## Thermodynamics

Laws of Thermodynamics

1st law:

Energy is conserved. The total amount of energy in the universe is constant.

The universe can be thought of as simply a system we are interested in and its surroundings. For such a system,

DE (internal energy) = Q (heat) + W (work)
DE = Q + W

E is the internal energy of a system. It is the total of all the possible kinds of energy in the system. E cannot be measured, but DE can.
Q is positive if heat is added to a system from the surroundings and negative if the system gives up heat to its surroundings.
W is positive if work is done on the system by the surroundings (e.g. compressing gas in a container) and negative if a system does work on the surroundings (e.g. if a compressed gas is allowed to expand).

Enthalpy

Under the condition of constant pressure, Q = DH, the change in enthalpy. Most reactions occur under the essentially constant pressure of 1 atm.

If DH is negative, heat is generated and the reaction is said to be exothermic.

If DH is positive, heat is absorbed from the surroundings and the reaction is said to be endothermic.

2nd law:

Any spontaneous change that occurs must be accompanied by an increase in the entropy of the universe.

3rd law:

The entropy of a pure crystal at 0 K is zero. (Thus the absolute amount of entropy of a system is measurable.)

Gibb's Free Energy

Whether a chemical reaction is spontaneous (i.e. the formation of the products is favored) or not depends on two driving forces: DH and DS. Spontaneous reactions tend to occur when potential energy is released as heat through the breaking and formation of bonds (DH <0), or when the system becomes more disordered (DS >0), or both.

DG incorporates both DH and DS,as show below.

DG = DH - TDS

where G is Gibb's free energy (so named because it is the energy that is free to do work),
H is enthalpy (heat produced or consumed under conditions of constant pressure),
S is entropy (degree of disorder), and
T is temperature in K.

Why is DS multiplied by T? The higher the temperature, the greater the kinetic energy of the molecules and, thus, the greater the tendency for the system to go to a state of increased disorder (an analogy is the increased disorder an earthquake creates).

If DG <0, the forward reaction is spontaneous.

However, even if a reaction is spontaneous, if the activation energy is too high it will not proceed. Such a reaction is said to be under kinetic control and may require the use of a catalyst or energy input such as heat (which would also alter the equilibrium position).

If a reaction occurs as DG predicts, it is said to be under thermodynamic control.

Relationship between Gibb's Free Energy and Keq and E (cell potential for a reaction)

An indication of the equilibrium position of a reaction is provided by each of DG, Keq, and E. DG looks at the thermodynamics of a reaction, while E looks at the relative tendencies of reactants to be oxidized or reduced. Thus they are related to each other.

Keq = eDG°/-RT
Thus if DG is large and negative, Keq will be large.

And, Keq = enFE°/RT
If E is large and positive, Keq will be large.

Also, DG° = -nFE°
Thus, if E is positive, DG will be negative.

(Note: the symbol ° denotes that standard states exist, i.e. the concentration of each reactant and product is 1 M if in solution, and 0.1 MPa if gaseous.)

State Functions
A state function is a quantity whose value depends only on the state of the system and not on its history. X is a state function only if DX does not depend on the path used to go from the initial state to the final state of the system. V, G, P, H, E, S, and T are state functions.

Hess's law is a consequence of enthalpy being a state function. It states that DH of a reaction is the same regardless of whether the reaction occurs in a single step or in several steps.

LeChatelier's principle

When a system at equilibrium is subjected to a stress, it will shift in a direction that minimizes the effect of this stress.

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