Page 150 - Elements of Chemical Reaction Engineering 3rd Edition

122 Rate Laws and Stoichiometry Chap. 3

P3-2OC For families of reactions, the Polanyi-Semenov equation can be used to esti-
mate activation energies from the heats of reaction, AH, according to the
equation

E = C - ct(-AHR) (P3-20.1)
where 01 and C are constants. For exothermic reactions ct = -0.25 and C =
48 kJ/mol, while for endothermic reactions ct = -0.75 and C = 48 kJ/mol.
However, these values may vary somewhat from reaction family to reaction
family [K. J. Laidler, Theories of Chemical Reaction Rates (New York, R. E.
Krieger, 1979), p. 381. (Also see Appendix J)
(a) Why is this a reasonable correlation?
Consider the following family of reactions:

E -AHR
(kcallmol) (kcaVmo1)
H + RBr --+ HBr + R 6.8 17.5
H + R'Br 4 HBr t R' 6.0 20.0

(b) Estimate the activation energy for the reaction
CH3. + RBr --+ CH3Br + R.

which has an exothermic heat of reaction of 6 kcal/mol (Le., AH, = -6
kcai /mol).
P3-21B The gas-phase reaction between chlorine and methane to form carbon tetra-
chloride and hydrochloric acid is tb be carried out at 75°C and at 950 kPa in
a continuous-flow reactor. The vapor pressure of carbon tetrachloride at 75°C
is approximately 95 kPa. Set up a stoichiometric table for this reaction with
phase change. Calculate the conversion of methane at which condensation
begins. Plot the concentrations and molar flow rates of each species as well as
the total molar flow rate as a function of conversion for a stoichiometric feed.
The volumetric flow rate is 0.4 dm3/s.
P3-22B The reaction
CzH,(g) + 2Brz(g) --+ C,H4Brz(g,C) + 2HBrk)
is to be carried out at 200°C and 2500 @a. The vapor pressure of 1,Zdibro-
moethane at 200°C is 506.5 Wa. With k = 0.01 dm6/mo12.min. The reaction
is first order in C,HS and second order in Br,. Calculate the conversion of
ethane at which condensation begins. Plot the concentration and molar flow
rates of cach species as well as the total molar flow rate as a function of con-
version for a stoichiometric feed. The volumetric flow rate is 0.5 dm3/s. (Ans.:
Xcond = 0.609.) Are there a set of feed conditions (e.g., equal molar) such that
the concentration of C2H6(g) will be constant after condensation begins?
P3-23B Chemical vapor deposition (CVD) is a process used in the microelectronics
industry to deposit thin films of constant thickness on silicon wafers. This
process is of particular importance in the manufacturing of very large scale
integrated circuits. One of the common coatings is Si,N,, which is produced
according to the reaction

3SiH4(g) + 4NH3(g) __j Si3N4(s) + 12H2(g)