = -nFE

Relationship between S and Cell Potential

∆_{r}S = nF(∂E/∂T)

Simple Rate Constant equation

k = A e^{- Ea/RT}

Arrhenius Constant for Simple Rate Constant

A = σ c_{rel} N_{A}

Collision rate - simple theory

Z = C_{A} C_{B} c_{rel} σ

Relative mean speed

c_{rel} = √(8k_{B}T / πµ)

Collision Area, σ

σ = π(r_{A} + r_{B})^{2}

Trick for Michaelis-Menton Enzyme Kinetics

[E]_{0} = [E] + [ES]

[E]_{0} is therefore a constant