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52 Basic physical chemistry

rate coefficients for (i) and k2r and k2• are the corresponding quantities
for (ii), we have

and,

i
Solving each of these equations for the n termediate N03(g), equating
the results and rearranging leads to
k1r k2r [Ni0s(g)] [Oz(g)]
k1• k2• [N02(g)]2[0 (g)]
3
But, the right-hand side of the last expression is the equilibrium con­
stant Kc for the forward reaction of the overall equation. Hence,

k rk2r
1
K =
c
k1.k2r
3.4 Collision theory of gaseous reactions
In this section we consider the factors that determine the magnitude of
the rate coefficient for a gaseous bimolecular reaction.
If the effective circular cross section of the molecule for collisions
has diameter p, two molecules will collide if their centers come within
a distance p of each other. If we now imagine that all of the molecules
except one (which we will call X) shrink to points, X will still collide
with the other molecules when they come within a distance p of each
other provided that we artificially expand the diameter of X to 2p.
Now, in unit time the expanded molecule X, which has an artificial
2
radius p, will sweep out a volume np c, where c is the average speed
of a molecule. Therefore, if there are n "point" molecules per unit
volume, and we assume that all of these molecules are stationary,
the number of molecules with which X will collide i n unit time will
2
be 1Tp cn . 3
If we now consider molecules A (in concentration nA) colliding with
molecules B (in concentration n8), the number of collisions per second
that one A molecule makes with the B molecules is 1Tp2cn • This
8
expression gives the maximum chemical reaction rate, assuming that
each collision between A and B molecules results in a reaction.
Exercise 3 .5 . Calculate the approximate maximum rate for a gaseous