Page 85 - Introduction to chemical reaction engineering and kinetics

4.2 Gas-Phase Reactions: Choice of Concentration Units 67

SOLUTION

Assume ideal-gas behavior (T, V constant). Then,

P V = n,RT a n d pAV = nART

At any instant,
nt = nA + ng + nc + nD

dn, = dnA + dn, + dn, + dn,
= dil, + dn, - (1/2) dn, - dn,
= (l/2)d?ZA

att = 0 dnro = (1/2) dnAo

Thus, from the equation of state and stoichiometry

and (dp,/dt), = 2(dP/dt), = 2(-7.2) = -14.4 kPa rnin-’

4.2.2 Rate and Rate Constant in Terms of Partial Pressure

If pi is used in the rate law instead of ci, there are two ways of interpreting ri and hence
ki. In the first of these, the definition of ri given in equation 1.4-2 is retained, and in the
second, the definition is in terms of rate of change of pi. Care must be taken to identify
which one is being used in a particular case. The first is relatively uncommon, and the
second is limited to constant-density situations. The consequences of these two ways
are explored further in this and the next section, first for the rate constant, and second
for the Arrhenius parameters.

4.2.2.1 Rate Defined by Equation 1.4-2
The first method of interpreting rate of reaction in terms of partial pressure uses the
verbal definition given by equation 1.4-2 for ri. By analogy with equation 4.1-3, we write
the rate law (for a reactant i) as

(4.2-4)
i = l

where the additional subscript in k;p denotes a partial-pressure basis, and the prime dis-
tinguishes it from a similar but more common form in the next section. From equations
4.1-3 and -5, and 4.2-3a and -4, it follows that ki and kip are related by

ki = (RT)“k&, (4.2-5)

The units of kjp are (concentration)(pressure)-“(time)-’.