NAME: ~ I~PERIOD:

SUGGESTED HOMEWORK PROBLEMS - CH 12

a. Read Chapter 12b. Review your notes.c. Answer the following:

I. The reaction: 2 NO (g) + CIz (g) -+ 2 NOCI (g)

was studied at _10°C. The following results were obtained where:

Rate = - MCl1]L1t

KblQ (mol/L) Initial Rate (mol/L . min)

0.100.100.20

0.100.200.20

0.180.361.45

= k It-·IOJ'' [ell ] ~\(a). What is the rate law? f</-\-r£

.k (0"0) '1 (0. JO) •..•

A< (O,IO)"(O,IO)W1

~.:- C) WI

j'\ 1 z: I

l'\ )WIr3 I. t/s k(o,.,;)o) (O,OlO:; :

.--k (0.10 ) 11 (0,;)0) "1r;; • :?~

Aft 0 = rJr}

(b). What is the value of the rate constant?

I'\-\~ ) Q( M.~)= X (.10 L ./0 L

OVER

2. The following data were obtained for the following reaction:

2 CI02 (aq) + 2 OH- (aq) - CIO)- (aq) + CI02- (aq) + H20 (I)

Where rate = - MCI021t;t

rCIOZ]Q(mollL) (OH-lQ (mollL)

0.1000.1000.0500

Initial Rate (mol/L' s)

0.05000.1000.100

5.75 X 10-2

2.30 X \0-11.15x10-1

(a). Determine the rate law. RaTF " k [C.!O$ I" [OH - J"".,k (,IO(»)'1 (./00)'-1

=A( (.O.soo)" (.IOO)~

-#J.JO"(..IO

z S. IS 'f- (0- 2-

d. 30 '1-10 -/

1.13'1./0-'

d s: ,;) rY1

n1 t: I

.,k (.100) '1 (./OO)1\c1

A::. (.100) f) (.osoo)....,= ::

(b). Determine the value of the rate constant.

3 tl1.~ (~rrI ) 1.. ( M~ ),.1 W z -k ,/00 L ./00 t:

---···-------i-------.,-- L Il )(:: c1,3 0 /Vir! 2 s ((c). Determine the rate if [CI02]o = 0.175 mol/L and [OH-]o = 0.0844 mollL.

-

3. The following data were measured for the reaction

SF3 (g) + NHJ (g) -+ FJBNHJ (g)Trial WFJJ (mol/L) fNH3] (moI/L)I 0.250 0.2502 0.250 0.1253 0.200 0.1004 0.350 0.1005 0.175 0.100a. Determine the rate law for the reaction.

Initial Rate (mol/L . s)0.21300.10650.06820.1193

.0.0596

)'" ~r; . ;)130 ...k ( , .:150 (. ~50)= =I).. ,101.0 S ..-k.{.:J50)'" (./~:)tI.t

.;2_-~iIf1

W\~ I

r'j . II q3" ) M.A( (, 35 c) (: I 0 0= - ::IS .os'lf.,

J( ( .t : S) "I (,100)""

b. Determine the overall order of the reaction.

SECOND

c. Determine the value of the rate constant.!<A'll: .: "k [~i=;] [N I-t~]

""-~ M.../)( M~)• J.{ 30 L'S =)c: (..JSO -Z ,;)£0 L

m...f )~----,-*:: ,.2/3{) L::5 L

(,JSO)Z M~l = ~, c() fI1~'S

d. Determine the rate when [SF3J = 0.100 mol/l, and (NH3J = 0.500 mol/L.

i1An=- .: A~rt3FJ ] [tJ H :1 ]

s: (3. 'II M~'S )(.IOO ••..~ ) (. SOD ""t )h-t ..j

-= 0, 170,-{ L'S

OVER

-

4. a. Determine how the rate at which ozone disappears is related to the rate at which oxygen appears in thereaction:

2 03 (g) -+ 3 O2 (g)o [03] o [OtJ.l. IAAn; .-:: 2-

(\tz: 3 -Qt-

e [031~/3 [O~ j

bot z:At

•b. If the rate at which O2 appears is 6.00 x JO's mollL· s at a particular instant, at what rate is 0

3disappearing at

this same time?

:

[0,.]-~-t;:

5. What is meant by reaction rate?

JAtcJtaAfj~ .J.1"- . ik~~t v-b /;twd«.&to ~I •.•~~~ .c« a.

a,;~~re;Pac::'~~ a~ec~te ~~e;~he~1~~f1eac;~n.A oJlkv.~ ,,'U~~ •

W~\,(,.l~~,-, C"~ 1I.ut-c1a-~vta ,.. ~tk~ o..",.d -:d.t jJ'\l.WHC(.

- '~\~b~~\LA ~i-U.o..ctal,k t1'b a. ~7. What are the units usually used to express the rates of reactions occurring in solution?

MIi'"~

L' S

•8. What is the difference between average rate and instantaneous rate?

A.v-t·t.d l "u."n. M :ttU ~. rl<A.. t!1- fL~J 0-6 .:t.:~\.J..J ~v,,-Jt~~~~ AA--tlM & -wtt t>..t tL ~ ;t.;.~~,

9. Define the following symbols that are encountered in rate equations:

a. [A)o ~ c,.,~~" 1> A ~i 1~ Q~o );d\l. ~..:.t.J1CAn~.:t;.d~ (;D 4b. tll2 ~~ - .t:b<- ') ~ .;~~I.L 4~.J 10 "u~ [AJ 0 ~ A .. ~j~ r6 ~c. [A) ~j,~ C\n\.U..~JJ,,, "'6 4 at :t~\4 t .

10. What quantity, when graphed versus time, will yield a straight line for a first order reaction?

II. For a second order reaction, what quantity, when graphed versus time, will yield a straight line?~ I

[ tf:J 1y.J. L'-t12. The decomposition of hydrogen peroxide was studied, and the [HZ02J data was plotted versus time. The slopeof the resulting line was determined to be:

Slope = -8.33 x 10.4 S·l

(a). Determine the rate law.

The reaction was found to be first order with respect to the hydrogen peroxide.

(b). Determine the integrated rate law.

(c). Determine the value of the rate constant.

(d). Determine the [H202l at 4000 s after the start of the reaction.s: [1·bO,,]

[H~O ••']0

i; [1·hOt-J/.00

::

=

G-(,-=-~-·_3_3_"'1.__ 1_O_-_tf_s -J

13. A certain first-order reaction is 45.0% complete in 65 s. What are the rate constant and the half-life for thisprocess?

Ji [f.\Jo ;0 100. 0 ~ +[AJ;c 55.0

~ ( [AJo) ~ k t[AJ

/00) ~ ( )~ (SS :: c ~S s

-k .: q, JO '1.10-3

~ S .s)

t..L .:L

OVER

. (,93_A(..~

-3q. JO'lIO

-_._ .... _-----

14. The gas phase decomposition of sulfuryl chloride is:

Concentration versus time data were collected and a plot of In[A] vs. time resulted in a straight line with a slopevalue of -2.20 x 10-5 s'. [S02CI2]o = 1.75 x IO-J mollL.

a. Determine the rate law, integrated rate law, and the value of the rate constant for this reaction.

~A11: =.-k L SO~ CJ;J J~ l sO;lCll 1"" - ~(t 4 ~ t sOJ CJ ~J 0

I~(~ a. ~_~__~ ..!.-.~~_.~_~

b. Determine the half-life for this reaction.J. .(,q3L y~: _

.A<

31 soo s •c. How much time is required for the concentration ofS02CI2 to decrease to 3.50 x 10-4 mollL?

- (~.;;lO '1fO-S)+

(-J,')O'lIO-S)-t

( - 01, ~O '1-1 0 - s: ) t

~ L; (/.73 Y-10 -3)

- ~.3C(8f39c{ql

f\ - lC ).X/V\ (3.So'J'O ::-

- 7. q S 7S 77 t(03 z

t: 73/S(/, S

[7.3J_)(~

•

N02 (g) - NO (g) + Yz O2 (g)

15. The gas phase decomposition of nitrogen dioxide at 300°C is:

A plot of l/[N02l vs. time results in a straight line. [N02lo = 0.0100 mol/L. Slope = 0.543 Umol . s.

a. Determine the rate law, integrated rate law, and the value of the rate constant for this reaction.

«An; =.k [ r--JOOI J 0)

LNO;) )';;. --Ie t: ~ [tJOOl J 0

L

~< .: O. SL( 3 M,.e • .s

b. Determine the half-life for this reaction..-l-

.:: (.Stf3)( .0100)

How much time is required for the concentration of N02 to decrease to 3.80 x 10.3 mol/L?I

c.

.01

~(,3.ISI8qt{7 -100 =

ICe 3, IS781C./7

• S(/3

5tf3 t

- L-r: :.

16. The radioactive isotop7e32p decays by first-order kinetics and has a half-life of 14.3 days. How long does it takefor 95.0% of a sample of -P to decay? 0 J

. • &; f3 OJ, q q s7 3 J J7 l( .: . () «?V ~I S 3 ss r~ YiI- -: T ::/i,3d

J:: z: o.oI.{8({C,fS 38'5

s: ( C;~~) z: jc t~ ( I~o ) " (,0 </ 8(/(,I j 3 r5) t

OVER

--------------- ----- --------_ ...

-

17. In 6M Hel the complex ion Ru(NH)/+ has a half-life of 14 hours at 25.0°C. Under these conditions, how longwill it take for the Ru(NHJ)6

3+ to decrease to 12.5% of its initial value? (Assume first-order kinetics).

1_, z: .~q3 /1.2. ~:: li..fh d,079t/l//SrfJ z: O,OL{qS-C

~( : 0. o qq s {t z: ~J, 0 hr-S :]

s: [A J 0 --k-r~ ::

[A]

h 100 O. OVC}5 f-- z1J..:>

18. Americium-241 is used in smoke detectors. It has a rate constant for radioactive decay of k = 1.6 x 10.3 yr ,1.

By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay ofk=O.OII day ".

(a) Assuming a first order reaction decay, what are the half-lives of these two isotopes?OlLI/ i YL

' ~q3AfV\ . .:

'.(''l-/O-~-. Xf330t-•

I~SI -t't • (,'13fc 3. Od~• - = •• -L .0 I'

(b) How much ofa 1.00 rng sample of each will remain after 3 half-lives?

1.00 . soo • J $"0 -

19. It took 143s for 50.0% of a particular substance to decompose. If the initial concentration was0.060 M and the decomposition reaction follows second order kinetics, what is the value of the rate constant?

Iil. - .k [Alo'2.. -

-+- ::: t'tL [A]0

,Jk (143s)(,O~O

""...(l)z: Ll----..·-·-·L·-....·-·-'

z: , O. I \ 7 ",..l.s \,._------------

•

20. The rate law for the reaction: 2 NOBr (g) -+ 2 NO (g) + Br, (g)At some temperature is:

Rate = - t.[NOBr]~t

Or rate = k[NOBr]2

(a). lfthe half-life for this reaction is 2.00s when [NOBr]o = 0.900 M, calculate the value of"k" for this reaction.I I

i~ .z: --k Ur)lI or .A< z: T'll lA]o

/

A< t ~1.o"s)( .o oo d )s: ,. ~s:

L

[k L Jc- 0, .s:)l,f\1~ • s

(b). How much time is required for the concentration ofNOBr to decrease to 0.100 M?,

. (

/0.:: (.:5s(,)1 + /.1/

21. Write the rate law for the following elementary reactions:

(b). 03 (g) + NO (g) -+ O2 (g) + N02 (g)

(d). 03 (g) + 0 (g) -+ 2 O2 (g)

OVER

«.o: I

--- --- _._---

22. A proposed mechanism for a reaction is:

slow

fast

fast

(a). Write the rate law expected for this mechanism.

(b). What is the overall balanced equation for the reaction?

is 125 kJ/mol, and L'lE for the reaction is -216 kJ/mol. . What is the activation energy for the reverse reaction?

JJ 0 a (j) of CO <j l -'7 IJ 0 5 ) ~ CO.H,)~Ct. :; I"dS k:Tlfil~ f.:> E s: - ~ t/.c )f.:rllf,(~

(c). What are the intermediates in the proposed mechanism?

eLf f-/q of ~ C <{ /-I? OHi} +-

23. The activation energy for the reaction

NOig) + CO (g) -+ NO (g) + CO2 (g)

;J()Cj' ~ CO.;)lj) -'I tJO'}fj)'" COfj}

t:Q ~ r;;; / ~ jt.J/t>j~ -f I;):S ia.;'..,..f

z: L3 lol/ ~tT/M~)

IJ5

24. For a certain process, the activation energy is greater for the forward reaction than for the reverse reaction.Does this reaction have a positive or negative value for LlE?

... ----------- ---

•

25. At 25°C the first order rate constant for a reaction is 2.0 x 103 s'. The activation energy is15.0 kJ/mol. What is the value of the rate constant at 75°C?

fa, (.J.... _ ..l.)ff" T, r,

3 J/IS.O ¥..IO /M~

g.. 31 Y %..t K..3

J,Q 'f 10

;~)? 3 I II

(~.OVIO·3)( 0), a8(,t{~~3q)

A.(, ~ 'X I 0 3 J -, J

s(" S8-0 77 sJ,)

£~ ;.(3, rJ073 fC,7{J/ XJO-S)

%J - /tP. g j~~

26. A first order reaction has a rate constant of 4.6 x 10.2 s' at OOCand 8.1 x 10'2 s' at 20°C. Calculate the value ofthe activation energy.

~ ( J~,) z: Er<-~ ( ;1~(~) z:

.Ol(V

I got I J. q

27. A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 22°C to ahigher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.

a .kz..) EC{ (-.-!- ...L )~ (T, = i<. T, r,

7,k Stj '( 103 ;r/r-t~~ ( lZ):; ~.31L{ %,(/(

h1 (-L -t)- ~1qV. , 7797:) I<. ~C;~ ---if _I- I

0) • qa'I'lo q q X 10 = cJ9S~

# 0030 90J/f./« Iz:

TJ.

;-

OVER

28. One mechanism for the destruction of ozone in the upper atmosphere is

03 (g) + NO (g) - N02 (g) + O2 (g) slow

N02 (g) + 0 (g) - NO (g) + O2 (g) fast

(a). Write the equation for the overall reaction.

(b). Which species is a catalyst?

NO

(c). Which species is an intermediate?

(d). The E. for the uncatalyzed reaction is 14.0 kJ. The E. for the catalyzed reaction is 11.9 kl. What is the ratio ofthe rate constant for the catalyzed reaction to the uncatalyzed reaction at 25°C? Assume the frequency factor, A, isthe same for each reaction. _ (f I , q 'f-I oj )

t={.l ~ : Ilf.O,t::r e U-.511f )(l..ctf)

~ (1 ~ e.d ::- I I ,Cj --lc.T ~(ec.J_

.l. .: A e - fo/fL T ~(,uMJ

.00 li-Jo,,7 3atf.003:511, J7J-q =

29. The gas phase rearrangement of methyl isonitrile occurs as follows:

At 198.90C the rate constant for this reaction is k = 5.25 X 10'5 s ., and at 251.2°C is k = 3.16 X 10.3 s ". Using thesevalues, calculate E, for this reaction.

h ( -tJ-) : ~ (I ...L )-¥. r<. T, -r;

~(3.'~ ~IO-3 ) £a. J )( I- --!> = l{7/.0, S;;'-I. ~$', J. ~ '1r 0 ~. 31lt

.FA(~.II t.f().C(lqt;J i 10-")1.0Cj ·75 It( I J 7 s:

e. sIll

1~!l3q, f./st)f.: Ea.

LEA ' ~;;~Jj,~7_.. _-_ ..•........ " .._-----_ .. ,,- ...__ .... ---

•30. A certain first-order reaction has a rate constant of k = 2.75 X 10'2 s " at 20.0oC. What is the value of kat60.0oe if the activation energy is 75.5 kl/mol?

( ¥;1. ) 75.S1103

h J. 7S;/O - ~::. 6.3/'-{ ( 019 3

3. 7 dd?O 7 fl9-'l.;).7S'l-/0

=

--Ie()..: (J,-'S,(IO-3)(~/, 37(,;;Jf020.3J

=L~-'~;;'-~'''=j731. The following mechanisms have been proposed for the reaction of H2 with lei:

H2 (g) + reI (g) ....•HI (g) + HCI (g)

HI (g) + reI (g) -+ 12 (g) + Hel (g)

(a) Write the balanced equation for the overall reaction.

(b) Identify any intermediates in the mechanism.

/-1 T

(c) If the first step is slow and the second step is fast, what rate law do you expect to be observed for the overallreaction?

RATE s: J [I-/~ ] [L C-i]

OVER