Download - Topic 7 kft 131
27
TOPIC 7 - THE RATE OF CHEMICAL REACTIONS
Examples of Solved Problems
1. The rate of formation of C in the reaction 2A + 3B → C + 4D is 2.7 mol dm-3
s-1
. State
the rates of formation and consumption of the participants.
Answer:
1313
1313
1313
13
8.10)7.2(4][
D, offormation of rate The
1.8)7.2(3][
4.5)7.2(2][
2][
AofnconsumptioofrateThe
][
4
1][][
3
1][
2
1
7.2dt
d[C]C offormation of rate The
−−−−
−−−−
−−−−
−−
==
==−
===−
==−=−=
==
sdmmolsdmmoldt
Dd
sdmmolsdmmoldt
Bd
sdmmolsdmmoldt
Cd
dt
Ad
dt
Dd
dt
Cd
dt
Bd
dt
AdRate
sdmmol
2. The rate law for reaction A + 2B → 3C + 4D was reported as
d[C]/dt= kr[A][B][C]. Express the rate law in terms of the reaction rate; what is
the units for kr in each case?
Answer:
162
33
13
)(]][][[
;
]][][[][
4
1][
3
1][
2
1][
−−
−
−−
===
===−=−=
sdmmoldmmol
sdmmol
CBA
Ratek
kofUnit
CBAkdt
Dd
dt
Cd
dt
Bd
dt
AdRate
r
r
r
3. At 518 oC, the rate of decomposition of a sample of gaseous acetaldehyde,
initially at a pressure of 363 Torr, was 1.07 Torr s-1
when 5.0 percent had reacted
and 0.76 Torr s-1
when 20.0 per cent had reacted. Determine the order of the
reaction.
Answer:
( )
reactionordersecond00.299.10746.0
1486.0
1875.1log
4079.1log
1875.1log4079.1log1875.180.0
95.04079.1
)20.0(
)05.0(
%)20(
%)5(
76.0
07.1
2
1
)()(Pr][
1
1
≈===
==
=
−
−=
−
−==
−=∝∝
−
−
n
n
PPk
PPk
Pk
Pk
sTorr
sTorr
rate
rate
xPkrateAessureARate
n
n
n
oo
n
oo
n
o
n
o
n
o
nn
28
4. At 518 oC, the half-life for the decomposition of a sample of gaseous
acetaldehyde, initially at 363 Torr was 410 s. When the pressure was 169 Torr,
the half-life was 880 s. Determine the order of the reaction.
Answer:
reactionordersecond00.2999.1999.01
999.03320.0
3317.0
1479.2log
4659.0log)1(
1479.2log)1(4659.0log
)1479.2()169(
)363(4659.0
880
410
)2(
)1(
1
][
1,
1
1
1
2/1
2/1
1
1
0
12/1
≈=+=
−=−
==−
−=
====
∝∝∝−
−
−
−
−
−−
n
n
n
C
C
s
s
t
t
PPA
tlifeHalf
n
n
n
n
onn
o
5. A second-order reaction of the type A + B →P was carried out in a solution that
was initially 0.075 mol dm-3
in A and 0.060 mol dm-3
in B. After 1.0 h the
concentration of A had fallen to 0.020 mol dm-3
. Calculate the rate constant.
113510754.166326
2231.03863.12231.0663263863.1
060.0
075.0ln)60601()060.0075.0(
055.0060.0
020.0ln
055.0020.0075.0][][][][
][
][ln][][
][
][ln
][
][ln:lawratedintergrateThe
,:typereactionsecFor
−−−×=
−=+=
+××−=−
=−=−=−=
+−=−
−=
→+−
smoldmkk
sk
BBAAx
B
AktBA
xB
xA
B
A
PBAorderond
oo
o
o
oo
o
o
6. A reaction 2B →P has a second–order rate law with k = 4.30×10-4
dm3 mol
-1 s
-1.
Calculate the time required for the concentration of B to change from 0.210 mol
dm-3
to 0.010 mol dm-3
.
( )
sst
tsmoldmmoldmdmmoldmmol
kktBB
BBBB
dtkBdBB
Bd
Bkdt
BdPBorderond
ot
tt
tB
B
B
B
t
o
t
o
5
113413
33
1
0
112
0
12
0
][
][
2
][
][
2
2
1011.1110742
1060.8)762.4100(210.0
1
010.0
1
022][
1
][
1
1
][
1
][
12
][
12
][
2][][][
][
][2][
:lawrateThe,2:typereactionsecFor
×==
×=−=−
−=−=−
+−
−=
+−−−
+−−
=−=−
=−→−
−−−−
−−
−−+−+−
−
∫∫∫
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7. Hydrogen peroxide reacts with thiosulfate ion in slightly acidic solution as
follows: H2O2 + 2S2O32-
+2H+
→ 2H2O + S4O62-
This reaction is second order, independent of the hydrogen ion concentration in
the pH range 4 to 6. The rate constant, k = 9.1×10-2
mol-1
L min-1
were obtained at
25 o C and pH 5.0, and initial concentrations: [H2O2] = 0.036 mol L
-1, [ −3
32OS ] =
0.024 mol L-1
. How long will it take for 50% of the thiosulfate ion, −3
32OS to
react?
Answer:
stt
t
xBxbx
baOSBOHA
B
AktBaAb
bxB
axA
BAkdt
AdPbBaA
o
o
o
oo
o
o
06.117405.01068.49163.0
024.0
036.0ln)101.9))(024.0(1)036.0(2(
)100.6(2024.0(
)100.6036.0(ln
100.6024.025.0,]%[502
2,.1,][],[][
][
][ln)][][(
)]([
)]([ln:equationrateedinteragratThe
]][[][
:lawrateThe,:typereactionordersecondFor
3
2
3
3
3
2
3222
=+×=
+×−=×−
×−
×=×===
====
+−=−
−
=−→+−
−
−
−
−
−
−
Exercise 7a
1. If the reaction aA → Products is xth
-order, where x = 0, x = 1, x = 2 and x = n (any
integer ≠1). Write the rate law, derive the integrated rate law, and also derive the
expression for half-life in terms of a, k, n and [A]o for each order.
2. The gas-phase formation of fosgene, CO + Cl2 → COCl2, is ½ order with respect to
CO. Derive the integrated rate equation for ½-order reaction and derive the
expression for the half-life.
3. The rate of the reaction A + 2 B → 3 C + D was reported as 1.0 mol dm−3
s−1
. Which
of the following states of the rates is NOT TRUE.
A. –d[A]/dt =1.0 mol dm−3
s−1
B. –d[B]/dt =2.0 mol dm−3
s−1
C.-d[C]/dt=3.0 mol dm−3
s−1
D.- d[D]/dt= -1.0 mol dm−3
s−1
4. The rate law for the reaction A + 3 B → C + 2 D was found to be v = k[A][B].
Which of the following state(s) is/are true.
I The unit of the rate of reaction is mol-1
L s-1
II The unit of k is mol-1
L s-1
III The reaction is second order reaction IV Rate = ]][[/][ BAkdtCd =−
A. I and III B. II and III C. I, II , and III D. IV only
5. Nitrogen pentoxide gas decomposes according to: 2N2O5 (g) →4 NO2(g) + O2(g) .
At 328 K the rate of reaction v under certain conditions is 3.38 × 10−5
s−1
. Assuming
that none of the intermediates have appreciable concentrations. Which values is true.
A. -d[N2O5]/dt=3.38 × 10−5
s−1
B. –d[NO2]/dt=3.38 × 10−5
s−1
C.-d[O2]/dt= 3.38 × 10−5
s−1
D. d[O2]/dt=3.38 × 10−5
s−1
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6. In studying the decomposition of ozone: 2O3(g) = 3O2(g)
in a 2-L reaction vessel, it is found that d[O3]/dt = -1.5×10-2
mol L-1
s-1
. What is the
rate of reaction in mol L-1
s-1
?
A.7.5×10−3
B.1.5×10-2
C. -1.5×10-2
D. - 7.5×10−3
7. Under certain conditions, it is found that ammonia is formed from its elements at a
rate of 0.10 mol L-1
s-1
. N2(g) + 3H2(g) = 2NH3(g) . Calculate the value of d[H2]/dt?
A. 0.10 mol L-1
s-1
B. 0.20 mol L-1
s-1
C. 0.30 mol L-1
s-1
D. -0 .30 mol L-1
s-1
8. The decomposition of N2O5: 2N2O5 = 4NO2 + O2 is studied by measuring the
concentration of O2 as a function of time, and it is found that
d[O2]/dt = (1.5 ×10-4
s-1
)[N2O5] at constant temperature and pressure. Under these
conditions the reaction goes to completion to the right. Calculate the half-life of the
reaction under these conditions?
A. 4621s B. 2310 s C. 1155 s D. 577 s
9. At 400 K, the t1/2 for the decomposition of a sample of a gaseous compound initially at
55.5 kPa was 340 s. When the P was 28.9 kPa, the t1/2 was 178 s. The order of the
reaction is
A. n = 0 B. n =1 C. n = 2 D. n = 3
10. The composition of HI to H2 + I2 at 508 oC has a t1/2 of 135 min when the initial
pressure of HI is 0.1 atm and 13.5 min when the pressure is 1 atm. What is the order
of the reaction?
A. n = 0 B. n =1 C. n = 2 D. n = 3
11. The rate constant for the first-order decomposition of a compound A in the reaction
2A → P is k = 2.78 × 10−7
s−1
at 25°C. Calculate the half-life of A?
A. 2.78 × 10−7
s−1
B. 1.25 ×10−6
s−1
C. s4105.2 × D. 1.25 × 10
6 s
−1
12. The first-order reaction 2A→ 2B + C is 35% complete after 325 s. How long will it
take for the reaction to be 70% complete?
A. 325 s B. 650 s C. s908 D. 6.63 ×104 s
13. The t1/2 of a first-order reaction A → P is 12 min. What % of A remains after 50 min?
A. 5.6 % B. 6.5 % C. %08.9 D. 16.63 %
14. The decomposition of ammonia at 1000 oC was a zero-order reaction with rate constant,
k = 4.30 mol dm-3
s-1
.What is the t1/2 for this reaction in which the initial concentration,
[NH3]o=0.0560 M?
A. 77 s B. 4.15 s C. 1.30×10−2
s D. 1.61×10−1
s
15. A solution of A is mixed with an equal volume of a solution of B containing the same
number of moles, and the reaction A + B = C occurs. At the end of 30 min. A is 75%
reacted. How much of A be left at the end of 50 min if the reaction is zero order in
both A and B?
A. 85% B. 60% C. 40% D. 15%
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Exercise 7b
1. The rate law for the reaction 2A →A2 was found to be r = k [A]2. Which of the
following state(s) is / are FALSE.
A The unit of the rate of reaction is mol L-1
s-1
C. The unit of k is mol L-1
s-1
B The reaction is second order reaction D. - 2
2 ][/][ AkdtAd A=
2. A solution of A is mixed with an equal volume of a solution of B containing the same
number of moles, and the reaction A + B = C occurs. If the reaction is first order in
both A and B, what is the rate law?
A. Rate = k[A][B] C. d[B]/dt = k([A]o-x)([B]o-x)
B. d[C]/dt = k[A]2 = k[B]
2 D. -d[B]/dt = k([A]o-x)([B]o-x)
3. The half-life, t1/2 of a reaction is the time required for half of the reactant to disappear.
Which of the following state(s) is / are true?
A. For a zero-order reaction, t1/2 is dependent of the initial concentration.
B. For a first-order reaction, t1/2 is independent of the initial concentration.
C. For a 2rd
-order reaction, t1/2 is inversely proportional to the initial concentration
D. All of the above are true.
4. A dimer is formed in the solution reaction 2A →A2. The rate law is r = 2k[A]2,where k
= 0.015 M-1
s-1
. What is the half-life of A when [A]o = 0.05 M?
A.1333 s B.667 s C. 1.5 s D. 1.5×10−2
s
5. A reaction 2 A → P has a rate law with k = 3.50 ×10−2
dm3 mol
−1 s
−1. Calculate the
time required for the concentration of A to change from 0.26 mol L−1
to 0.11 mol L−1
A. 75 s B. 150 s C. 750 s D. 1333 s
6. A gas reaction 2A → B is second order in A and goes to completion in a reaction
vessel of constant volume and temperature with a half-life of 600 s. If the initial
pressure of A is 1 bar, what are the partial pressure of A at 800 s?
A. 0.328 bar B. 0.430 bar C. 0.504 bar D. 0.845 bar
7. A solution of A is mixed with an equal volume of a solution of B containing the same
number of moles, and the reaction A + B = C occurs. At the end of 30 min A is 65%
reacted. How much of A be left at the end of 50 min if the reaction is first order in
both A and B?
A. 84.8 % B. 75.6 % C. 48.8% D. 24.4%
8. Equal molar quantities of A and B are added to a liter of a suitable solvent. At the end
of 500 s one-half of A has reacted according to the reaction A + B = C. How much of
A will be reacted at the end of 800 s if the reaction is second order with respect to A
and zero order with respect to B?
A. 61.5 % B. 57.6 % C. 38.5% D. 26.0%
9. The second-order rate constant for an alkaline hydrolysis of ethyl formate in 85%
ethanol (aqueous) at 29.86 o
C is 5.43 L mol-1
s-1
. If the reactants are both present at
0.01 mol L-1
, calculate the t1/2.
A.0.13 s B. 5.43 s C. 18.42 s D. 85 s
32
10. A second-order reaction of the type A + B → P was carried out in a solution that
was initially 0.050 mol dm−3
in A and 0.080 mol dm−3
in B. After1.0 h the
concentration of A had fallen to 0.020 mol dm−3
. Calculate the rate constant?
A. 0.00413 mol-1
Ls-1
B.0.0 413mol-1
Ls-1
C. 0.248 mol-1
Ls-1
D. None of the above
11. A second-order reaction of the type A + 2 B → P was carried out in a solution that
was initially 0.75 mol dm−3
in A and 0.80 mol dm−3
in B. After1.0 h the concentration
of A had fallen to 0.65 mol dm−3
. Calculate the rate constant.
A. 8.03×10
-4 mol
-1Ls
-1 B. 5.74×10
-5 mol
-1Ls
-1 C. 1.34×10
-5 mol
-1Ls
-1 D. None of the above
12. The second-order rate constant for the reaction 2A + B → C is 0.21 dm3 mol
−1 s
−1.
What is the concentration of C after 10s when the reactants are mixed with initial
concentrations of [A] = 0.15 mol dm−3
and [B] = 0.25 mol dm−3
?
A.0.184 mol dm−3
B. 0.046 mol dm−3
C. 0.021 mol dm−3
D. 0.07 mol dm−3
13. The reaction CH3CH2NO2 + OH- → H2O + CH3CHNO −
2
is second order, and k at 20
o C is 9.1×10
-2 mol
-1 L min
-1. An aqueous solution is
0.006 molar in nitroethane and 0.007 molar in NaOH. How long will it take for
10% of the nitroethane to react?
A. 1.44×10-3
s B. 15.82 s C. 15.82 min D. 9.1×102
min
14. The second-order rate constant for the reaction:
CH3COOC2H5 (aq) + OH−
(aq) → CH3CO2−
(aq) + CH3CH2OH(aq)
is 0.11 dm3 mol
−1 s
−1. What is the concentration of ester (ROOR) after 10 s when
ethyl acetate is added to NaOH so that the initial concentrations are [NaOH] = 0.050
mol dm−3
and [CH3COOC2H5] = 0.100 mol dm−3
?
A. 0.100 mol dm−3
B. 0.095 mol L-1
C. 0.050 mol dm−3
D. 0.045 mol L-1
15. The rate constant, k, for second-order decomposition of HBr at 1000 K is 6.2×10-3
dm3mol
-1 s
-1. In a reaction in which the initial concentration, [HBr]o is 0.65 mol dm
-3,
at what time [HBr]= 0.12 mol dm-3
?
A. 18 .27 s B. 109 s C. 182 s D. 1.1×103
s
16. The following table gives kinetic data the following reaction at 25 oC: A+ B + C = D
[A] /molL-1
[B] /molL-1
[C] /molL-1
d[D]/dt /10-4
mol L-1
s-1
0.01 0.005 4.00 1.75
0.01 0.004 4.00 1.75
0.01 0.003 8.00 3.50
0.001 0.002 4.00 0.55
What is the rate law for the reaction?
A. ][][ 2/1 CAkr = B. ][][][ 12/1 CBAkr −= C. ]][[ CAkr = D. ]][][[ CBAkr =
17. A second-order reaction of the type A + B → P , the reaction is 60 % complete in
60 seconds when [A]o= 0.1 M and [B]o= 0.5 M. What is the rate constant for this
reaction?
A. 0.0041 mol-1
Ls-1
B. 0.041mol-1
s-1
C. 0.248 mol-1
L s-1
D. None of the above