Question

PLEASE SOLVE ONLY E$,$ F AND G$.$ THANK YOU.

$4\mathrm{.}16$

$$of the textbook.

$4\mathrm{.}16$

$.$

$$Consider the following chain

$-$

reaction mechanism for the high

$-$

temperature formation of

nitric oxide, i

$.$

e

$.$

$,$

$$the Zeldovich mechanism:

O

$+$

$$N

$2$

$-$

$>$

$$NO

$+$

$$N

$(2$

a

$)$

N

$+$

$$O

$2$

$-$

$>$

$$NO

$+$

$$O

$(2$

b

$)$

The reaction rates of Eqs.

$(2$

a

$)$

$$and

$(2$

b

$)$

$$are k

$1$

f and k

$2$

f

$,$

$$respectively$.$

A

$.$

$$Write out expressions for d

$[$

NO

$]/$

dt and d

$[$

N

$]/$

dt

$.$

B

$.$

$$Assuming N atoms exist in steady state and that the concentrations of O

$,$

$$O

$2$

$,$

$$and N

$2$

are at their equilibrium values for a specified temperature and composition, simplify your

expression obtained above for d

$[$

NO

$]/$

dt for the case of negligible reverse reactions.

$($

Answer:

d

$[$

NO

$]/$

dt

$=$

$2$

k

$1$

f

$[$

O

$]$

eq

$[$

N

$2]$

eq

$)$

C

$.$

$$Write out the expression for the steady

$-$

state N

$-$

atom concentration used in part B

$.$

D

$.$

$$For the conditions given below and using the assumptions of part B

$,$

$$how long does it

take to form

$50$

$$ppm

$($

mole fraction

$\backslash$

times

$106)$

$$of NO

$?$

$$T

$=$

$2100$

$$K

$,$

$\backslash$

rho

$=$

$0\mathrm{.}167$

$$kg

$/$

m

$3$

$,$

$$M W

$=$

$28\mathrm{.}778$

$$kg

$/$

kmole

$,$

$\backslash$

chi O

$,$

eq

$=$

$7\mathrm{.}6\backslash$

times

$105$

$$mole fraction,

$\backslash$

chi O

$2$

$,$

eq

$=$

$3\mathrm{.}025\backslash$

times

$103$

$$mole fraction,

$\backslash$

chi N

$2$

$,$

eq

$=$

$0\mathrm{.}726$

$$mole fraction, and k

$1$

f

$=$

$1\mathrm{.}82\backslash$

times

$1014$

$$exp

$38370/$

T with units of cm

$3/$

gmol

$-$

s

$.$

E

$.$

$$Calculate the value of the reverse reaction rate coefficient for the first reaction, i

$.$

e

$.$

$,$

$$O

$+$

$$N

$2$

$$NO

$+$

$$N

for a temperature of

$2100$

$$K

$.$

F

$.$

$$For your computations in part D

$,$

$$how good is the assumption that reverse reactions are

negligible? Be quantitative.

G

$.$

$$For the conditions of part D

$,$

$$determine numerical values for

$[$

N

$]$

$$and

$\backslash$

chi N

$.$

$$Note: k

$2$

f

$=$

$1\mathrm{.}8\backslash$

times

$1010$

T exp

$4680/$

T with units of cm

$3/$

gmol

$-$

s

$.$

Hint: The answer to part

$($

D

$)$

$$is: about

$37$

$$msec$.$ The answer to part

$($

G

$)$

$$is: about

$9\mathrm{.}4\backslash$

times

$103$

ppm