Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

OTHER REACTION ORDERS 151

which is our solution for the Laplace transform of both sides of the rate equation. Now

take the inverse Laplace transform. The Laplace transformb(s) inverse transforms,

of course, toB(t) and the inverse transform of

1

(s+k 1 )

1

(s+k 2 )

is

1

(s+k 1 )

1

(s+k 2 )

inv transform

−→

1

k 1 −k 2

(

e−k^1 t−e−k^2 t

)

so

B(t)=k 1 A 0

1

k 1 −k 2

(

e−k^1 t−e−k^2 t

)

10.3.3 Reversible Reactions

No reaction goes to completion. Reactions we call “complete” are those in which

the concentration of, for example, reactant A is negligible or not detectable in the

reaction

A→B

This is the case when the standard free energy of A is much larger than that of B, so

that the reaction is accompanied by a significant decrease in free energy and leads to

B more stable than A.

In many cases, something closer to a free energy balance exists. We write the

reaction as an equilibrium characterized by an equilibrium constantKeq(Chapter 7).

Kinetic rate constantskfandkbfor forward and back reactions compete to establish

the equilibrium balance:

A

kf

←→

kb

B

kf

kb

=Keq=

B

A

When A and B are mixed in concentrationsAandBthat are not the equilibrium

concentrations, either the forward or the back reaction is faster than the other and the

system is displaced so as to approach equilibrium.

The rate of depletion of A,

(

−

dA

dt

)

obs

=kfA−kbB

is smaller than the rate that would be found if the reaction went to completion or if

we had some mechanism for removal of B immediately as it is formed. The rate of