Page 207 - Essentials of physical chemistry

More Kinetics and Some Mechanisms 169

k 1 [M] [A] d[B] k 2 k 1 [M] [A]
and then ¼ rate.
We can solve this for [A*] as [A*] ¼ ¼ k 2 [A*] ¼
k 2 þ k 1 [M] dt k 2 þ k 1 [M]
Now suppose that [M] !1 meaning that there is some other gas present that is at a much greater

d[B] k 2 k 1
concentration than [A]. In that case, we see that ! [A] ¼ k 1 [A], which is what we
dt k 2
thought initially. This can happen whether M is some other gas in great abundance or whether
M ¼ A at a high concentration (pressure) of A itself. Now consider that the whole system is a low

d[B] k 1 k 2 [M]
pressure. Then we have ¼ [A] ¼ k obs [A] as the general solution, but what if
dt k 2 þ k 1 [M]
there is no [M] and the only other gas for collisions is when [M] ¼ [A]? Thus, at relatively low
pressure and only A present we have:

d[B] k 1 k 2 [A] 2 2
’ k 1 [A] ,
dt k 2 þ k 1 [A]
¼
assuming k 1 k 2 . Thus, the reaction will appear to be first order at high pressure and second order
at low pressure. We also can see that adding an inert gas such as He or Ar (not totally inert) could be
used to change the order of such a reaction depending on the pressure of the inert gas. The mathematics
of the steady-state treatment is easy here but the thought process of this type of problem involves
careful reading of the gas pressures and numerical values of the individual rate constants.

ENZYME KINETICS
Although enzymology is a specialty field in biochemical=pharmaceutical chemistry, it is so important
to all health sciences that we need to include a basic part of it in our list of ‘‘essential’’ topics in physical
chemistry. Enzymes are very special in many ways. First, they are usually large linear polypeptides
with specific sequences of amino acid ‘‘residues’’ which have the amazing ability to coil up in solution
from a single strand into a globular shape with a special ‘‘active site’’ and remain water soluble. Think
back to experiments in an organic chemistry laboratory course, how many organic reactions were
carried out in water? Then again consider that the human body is approximately 70% water and that
planet Earth is about 70% covered by water. Water is a polar solvent and most organic compounds are
not very soluble in water. We should ponder how nature enables complicated organic reactions in an
aqueous medium. The answer is that enzymes are little floating organic laboratories which can carry
out highly specific(often stereospecific) organic reactions while in an aqueous medium. This situation
is accomplished by wrapping a special catalytic arrangement of the side chains inside the polypeptide
with a hydrophobic shell, a concept formulated by Prof. Walter Kauzmann in Figure 8.5. A crude
analogy would be an oil drop in water where the oil drop includes a special active site in the interior.
Considering that enzymes have to carry around their laboratory building in water, they turn out to be
amazingly efficient and often the turnover rate for an enzymatic reaction is many thousand times faster
than the reaction would be if the reactants were refluxed in an organic chemistry pot. Finally, enzymes
can often do organic reactions in a single step which would require many, many steps using organic
synthesis techniques. One of the reasons for successful specificity and efficiency of enzymes is that
often the pocket of the active site gently assists the ‘‘substrate’’ molecule into the conformation of the
activated complex for that reaction. Enzymatic oxidation–reduction reactions often have metal atoms
in the active site, although not all enzymes have metal atoms. The fact that Copper can be either þ1or
10
9
1
2
þ2 and the small difference in the energy of Cu as (Ar)3d 4s or Cu as (Ar)4s 3d makes it ideal for
oxidation–reduction reactions. The Cu–O–Cu active site in catechol oxidase is special in an electro-
chemical sense as well as having some geometric specificity (Figure 8.6).
Previous examples have introduced the very useful concept of the ‘‘steady state’’ and that applies
here as well. In addition, the rapid forward and backward reactions in an equilibrium still apply for