Energy

Chemical reactions proceed if the products of the reaction have lower free energies than do the reactants. What does the term free energy mean? Free Energy is defined in the field of thermodynamics. Thermodynamics is simply the formulation of some rules and definitions that can be extended to non-ideal states.

Thermodynamics defines two terms:

Enthalpy ( H )

2. Entropy ( S )

It also relates these terms to each other in the definition of free energy. In this course we will greatly simplify. For a biological system define enthalpy ( H ) as the internal energy of a system. More simply enthalpy is equal to the heat of a system.

Define entropy (S) as:

S = klnW

Entropy is equal to a constant times the natural log of the number of ways something can be arranged. This equates to a measurement of the randomness of a system. The entropy of the universe is increasing. Any localized decrease in entropy must be balanced by a greater increase in the total entropy of the universe.

Define Gibbís Free Energy:

G = H - TS
DG = DH - TDS

A careful analysis of the meaning of the terms utilized to define G yields the fact that changes in G may be equated to the useful work that may be obtained from a system. When proper substitutions are made:

D G = - RT ln Keq

If a mole of A plus a mole of B equals 0.999 moles of C at equilibrium, Then:

A + B = C

Keq = 9.99 x 105

If the reaction occurred at 25 C = 298 K, then:

D G = -1.987 x 298 x lnKeq
ln 9.99 x 105 = 13.8
D G = -1.987 ( 298 ) ( 13.8 )
D G = 8.2 Kcal/mole

Reaction Rates

Define Q10 = Ratio of reaction rates for a 10 C change

The normal range of Q10 is usually from 2 to 5.

Arrhenius Equation:

k = Ae-Ea/RT

A plot of ln K versus yields:

If the equation is evaluated between k1 and k2 at T1 and T2:

Can solve for Ea. In practice, any property proportional to k can be used. Chemical reactions occur when collisions between molecules of high enough energy occur.

k = PZe-Ea/RT

Where:

P = probability of a reaction occurring

Z = number of collisions per unit volume

e-Ea/RT = fraction of total number of molecules with an energy of Ea or greater.

Assume that P is independent of temperature and that Z is directly proportional to temperature, then:

For a 10 C change, D Z = 3.7%. This can be ignored. Then:

Where:

n1 = number of molecules with an energy of Ea or greater

n = the total number of molecules

If Ea = 12,000 cal/mole and T = 27 C, Then:

If the temperature is increased to 37 C, Then:

The ratio of the two rates is

Thus for a reaction with an energy of activation of 12,500 cal/mole if the temperature is increased 10 C the rate of the reaction will increase by 1.97 times or approximately double.