Page 86 - Introduction to chemical reaction engineering and kinetics

68 Chapter 4: Development of the Rate Law for a Simple System

4.2.2.2 Rate Defined by - dpildt
Alternatively, we may redefine the rate of reaction in terms of the rate of change of
the partial pressure of a substance. If density is constant, this is analogous to the use
of -dcJdt (equation 2.2-lo), and hence is restricted to this case, usually for a constant-
volume BR.
In this case. we write the rate law as

(-ri,) = -dp,ldt = ki, ~ pgf (constant density) (4.2-6)
i = l

where rip is in units of (pressure)(time)-l. From equations 2.2-10 and 4.2-3a, and the
first part of equation 4.2-3, rip is related to ri by

‘ip - - (constant density) (4.2-7)
-= dpi _ RT
ri dci

regardless of the order of reaction.
From equations 4.1-2 and -5, and 4.2-3a, -6, and -7, ki and kip are related by

The units of kip are (pressure)l-n(time)-l.

For the gas-phase decomposition of acetaldehyde (A, CHsCHO) to methane and carbon
monoxide, if the rate constant kA at 791 K is 0.335 L mol-‘s-t,

(a) What is the order of reaction, and hence the form of the rate law?
(b) What is the value of kAp, in Pa-’ s-l for the reaction carried out in a constant-
,
volume BR?

SOLUTION
(a) Since, from equations 4.1-3 and -5, the units of kA are (concentration)l-n(time)-‘,
1 - rz = - 1, and rz = 2; that is, the reaction is second-order, and the rate law is of
the form (-rA) = kAci.
(b) From equation 4.2-8,

kAp = k,(RT) * -’ = 0.335/8.314(1000)791 = 5.09 X lo-* Pa-l s-l

4.2.3 Arrhenius Parameters in Terms of Partial Pressure

4.2.3.1 Rate Dejined by Equation 1.4-2
We apply the definition of the characteristic energy in equation 3.1-6 to both ki and k:P
in equation 4.2-5 to relate EA, corresponding to ki, and E,&, corresponding to kf,. From