Page 333 - Advanced thermodynamics for engineers
P. 333
322 CHAPTER 14 CHEMICAL KINETICS
P14.3 The rate of formation of nitric oxide (NO) is controlled by the three reversible chemical
reactions
k þ 1
O þ N 2 5 NO þ N
k 1
k þ 2
N þ O 2 5 NO þ O
k 2
k þ 3
N þ OH 5 NO þ H:
k 3
Use the steady state approximation for the nitrogen atom concentration and the assumption
of partial equilibrium for the reactions governing the concentrations of O, O 2 ,HandOH
show that
dR þ a
b ¼
aR þ 1
where b ¼ [N]/[N] e , d ¼ [N 2 ]/[N 2 ] e , a ¼ [NO]/[NO] e , R ¼ R 1 /(R 2 þR 3 ), and R j is the
equilibrium reaction rate of reaction j, and [ ] denotes the molar concentration, and [ ] e is the
equilibrium molar concentration. Derive an expression for d[NO]/dt in terms of R 1 , b, a and d.
At a particular stage in the formation of nitric oxide the values of R and a are 0.26 and 0.1 re
spectively. Why is d ¼ 1 likely to be a good approximation in this case? What is the error if the
rate of formation of NO is evaluated from the larger approximation d½NO=dt ¼ 2R 1 ,rather than
the equation derived in this question?
[3.64%]
P14.4 The rate of change of mole concentration of constituent A in a chemical reaction is
expressed as
d½A n
¼ k½A :
dt
While mole concentration is the dominant property in the reaction it is much more usual for
engineers to deal in mole fractions of the constituents. Show that the rate of change of mole
fraction of constituent A is given by
dx A n n 1
f kx r :
A
dt
where r ¼ density. Also show how the rate of change of mole fraction is affected by pressure.
½dx A =dtfp n 1