13
Rates of Chemical Reactions
13.1
Rates of Chemical Reactions
13.2
Expressions of Reaction Rates in Terms of Rates of Changes in Concentrations of Reactants or Products
1
13.3
Methods of Measuring Reaction Rates
13.4
Factors ffecting Reaction Rates
Chemical Kinetics A study of (1)reaction rates (2)
the factors ors affecting rea reaction rat rates
(3)
reaction mechanisms
(the detailed steps involved in reactions)
2
Explosive reactions 2H2(g) + O2(g) → 2H2O(l)
3
Vigorous reactions 2K(s) + 2H2O(l) → 2KOH(a") + H2(g)
otassium reacts !ith !ater vigorously 4
Very rapid reactions $ormation of insolu%le salts +
#
Ag (a") + Cl (a")→ AgCl(s)
5
Very rapid reactions $ormation of insolu%le %ases #
$e (a") + 3OH (a")→ $e(OH)3(s) 3+
6
Very rapid reactions Acid&al'ali neutraliation reactions #
H (a") + OH (a")→ H2O(l) +
7
*1 Ag+(a") + Cl#(a")→ AgCl(s) #
$e (a") + 3OH (a")→ $e(OH)3(s) 3+
H+(a") + OH#(a")→ H2O(l)
All involve oppositely charged ions
8
Rapid or moderate reactions ,isplacement reactions of metals - & n(s) + 2Ag+(a") → n2+(a") + 2Ag(s)
9
Rapid or moderate reactions ,isplacement reactions of metals - & n(s) + 2Ag+(a") → n2+(a") + 2Ag(s) ,isplacement reactions of halogens - & Cl2(a") + 2.r−(a") → 2Cl−(a") + .r2(a")
10
Slow reactions $ermentation of glucose C/H12O/(a") → 2C2H0OH(a") + 2CO2(g)
11
Slow reactions 2nO−(a") + 0C2O2−(a") + 1/H+(a")
→
12
2n2+(a") + 1CO2(g) + 4H2O(l)
Very slow reactions 5usting of iron $e(s) + 3O2(g) + 2nH2O(l) → 2$e2O3 6 nH2O(s)
13
Extremely slow reactions +
2+
CaCO3(s) + 2H (a") → Ca (a") + CO2(g) + H2O(l) .efore corrosion
14
After corrosion
7!o 8ays to 9:press 5eaction 5ates 1* Average rate 2* ;nstantaneous rate (rate at a given instant)
15
Average rate of reaction 7otal change in amount of a product or a reactant = 7otal time ta'en for the change to occur
Amount is usually e:pressed in Concentration Mass Volume Pressure 16
mol dm#3 g cm3 or dm3 atm
Q. *3/ g of magnesium reacted !ith 0* cm3 of 1* hydrochloric acid to give 3/ cm3 of hydrogen under room conditions* 7he reaction !as completely in < seconds*
g(s) + 2HCl(a") → gCl2(a") + H2(g)
*3/ g −3 −1 (a) Average rate = = * × 1 g s < s
17
Q. *3/ g of magnesium reacted !ith 0* cm3 of 1* hydrochloric acid to give 3/ cm3 of hydrogen under room conditions* 7he reaction !as completely in < seconds*
g(s) + 2HCl(a") → gCl2(a") + H2(g)
3/ cm3 3 −1 (%) Average rate = = * cm s < s
18
2* (c)
g(s) + 2HCl(a") → gCl2(a") + H2(g) *3/ g −1 = *10 mol 2*3 g mol =o* of moles of HCl = 1* mol dm 3 × *0 dm3 = *0 mol
=o* of moles of g =
−
g is the limiting reactant =o* of moles of HCl reacted = 2 × *10 mol = *3 mol
,ecrease in concentration of HCl(a") in < s
=
*3 mol −3 = */ mol dm *0 dm3
*/ mol dm&3 = /*> × 1&3 mol dm&3 s −1 Average rate = < s 19
g(s) + 2HCl(a") → gCl2(a") + H2(g)
2* (d)
5ate of reaction 5ate of reaction ? 2× !*r*t* HCl(a") !*r*t* gCl2(a") ;ncrease in concentration of gCl 2(a") in < s 1 2
= × */ mol dm−3 = *3 mol dm&3 *3 mol dm&3 Average rate = = 3*3 × 1&3 mol dm&3 s−1 < s
20
2* ;nstantaneous rate 7he rate at a particular instant of the reaction is called the instantaneous rate * $or the chemical reaction a! " #$
cC " d%
;nstantane ous rate d@C 1 d@, 1 − d@A 1 − d@. 1 ( )= ( )= ( )= ( ) = dt a dt % dt c dt d @B ? molarity of B 21
2* ;nstantaneous rate 7he rate at a particular instant of the reaction is called the instantaneous rate * $or the chemical reaction a! " #$
cC " d%
;nstantane ous rate d@C 1 d@, 1 − d@A 1 − d@. 1 ( )= ( )= ( )= ( ) = dt a dt % dt c dt d &nits - mol dm−3 s−1 mol dm−3 min−1 mol dm−3 h−1Detc* 22
'rap(ical Representation o) Reaction Rates * Rate curves ! rate curve is a graph plotting the amount of a reactant or product against time*
23
Consider the reaction A
→
(reactant)
24
.
+ C (product)
At any time t the instantaneo instantaneous us rate of the reaction e"uals t(e slope o) t(e tangent to t(e curve at that point* 7he greater the slope the higher the rate of the reaction*
25
&ve slope &ve slope of curve of reactant A
⇒ @A ↓ !ith time
26
+ve slope +ve slope of curve of product .
⇒ @. ↑ !ith time
27
7he rate at t is usually the )astest and is called the initial rate* 7he curve is the steepest !ith the greatest slope at time t*
28
7he rate of the reaction gradually ↓ as the reaction proceeds* $lat curve → reaction completed
29
B + E → 2
Q.3 # t c u d o r " p 3 f − o m n d l o i t o a m r ! t n e c n o C A 30
C B
Time of reaction !min"
1 0* mol dm Average rate = × 2 > min # t c u d o r " p 3 f − o m n d l o i t o a m r ! t n e c n o C A 31
−3 =
*3< mol dm −3 min−1
B + E → 2 C B
Time of reaction !min"
B + E → 2 # t c u d o r " p 3 f − o m n d l o i t o a m r ! t n e c n o C A 32
C B
;nstantaneous rate at A 1 (/* & *) mol dm −3 = × 2 (1*/ & *) min =
1*< mol dm 3 min −
1
−
1*/ Time of reaction !min"
B + E → 2 # t c u d o r " p 3 f − o m n d l o i t o a 2*> m r ! t n e c n o C A 33
C
0*1 B
;nstantaneous rate at . 1 (0*1 & 2*>) mol dm −3 = × 2 (3* & 1*) min =
*/ mol dm 3 min −
1
−
Time of reaction !min"
B + E → 2 # t c u d o r " p 3 f − o m n d l o i t o a m r ! t n e c n o C A 34
C B
;nstantaneous rate at C =
Time of reaction !min"
ethods of easuring 5eaction 5ates A*hysical measurements 1* Continuous measurements 2 ;nitial rate measurements (Cloc' reactions) .* Chemical measurements (7itration)
35
1* Continuous measurements 9:periment is done in +,E ta'e* 7he reaction rates are determined %y measuring continuously a convenient property !hich is directly proportional to t(e concentration of any one reactant or product of the reaction mi:ture* roperties to %e measured - F Gas volume Gas pressure ass Color intensity 9lectrical conductivity 36
1*1 easurement of large volume changes 9:amples(1) CaCO3(s) + 2HCl(a") → CaCl2(a") + H2O(l) + CO2(g) (2) n(s) + H2IO(a") → nIO(a") + H2(g) 37
→ 2H2O(l) + O2(g) (3) 2H2O2(a")
1*1 easurement of large volume changes
7emperature is 'ept constant
38
A typical la%oratory set&up for measuring the volume of gas formed in a reaction
n(s) + H2IO(a") → nIO(a") + H2(g) " 3
m c ! d e m r o f s a g f o e m u l o $ 39
dJ ∝ rate slope = dt
Time of reaction !min"
* (2) n(s) + H2IO(a") → nIO(a") + H2(g)
H2(g) is sparingly solu%le in !ater !hile CO2 is "uite solu%le in !ater* Jolume of CO2
Rate Rate
40
Sigmoid curve
1*2 easurement of small volume changes & ,ilatometry Capillary tu%e
i"uid phase reaction mi:ture CH3COOH(l) + CH3CH2OH(l) → CH3COOCH2CH3(l) + H2O(l) 41
1*3 easurement of mass changes CaCO3(s) + 2HCl(a") → CaCl2(a") + H2O(l) + CO2(g)
42
7he cotton !ool plug is to allo! the escape of CO2(g) %ut to prevent loss of acid spray due to spurting*
stop!atch cotton !ool plug limestone pieces of 'no!n mass
measured volume of standard hydrochloric acid electronic %alance
43
n(s) + H2IO(a") → nIO(a") + H2(g)
CaCO3(s) + 2HCl(a") → CaCl2(a") + H2O(l) + CO2(g) 8hich reaction is more suita%le to %e follo!ed %y mass measurement L Hydrogen is a very light gas* 7he change in mass of the reaction mi:ture may %e very small* 7he electronic %alance used in the school la%oratory may not %e sensitive enough to detect the small change* 44
( m K o ) s s o f m a s s
mfinal ? total mass loss
dm ∝ rate slope = dt
time m
f i n a l
& m
t
45
mfinal ? mfinal F m
(∵ m ? )
d@H+ slope ∝ ? − rate ×2 dt time
1* Colorimetry ∵
colour intensity ∝ @coloured species d(colour intensity) rate ∝ ± dt
46
H2O2(a") + 2H+(a") + 2;−(a") → -a/0 + 2H2O(l)
colour intensity ↑ as reaction proceeds CH3COCH3(a") + -a/0 → CH3COCH2;(a") + H+(a") + ;−(a") $ra/0 + HCOOH(a") → 2H+(a") + 2.r−(a") + CO2(g) Mn+ a/0 + 1/H+(a") + 0C2O2−(a") → 2n2+(a") + 1CO2(g) + 4H2O(l)
colour intensity ↓ as reaction proceeds 47
48
cuvettes
A colorimeter 49
Eello! light
Eello! filter
.lue solution
Complementary colours
50
5ed ↔ C yan
airs of opposite colours are complementary colours
51
5ed ↔ C yan Green ↔ agenta
airs of opposite colours are complementary colours
52
5ed ↔ C yan Green ↔ agenta .lue ↔ Eello! CEK airs of opposite colours are complementary colours
53
8hen mi:ed in the proper proportion complementary colours produce a neutral color (grey !hite or %lac')* 54
- 2
; 3 ? ; ?
55
-
intensity %efore a%sorption
intensity after a%sorption
- 2
; × 1M M transmittance = ;
56
-
; A%sor%ance = log1 ;
;f ; ? ;
;f ; ?
4 ? 1M
4 ? M
! ? log11 ?
! → log1∞ → ∞
ero a%sorption
complete a%sorption
A ? ε%C .eerNs la!
57
A
,eviation at higher concentrations
A cali%ration curve is first constructed for A→C conversion
C 58
*0
@;2
d@;2 = −rate slope = dt time A
dA ∝ −rate slope = dt
59
time
1*0 easurement of electrical conductivity ,a"+5 a/0 " C53C++5a/0 ∵
conducting mo#ility 6 +5
∴ conductivity
60
C53C++ ,a"a/0 " 5+l0 7 C53C++
as t(e rx proceeds
1*0 easurement of electrical conductivity Mn+ a/0 " 185"a/0 " 9C+ a/0 Mn"a/0 " 12C+g0 " :5+l0 ∵ total num#er o) ions ∴ electrical conductivity
61
as t(e rx proceeds
1*/ easurement of pressure changes
d(7 ) rate ∝ ± dt 7 ? total pressure of the reaction mi:ture
62
*/ (i) 2=O(g) + 2H2(g) → =2(g) + 2H2O(g) (ii) 3H2(g) + =2(g) → 2=H3(g)
At fi:ed J and 7 7 ∝ n ;n %oth reactions n ↓ as the reactions proceed
⇒ 7 ↓ as the reactions proceed
63
suction )las< dilute (ydroc(loric acid
pressure sensor
magnesium ri##on to data;logger inter)ace and computer
g(s) + 2HCl(a") → gCl2(a") + H2(g) 64
A(g) + .(g) → products
65
A c(emical cloc< is a comple: mi:ture of reacting chemical compounds in !hich the concentration of one or more components e:hi%its periodic changes* ;n cases !here one of the reagents has a visi%le color crossing a concentration threshold can lead to an a%rupt color change in a reproduci%le time lapse*
66
. -nitial Rate Measurements;Cloc< Reactions
1* A set of e:periments is done in !hich all reaction conditions %ut one are 'ept constant* I2O32F(a") + 2H+(a") → IO2(a") + H2O(l) + I(s)
67
9:periment
@I2O32−(a")
@H+(a")
1 2 3
*1 *4 * *2
1 1 1 1
. -nitial Rate Measurements;Cloc< Reactions
I2O32F(a") + 2H+(a") → IO2(a") + H2O(l) + I(s) yello! precipitate 2* 7he time ta'en for the reaction to arrive at a particular point at the early stage of the reaction is measured*
68
7he %ea'er containing the reaction mi:ture is placed over a cross mar'ed on a !hite tile* 69
As more sulphur forms the reaction mi:ture %ecomes more cloudy* 70
7he cross %ecomes more and more difficult to see and finally disappears* 71
2F
+
I2O3 (a") + 2H (a") → IO2(a") + H2O(l) + I(s) yello! precipitate
Average rate in the early stage
Amount of I re"uired to %lot out the mar' ? 7ime ta'en to %lot out the mar' Iince the amount of I re"uired to %lot out the mar' is a constant 1 Average ∝ rate time ta'en to %lot outN the mar' 72
1 Average ∝ rate time ta'en to %lot outN the mar'
7he average rate of reaction is inversely proportional to the time ta'en to %lot outN the mar'* 7he faster is the reaction the shorter is the time ta'en for the mar' to disappear*
73
dI dt ∆I slope = average rate = ∆t
slope = initial rate =
amount of I ;f ∆I and ∆t are small(early stage)
dI PI ≈ dt Pt time 74
dI PI ≈ dt Pt
Iince ∆I is a constant
dI PI 1 ≈ ∝ dt Pt t
75
-nitial rate <=S+3 a/0>x=5"a/0>y
Iince HCl is in large e:cess @H+(a") y ≈ constant at the early stage -nitial rate <=S+3 a/0>x=5"a/0>y x
PI 1 ∝ ;nitial rate ≈ Pt t
1 QQ 2− : = ' @I2O3 (a") t 76
9:pt*
77
@I2O32−(a") @H+(a") () ()
7ime ta'en (t) to mas' the mar' s
1
*1
1
1
2
*4
1
13
3
*
1
20
*2
1
0
1 t
s− 1
Q.@ 1 t
1 t
2− 3
= ' @I2O (a") QQ
:
inear ⇒ : ? 1
@I2O32−(a") 78
+t(er Examples o) Cloc< Reactions 6 ; 0;−(a") + ;O3−(a") + /H+(a") → 3;2(a") + 3H2O(l) Imall and fi:ed amounts of I 2O32(a") and starch are added to the reaction mi:tures in all runs* ;2(a") + 2I2O32−(a") → 2;−(a") + IO/2−(a") (fi:ed) (fi:ed) ;2(a")
+
starch → deep %lue comple:
(e:cess) (fi:ed) 7ime ta'en for the reaction mi:ture to turn deep %lue is measured* 79
+t(er Examples o) Cloc< Reactions 6 ; 0;−(a") + ;O3−(a") + /H+(a") → 3;2(a") + 3H2O(l) ;2(a") + 2I2O32−(a") → 2;−(a") + IO/2−(a") (fi:ed) (fi:ed) ;2(a")
+
(e:cess)
starch → deep %lue comple: (fi:ed)
.y changing the concentration of any one of the reactants deep %lue colour !ill appear in different time lapses → a chemical cloc' R
Hallo!een cloc'
80
+t(er Examples o) Cloc< Reactions 6 ; 0.r−(a") + .rO3−(a") + /H+(a") → 3.r2(a") + %& 3H2%& O(l) 'r
+
(fi:ed) .r2 + (e:cess) 81
'r
3.r2 (fi:ed)
'r
methyl red → colourless (fi:ed)
Advantages of physical measurements 1* Iuita%le for fast reactions* 2* Imall sample sie 3* ore accurate than chemical method (titration) * =o interruption → continuous measurements 0* Can %e automated*
82
,isadvantages of physical measurements 1* ore sophisticated 2* ore e:pensive 3* ore specific F only suit a limited num%er of reactions*
83
$. C(emical Measurements 4itration Met(ods0
1* Itart a reaction !ith all reaction conditions %ut one fi:ed* 2* 8ithdra! and "uench fi:ed amounts of the reaction mi:ture at different times*
84
Quenching methods:
7emperature ↓ •
•
•
85
Cooling the reaction mi:ture rapidly in ice* ,iluting the reaction mi:ture !ith a sufficient amount of cold !ater or an appropriate solvent* Concentration ↓ 5emoving one of the reactants or the catalyst (if any) %y adding another reagent*
$. C(emical Measurements 4itration Met(ods0
1* Itart a reaction !ith all reaction conditions %ut one fi:ed* 2* 8ithdra! and "uench fi:ed amounts of the reaction mi:ture at different times* 3* 7itrate the "uenched samples to determine the concentration of one of the reactants or products*
86
C53C+C53 " -
H+ as catalyst
C53C+C5- " 5-
*4 7he reaction is "uenched %y adding to it =aHCO 3(a") that removes the catalyst* HCO3−(a") + H+(a") → H2O(l) + CO2(g)
87
C53C+C53 " -
H+ as catalyst
C53C+C5- " 5-
*< 7itrated !ith standard solution of =a 2I2O3(a") using starch as indicator (added !hen the end point is near) 2− 3
2− /
−
2I2O (a") + ;2(a") → IO (a") + 2; (a") Colour change at the end point - deep %lue to colourless
88
C53C+C53 " -
H+ as catalyst
C53C+C5- " 5-
*1 7he e:cess I2O32−(a") !ould react !ith H + to give a cloudy mi:ture cloudy mi:ture !ith a pungent pungent smell* smell* I2O32−(a") + 2H+(a") → I(s) I(s) + + IO2(g) (g) + + H2O(l)
89
Advantages of titrimetric method 1* Only Only simp simple le appa appara ratu tuss are are re" re"ui uired red** 2* Can Can %e applie applied d to a great great variet varietyy of slo! reactions*
90
,isadvantages of physical measurements 1* =ot suita%le for )ast reactions* ;t ta'es time to !ithdra! samples and perform titration* 2* 5eacti 5eactions ons are dist distur% ur%ed ed F =O7 =O7 cont continu inuous ous 3* 7ime 7ime con consu sumi ming ng F =O7 =O7 aut autom omat ated ed
91
Factors Afecting Reaction Rates 92
Collision 7heory =o reaction Iufficient K*9* ;ncorrect orientation
93
Collision 7heory =o reaction Correct orientation ;nsufficient K*9*
94
Collision 7heory
Iufficient K*9* Correct orientation
9ffective collision 95
Collision 7heory Activation energy
.ond %rea'ing and %ond forming occur at the same time 9a S .*9*(s) of the %ond(s) to %e %ro'en 96
Collision 7heory Activation energy
Higher 9a
→ more K*9* re"uired for effective collision → slo!er reaction 97
Collision 7heory Activation energy
o!er 9a
→ less K*9* re"uired for effective collision → faster reaction 98
Collision 7heory Activation energy
5ate of reaction depends on 9a !hich in turn depends on the nature of reactants* 9*g* K is more reactive than g 99
$actors Affecting 5eaction 5ates concentration concentration
100
particle sie sie particle
pressure pressure
catalyst catalyst
temperature temperature
light light
9ffect of concentration •
101
e*g* 5eaction %et!een g and HCl
9ffect of concentration (a) 2* 2* HCl HCl (a) (%) 1* 1* HCl HCl (%) (c) *0 *0 HCl HCl (c) 5eaction raterate5eaction (a) TT (%) (%) TT (c) (c) (a)
102
9ffect of concentration 7ime for for reaction reaction to to 7ime complete- tt11 S S tt22 S S tt33 completeHigher @HCl(a") @HCl(a") Higher → $aster $aster reaction reaction →
103
@B
→ 5eactant particles are more cro!ded → Collision fre"uency → =um%er of effective collisions → 5eaction rate
104
$or the reaction
a! " #$
cC " d%
5ate = '@A:@. y !here x and y are the orders o) reaction !ith respect to ! and $ < is the rate constant units mol dm 3 s 1Amol dm 30x"y
105
$or the reaction
a! " #$
cC " d%
5ate = '@A:@. y x and y can %e ± integers or fractional x
y is the overall order of reaction*
x y can +,B %e determined experimentally*
106
9ffect of pressure Only applica%le to reactions involving gaseous reactants*
107
ressure ↑
→ → → →
108
5eactant particles are more cro!ded Collision fre"uency ↑ =o* of effective collisions ↑ 5ate of reaction ↑
9ffect of temperature Applica%le to A reactions
109
7↑
→ K*9* of particles ↑ → Collision fre"uency ↑ (minor effect) and =o* of particles !ith K*9* T 9a ↑ (maUor effect) → =o* of effective collisions ↑ → 5ate of reaction ↑
110
5ate
5ate of reaction ↑ exponentially !ith temperature
5ate ∝ e
−9a 57
;n general a 1oC ↑ in 7 dou%les the rate* 7 °C 111
9ffect of particle sie $or a fi:ed volume of solid Imaller particle sie → greater surface area
112
CaCO3(a") + 2H+(e:cess) → CaCl2(a") + H2O(l) + CO2(g)
5ate involving involving 5ate po!dered solid po!dered solid reactant isis higher higher reactant 5eason- higher higher 5easonchance of of contact contact chance %et!een reactant reactant %et!een particles particles 113
*11
*0 g po!der *0 g granule
114
9ffect of Catalyst A catalyst is a su%stance that alters the rate of a chemical reaction %y providing an alternative reaction pat(way !ith a different activation energy. ! positive catalyst speeds up a reaction %y providing an alternative reaction path!ay !ith a lower Ea* ! negative catalyst slows down a reaction %y providing an alternative reaction path!ay !ith a (ig(er Ea* 115
9ffect of Catalyst Catalysts remain c(emically unc(anged at the end of reactions*
116
H2O2(a")
nO2 as catalyst
2H2O(l) + O2(g)
hysical measurement
117
H2O2(a")
nO2 as catalyst
2H2O(l) + O2(g)
" 3
m c ! d e m r o f s a g f o e m u l o $ 118
Time of reaction !min"
7itrimetric method (*12) H2O2(a")
nO2 as catalyst
2H 2O(l) + O2(g)
ipette samples at different times 5emove nO2(s) %y filtration 7itrate !ith nO−(a")H+(a") 95+a/0 " Mn+ a/0 " 85"a/0 Mn"a/0 " :5+l0 " 9+g0 119
*13 @H2O2 8ithout nO2
8ith nO2 time 120
9ffect of light ight !ith specific fre"uency (E ( ) can provide sufficient energy to %rea' a particular chemical %ond in a reactant leading to a photochemical reaction* photochemical reaction*
.r F .r
h ν
.r⋅ + .r⋅
C/H1 + .r⋅ → C/H13⋅ + H.r → → → C/H13.rD 121
Autocatalysis Catalysis in !hich the product acts as the catalyst of the reaction 2nO−(a") + 1/H+(a") + 0C2O2−(a")
→ 2Mn"a/0 + 1CO2(g) + 4H2O(l) CH3COCH3(a") + ;2(a")
→ CH3COCH2;(a") + 5"a/0 + ;−(a") 122
*1 @nO−
5ate ↑
Iigmoid curve 5ate ↓
123
time
The END
124
13.1 Rates of Chemical Reactions !(' p.)"
$ac<
Example 13-1A
Ans!er *um+er of moles of C% 2 ,
-.10 g !12.- + 1/.- × 2" g mol 1
, -.--41 mol -.--41 mol erage rate , /- s , /.03 1- ) mol s 1 125
13.1 Rates of Chemical Reactions !(' p.)"
Example 13-1B
Ans!er 126
13.1 Rates of Chemical Reactions !(' p.)"
Example 13-1B
$ac<
*um+er of moles of % 2 ,
) cm 3 −1 3 24 --cm mol , 2.-0 1- 4 mol
erage rate , 2.-0 × 1- 4 mol !2- × /- × /-" s , 2.0 1- mol s 1
127
13.1 Rates of Chemical Reactions !(' p./"
Example 13-1C
128
13.1 Rates of Chemical Reactions !(' p./"
Example 13-1C With the use of the graph, calculate (a) the initial rate of the reaction; (b) the average rate for the time interval from the 1st to the 2nd minute; (c) the instantaneous rate at the 3rd minute. (ive !our ans"ers in mol dm #3 min#1.)
Ans!er
129
13.1 Rates of Chemical Reactions !(' p./"
Example 13-1C !a" 5nitial rate ,
(lope of the tangent to the cure at t −3 − !-.1--.1/-" mol dm , !1.2 − -" min , -.-) mol dm3 min1
130
13.1 Rates of Chemical Reactions !(' p./"
Example 13-1C !+" erage rate !-.-0- − -.11-" mol dm −3 , !2 − 1" min , -.-3 mol dm3 min1
131
13.1 Rates of Chemical Reactions !(' p./"
$ac<
Example 13-1C
!c" 5nstantaneous rate at the 3rd minute ,
(lope of the tangent to the cure at the 3 rd minute −3 , !-.-4/ − -.-66" mol dm !3.) − 2" min
, -.-21 mol dm3 min1
132
13.1 Rates of Chemical Reactions !(' p.0"
Chec' oint 13&1 (a) $n the h!drol!sis of an ester at a constant temperature of 3%& ', the concentration of the ester decreases from 1 mol dm#3 to .* mol dm#3 in + minutes. What is its average rate in mol dm #3 s#1 for that time interval Ans!er !a" erage rate at 30 7
, !1 -.6)" mol dm 3 ÷ !4 × /-" s , -.--1 -4 mol dm 3 s1
133
13.1 Rates of Chemical Reactions !(' p.0"
Chec' oint 13&1 (b) -he graph on the right sho"s the change in concentration of a reactant in a chemical reaction.
134
13.1 Rates of Chemical Reactions !(' p.0"
Chec' oint 13&1 With the use of the graph above, calculate (i)
the initial rate of the reaction;
(ii) the average rate for the time interval from the 2th to the 3th second; (iii) the instantaneous rate at the 1th second.
Ans!er
135
13.1 Rates of Chemical Reactions !(' p.0"
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Chec' oint 13&1 !i"
5nitial rate
, !-.-2 -.-1" mol dm !- − 1-" s
3
, 1 × 1-3 mol dm3 s1 3 ! -.-- -.--/" mol dm !ii" erage rate , !2- − 3-" s
, 3 × 1-4 mol dm3 s1 3 ! -.-10 -.-13" mol dm !iii" 5nstantaneous rate , !- − 1-" s
, ) × 1-4 mol dm3 s1 136
13.2 Expressions of Reactions Rates in Terms of Rates of Changes in Concentrations of Reactants or Products !(' p.1-"
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Example 13-2
aemoglobin (b) binds "ith carbon mono/ide according to the follo"ing e0uation +b 34
b+(4)3
5/press the rate of the reaction in terms of the rate of change in concentration of an! one of the reactants or the product. Ans!er
The rate of the reaction is expressed as8 Rate
137
=
d :&+ 4 !C%"3 9 dt
=
1 d :&+9 − × dt 4
=
1 d :C%9 − × dt 3
13.2 Expressions of Reactions Rates in Terms of Rates of Changes in Concentrations of Reactants or Products !(' p.1-"
Chec' oint 13&2
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5/press the rate of the follo"ing reaction in terms of the rate of change in concentration of an! one of the reactants or the product. 22(g) 42(g)
224(l)
Ans!er Rate ,
138
1 d :&2 %!l"9 dt 2
=
1 d :&2 !g"9 − dt 2
=−
d :% 2 ! g"9 dt
13.3 Methods of Measuring Reaction Rates !(' p.11"
Example 13-3A 6l7aline h!drol!sis of eth!l ethanoate (an ester) using sodium h!dro/ide solution is represented b! the follo"ing e0uation 34223(l) 8a4(a0) 3428a(a0) 324(a0) -he rate of the reaction can be follo"ed b! titrating small volumes of the reaction mi/ture "ith standard dilute h!drochloric acid at successive 9ve:minute intervals.
139
13.3 Methods of Measuring Reaction Rates !(' p.11"
Example 13-3A (a) uggest a method to 0uench the reaction mi/ture so that the concentration of sodium h!dro/ide solution can be determined accuratel!. 5/plain brieater. The cooling and dilution of the reaction mixture decrease the reaction rate sufficientl< for chemical anal
140
13.3 Methods of Measuring Reaction Rates !(' p.11"
Example 13-3A (b) 5/plain "h! the change in concentration of sodium h!dro/ide solution but not that of eth!l ethanoate is measured in order to determine the rate of the above reaction. Ans!er !+" (odium hith strong mineral acids almost instantaneousl<. Therefore? the titration of sodium h
141
13.3 Methods of Measuring Reaction Rates !(' p.11"
Ans!er
Example 13-3A
(c) 5/plain "hich option, 6 or =, is a reasonable set of e/perimental results for the above titration. 4ption 6 -ime after mi/ing >olume of l (min) added at the end point (cm3)
142
*
1
1
&
4ption =
-ime after mi/ing (min)
>olume of l added at the end point (cm3)
*
&
1
1
13.3 Methods of Measuring Reaction Rates !(' p.11"
Example 13-3A !c" (odium hith time? and hence the amount of dilute h
143
13.3 Methods of Measuring Reaction Rates !(' p.11"
Example 13-3A (d) 8ame a suitable indicator for the titration. !d" Meth
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144
Ans!er
13.3 Methods of Measuring Reaction Rates !(' p.13"
Example 13-3B 6 student recorded the follo"ing e/perimental results for the reaction of ?inc and dilute h!drochloric acid. @n(s) 2l(a0) -ime . 1. 2. 3. (min) >olume of 2(g) produce d (cm3) 145
@nl2(a0) 2(g) +. *. A. . &. %.
1* 2A 33 3&
+
+1 +2 +2 +2
13.3 Methods of Measuring Reaction Rates !(' p.13"
Example 13-3B (a) Blot a graph of volume of h!drogen gas produced against time.
Ans!er
!a"
146
13.3 Methods of Measuring Reaction Rates !(' p.13"
Example 13-3B (b) Cescribe the change in the rate of the reaction using !our graph in (a).
Ans!er
!+" s sho>n in the graph in !a"? the olume of heen the 1st and the 2nd minute" is greater than that near the end of the reaction !e.g. in the time interal +et>een the /th and the 6th minute". Therefore? the rate of the reaction decreases >ith time.
147
13.3 Methods of Measuring Reaction Rates !(' p.13"
Example 13-3B (c) 5/plain ho" !ou can measure the initial rate of the reaction graphicall!.
Ans!er
!c" The initial rate can +e found +< determining the slope of the tangent to the cure at time Aero.
148
13.3 Methods of Measuring Reaction Rates !(' p.13"
Example 13-3B
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(d) Cetermine graphicall! the rate of the reaction at the * th minute. tate the unit.
Ans!er !d" From the graph in !a"? rate of reaction , slope of the tangent to the cure at the ) minute 3 − !4/ 34" cm , !0 − 2" min
, 2 cm3 min1
149
13.3 Methods of Measuring Reaction Rates !(' p.1)"
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Chec' oint 13&3
uggest an e/perimental method for determining the rate of each of the follo"ing reactions (a) 24&2#(a0) 2$#(a0)
24+2#(a0) $2( a0)
(b) 3443(a0) $2(a0) 3442$(a0) $(a0) (c) 2Dn4+#(a0) *24+2#(a0) 1A(a0) 2Dn2(a0) 142(g) &24(l)
!a" Colorimetric measurement @ titration
(a0) !+" Colorimetric measurement 150
!c" Colorimetric mesurement @ titration
Ans!er
13.4 Factors ffecting Reaction Rates !(' p.16"
BetDs 4(in< 1
9:plain !hy sa!dust %urns e:plosively in pure o:ygen %ut slo!ly in air* higher concentration of ox
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151
Ans!er
13.4 Factors ffecting Reaction Rates !(' p.21"
Chec' oint 13& (a) Eist -F55 factors that aGect the rate of a chemical reaction.
Ans!er !a" Concentration of reactants @ pressure @ temperature @ surface area @ catal
152
13.4 Factors ffecting Reaction Rates !(' p.21"
Chec' oint 13& (b) -he 9gure belo" sho"s the laborator! set: up for measuring the change in mass of the reaction mi/ture "ith time in the course of the reaction a43(s) 2l(a0) 42(g)
153
al2(a0) 24(l)
