Review for Chemistry 182H:

Is there a way to describe a spontaneous reaction using the 1st law of thermodynamics?
Well, as it turns out, when we try to calculate delta U (internal energy which is a state function) in the case of isothermal expansion in two volumes connected by a valve using the first law of thermodynamics (U = w +q, or dU = dw + dq) , we can add an extra step to it since a state function is path independent. So...skipping the algebra and calculus since Dr. Smith's not going to ask us to derive the whole thing all over again, we find that delta U from initial to final states = 0, which goes back to the original problem again! Interesting...isn't it?

If the first law of thermodynamics doesn't explain the spontaneous reactions, what does?
Going back to the first question, we all know that when the valve is opened between the two volumes, gas from V1 is going to rush into the vacuumed V2 spontaneously to reach the equilibrium state. Therefore, equilibrium must be the most probable state of a system. The total number of possible state is defined by the number of particles (N) in V1, and V1 is less than Vtotal. Let W(V,N) = number of arrangements that are possible for N particles to be in that fraction of volume = (Vtotal/ V1)^N. (see how chemistry is related to statistics!) The natural log of W(V,N) = N lnV, which gives a linear relationship. So...here we go... This revised probabily of the arrangement of particles is now proportional to S (entropy). The change in entropy, delta S, would be the difference between the final and the initial entropies, or N ln(Vf/Vi). When S is positive, the entropy of a system increases, and vice versa. (Another way of expressing S is S = Kb lnW = N(Kb)ln(# of orientations), because W = (# of orientations)^N.) An important thing to remember is that when polarity increases, the electrostatic interactionis between the atoms increases and favors the more orderly structures.

Other ways to write delta S:
1. delta S = C ln (Tf/Ti) <-- when heating a sample
2. delta S = nR ln (Vf/Vi) <-- when temperature is constant
3. delta S = nR ln (Pf/Pi) <-- when pressure of an ideal gas changes
4. delta S = delta H / T <-- delta H is the change in enthalpy, when temperature is constant, q is reversible, and phase changes, can also be delta Ssurr
5. delta S = delta qrev / T
6. delta Stotal = delta S(system) + delta Ssurr (surrounding) <-- cannot decrease in an isolated system; when negative, the reverse process is spontaneous;

The more electrons in a molecule, the more disordered!

Molecules with same empiral formula: ring structure is generally more stable than the non-ring structure

When delta Stotal = 0 at isothermal condition, it is at equilibrium and it would be reversible

G = H - TS or delta G = delta H - T delta S <-- Gibbs Free Energy
spontaneous when G is negative
non-spontaneous when G is positive
at equilibrium when G = 0

Gr = sum of Gf (products) - sum of Gf (reactants)