chemical kinetics type 1

32 Pages·2011·0.77 MB·English

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Subject : CHEMISTRY
Topic : CHEMICAL EQULIBRIUM
R
Index
1. Key Concepts
2. Exercise I
3. Exercise II
4. Exercise III
5. Exercise IV
6. Answer Key
7. 34 Yrs. Que. from IIT-JEE
8. 10 Yrs. Que. from AIEEE
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THE KEY
M
CHEMICAL KINETICS : U
RI
It is a branch of physical chemistry deals with the "Rate of Chemical Reactions" including the effect of
B
I
temperature, pressure, concentration, etc., on the rates, and the mechanism by which the reaction takes place. L
I
U
Q
RATE OF CHEMICAL REACTION is defined as the change in concentration of a reactant (or a product) in E
M.
a particular time interval. Average rate of reaction, Instantaneous rate of reaction.
E
Units of Reaction Rate are unit of concentration divided by the unit of time (mol L–1s–1 or H
C
mol L–1min–1 or so on). 32
FACTORS AFFECTING REACTION RATES : 2 of
e
(i) Concentration of reactants and ag
P
(ii) Reaction temperature
Besides these, presence of catalyst and surface area (if a reactant or a catalyst is a solid) exposure to
radiation also affect the reaction rates.
L
A
mEXPRESSIONS OR THE RATE : P
O
o For a general reaction : aA + bB → cC + dD, H
s.c B
sse The rate of disappearance of A = – d[A] ; Rate of disappearance of B = – d[B] ; 1 ,
a dt dt 8
l 8
c 8
o 5
k d[C] d[D] 0
e Rate of appearance of C = & Rate of appearance of D = . 3
w.t dt dt 89
ww The positive sign shows that concentrations of C and D increases with time and the negative sign indicating 0 9
that concentrations of A and B decrease with time.Thus the rate of general reaction. 0,
te: 1 d[A] 1 d[B] 1 d[C] 1 d[D] 00
si rate : – = – = = . 0
b a dt b dt c dt d dt 0
weRATE EQUATION AND RATE CONSTANT : 32
m An expression which relates the rate of a reaction to the concentration of the reactants is called the Rate 5)-
o 5
r Equation or Rate Law. Rate ∝ [A]a · [B]b or Rate = k [A]a [B]b. The constant of proportionality, k is 7
f 0
ge known as the Rate Constant (specific reaction rate) and may be defined as the rate at unit concentrations H: (
a
k of the reactants. k depends on the temperature and is independent of the initial concentrations of the P
c )
Pa reactants. At a fixed temperature, k is constant characteristic of the reaction. Larger value of k indicates fast Sir
y reaction and small k indicates slow reactions. K.
udMOLECULARITY : R.
St S.
d Molecularity of a reaction is defined as the numbers of particles (atoms, ions, groups or molecules) of A (
a reactants actually taking part in a single step chemical reaction. Y
o I
l R
n
wMolecularity of a reaction is : A
K
Do(i) Always a whole number (not zero) and never a fraction. R.
E (ii) The value of molecularity of a simple or one step reaction does not exceed 3. G
E A
H
RORDER OF REACTION : U
F S
Ietx ipse driemfiennetda lalys dtheete srummin oefd t rhaet ee exqpuoanteionntss .(powers) of the molar concentrations of the reactants in the or :
t
If rate of reaction α [A]p [B]q [C]r or Rate of reaction = k [A]p [B]q [C]r ec
r
order of reaction = p + q + r & the order w.r.t. A, B & C are p, q & r respectively. Di
For a "Reaction of nth order", the order of the reaction is n and the rate equation (or Rate law) is S,
E
rate ∝ [A]n = k [A]n. S
S
The order of a reaction is obtained from the experimentally determined rate (and not from the stoichiometric A
L
C
equation) and may be zero, an integer or a fraction and never exceeds 3. In a multi-step complex O
reaction, the order of the reaction depends on the slowest step. K
E
T
ZERO ORDER REACTION :
M
A reaction is said to be of zero order if the rate is independent of the concentration of the reactants.
U
A → products ; Rate α k [A]° = k mol L–1 s–1 RI
B
I
L
EXAMPLES : I
U
Q
(i) H (g) + Cl (g) hν→ 2HCl (g) (ii) N O(g) hotPt.→ N (g) + 1 O (g) M. E
2 2 2 Surface 2 2 2 E
H
(iii) 2NH (g) MoorW→ N + 3H (iv) 2HI (g) Au→ H (g) + I (g) C
3 surface 2 2 surface 2 2 32
of
CHARACTERISTICS OF ZERO ORDER REACTION : e 3
g
(1) Concentration of reactant decreases lineraly with time. [A] = [A] – kt. Pa
t 0
(2) Units of k are, mol l–1 time–1.
[A] 0.5[A]
(3) Time required for the completion of reaction t = 0 & t = 0 L
k 1/2 k A
m P
FIRST ORDER REACTION : O
o H
s.c A reaction is said to be of first order if its rate is proportinal to the concentration of one reactant only. B
sse A → Products. 1 ,
cla at time t = 0 a (or C0) 0 888
o at time t = t a – x (or C) x 5
k t 0
e 3
w.t Rate α [A] = k [A] or dx = k (a – x) (1 st order differntial equation) 89
w 1 dt 1 9
w 0
e: Integrated 1 st order rate equation is k1 = 2.3t03loga−ax . 00,
t 0
si 0
b Exponential form of 1 st order equation is C = C e−k1t 0
we t 0 2
3
m Characteristics Of First Order Reaction : )-
5
ro(1) Unit of rate constant is time–1. 75
f 0
ge (2) Change in concentration unit will not change the numerical value of k1. H: (
ka 0.693 1 P
c(3) t = (Half-life); Average life = ; )
Pa 1/2 k1 k Sir
y k K.
ud(4) log (a – x) v/s t is a straight line with slope − 2.3103. R.
St S.
d EXAMPLES : A (
a Y
lo(i) Radioactive disintegration is a first order reaction. RI
n
A
w
Do(ii) C12H22O11 + H2O H+catalysedhydrolysis→ C6H12O6 + C6H12O6. R. K
E Inversion G
E (glucose) (fructose) A
H
R(iii) Mineral acid catalyzed hydrolysis of esters. U
F S
(iv) Decomposition of H2O2 in aqueous solution. r :
o
SECOND ORDER REACTION : ct
e
r
(i) When two molecules of the same reactant are involved or the concentrations of the both reactants are Di
equal reactions 2A → products or A + B → products. S,
E
S
dx S
Differential rate equation = k (a – x )2 A
dt 2 L
C
1 x 1 1 O
Integrated rate equation k = . or k t = − . K
2 t a(a−x) 2 a−x a E
T
(ii) When the initial concentrations of the two reactants are different;
M
A +B → products
U
a b RI
B
I
dx L
I
differential rate equation =k (a – x) (b – x). U
dt 2 Q
E
2.303 b(a−x) M.
Integrated rate equation k2 = t(a−b)log10 a(b−x) HE
C
CHARACTERISTICS OF SECOND ORDER REACTION : 32
of
(i) Unit of rate constant L mol–1 time –1. e 4
g
(ii) Numerical value of k will depend upon unit of concentration. Pa
(iii) t α a–1 (In general t α a(1–n); n = order of reactions).
1/2 1/2
(iv) 2nd order reaction conforms to first order when one of the reactant in excess.
L
EXAMPLES : A
m P
O
o(i) Saponification (hydrolysis of esters catalysed with alkali). H
asses.c(ii) CHHyd3rCoOgeOnCat2ioHn5 o+f eNthaaOnHe CH→ +C HH3CO10O0°NCa→ +C CH2H.5OH 81 , B
l 2 4 2 2 6 8
c 8
o(iii) 2 O → 3 O . 5
k 3 2 0
e 3
w.tnth ORDER REACTION. 89
w 9
w A → Product 0
e: 1  1 1  00,
t k t =  −  [n ≠ 1, n = order] 0
si n n−1(a−x)n−1 an−1 0
b 0
we 2
m t = 1 .2n−1−1 5)- 3
ro 1/2 kn(n−1)  an−1  75
f 0
ge SIDE OR CONCURENT REACTION : H: (
a
k P
udy Pac ; ln [[AA]]0t = (k1 + k2) t ; [[CB]]=kk12 R. K. Sir)
StCONSECUTIVE REACTION : S.
wnload A k1→ B k2→ C ; tmax = (k1−1k2) lnkk12 ; [B]max = [A]0 kk2 k1k−2k2 KARIYA (
Do 1 R.
E THRESHOLD ENERGY AND ACTIVATION ENERGY : G
E For a reaction to take place the reacting molecules must colloid together, but only those collisions, in HA
R U
F which colliding molecules possess certain minimum energy is called threshold energy (E ). S
ACTIVATION ENERGY (E ) : T r :
a to
The extra energy needed for the reactant molecules to be able to react chemically is known as Activation c
e
r
energy. Di
E = Threshold energy S,
T E
E = Activation energy of forward reaction S
a S
E' = activation energy of backward reaction A
a L
P = Potential energy of reactants C
1 O
P = Potential energy of products K
2 E
T
INFLUENCE OF TEMPERATURE ON REACTION RATES :
M
TEMPERATURE COEFFICIENT : U
RI
The temperature coefficient of a chemical reaction is defined as the ratio of the reaction rates at two B
I
L
temperatures differing by 10°C. Its value usually lies between 2 & 3. I
U
Q
k E
Temperature coefficient = t+10 . M.
kt HE
ARRHENIUS EQUATION : C
2
3
A quantitative relationship was proposed by Arrhenius k = A. e–Ea/RT Where, of
5
k = rate constant ; A = frequency factor (or pre – exponential factor); e
g
a
R = gas constant ; T = Temperature (kelvin) ; E =Activation energy. P
a
k E  1 1  d E
The Logarithmic expressions are log 2 = a  −  ;Vant Hoff 's Isochore lnk = a
10 k 2.303R T T  dt RT2 L
1 1 2 A
mGRAPHICAL REPRESENTATIONS ARE : OP
o H
s.c B
sse 1 ,
a 8
l 8
c 8
o 5
k 0
e 3
w.t 89
w 9
w 0
METHODS OF DETERMINATION OF ORDER OF REACTIONS : 0,
e:A few methods commonly used are given below : 0
t 0
si1. Hit & Trial Method : It is method of using integrated rate equations, where the experimental values of 0
b 0
we a, x & t are put into these equations. One which gives a constant value of k for different sets of a, x & t 2
3
m correspond to the order of the reaction. )-
5
o 5
r2. Graphical Method : 7
f 0
ge (i) A plot of log (a – x) versus 't' gives a straight lines for the First order reaction. H: (
a
k(ii) A plot of (a – x)– (n–1) versus 't' gives a straight line any reaction of the order n (except n = 1). P
c )
Pa 1n Sir
udy 3. Half Life Method : The half life of different order of reactions is given by an = 2 a0. R. K.
St By experimental observation of the dependence of half life on initial concentration we can determine n, S.
nload the order of reaction. n = 1 + llooggat12−−llooggat12 . RIYA (
A
w4. Initial rate method. Initial rate method is used to determine the order or reaction in cases where more K
Do than one reactant is used. It involves the determination of the order of different reactants separately. A R.
E series of experiments are performed in which concentration of one particular reactant is varied whereas G
E A
H
R conc. of other reactants are kept constant. In each experiment the initial rate is determined from the plot U
F S
orefa ccotinocn. ivs sl.. time, e.g., if conc. of A is doubled, and initial rate of reaction is also doubled, order of or :
t
MECHANISM OF REACTIONS : ec
r
Di
The path way which reactants are converted into the products is called the reaction mechanism. It should
S,
be clear that experimentally determined rate expression cannot be predicted from the stiochiometry of E
S
the reaction. For example for the reaction ; S
d A
NO (g) + CO (g) → CO (g) + NO(g), the rate expression is ; rate = − [NO ] = k[NO ]2 , L
2 2 dt 2 2 C
i.e. the expression has no dependence of CO (g) concentration. O
K
E
T
The reason is that the reaction occurs by a series of elementary steps.
M
The sequence of elementary processes leading to the overall stiochiometry is known as the "Mechanism
U
of the reaction". A in a sequence of reactions leading to the formation of products from reactants, the RI
n B
slowest step is the rate determining step. LI
I
U
The mechanism proposed for the above reaction is a two step one.
Q
E
NO2 + NO2 → NO + NO3 (step 1 : slow) M.
NO + CO → CO + NO (step 2 : fast) E
3 2 2 H
The sum of the two gives the stiochiometry & the slow step decided the rate expression. C
2
Nuclear Chemistry of 3
6
Neutron / proton ratio and stability e
g
a
(cid:1) P
For atomic number < 20, most stable nuclei have n: p ratio nearly
1 : 1 (except H & Ar).
(cid:1)
L
For n/p ratio > 1.5, nucleus is unstable. Largest stable nucleus is A
m P
O
o 209Bi for which n/p ratio is 1.52. H
s.c(cid:1) 83 B
sse For atomic number > 83, there are no stable nuclei. 1 ,
laMagic numbers and nuclear stability 88
c 8
oNuclei with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons are unusually stable and have a larger number of 5
k 0
estable isotopes than neighboring nuclei in the periodic table. These numbers are called magic numbers. They are 3
w.tsupposed to represent completely filled nuclear shells of energy levels. 89
w 9
w(cid:1) 0
Nuclei with magic number of protons as well as neutrons have notably high stabilities. 0,
site:(cid:1) [eg. 42He ,186O,4200Ca and 82208 Pb ]. 165 such stable nuclei are known. 0 00
b 0
we There exist 55 known nuclei with even number of protons and odd number of neutrons, and 50 known 2
3
m stable nuclei with odd number of protons and even number of neutrons. On the other hand, the number )-
5
o of known stable nuclei having odd numbers of both neutrons and protons is only 4. 5
r 7
ge fE1.xpectend/p e rmaitsiosi oanbos vfreo smta buinlisttya bbellet :n eulcelceturosn (β−) or neutron. H: (0
a
k P
c2. n/p ratio below stability belt: positron (β+) or K capture. )
Pa3. Atomic number > 83, various particles, including α−particles. Sir
y Radioactive decay K.
ud R.
St(cid:1) dN S.
ad Radioactive decay is a first order process. Hence − dt = λN or N = N0 e−λt YA (
lo where N = number of radioactive nuclei at any time t ; N= number of radioactive nuclei at t = 0 ; λ = decay RI
n
0 A
w constant. K
Do dN R.
EE (cid:1) Activity activity (a) = − dt = λN AG
H
R U
F S.I. units : disintegration per second (symbol s−1 or dps). This unit is also called becquerel (symbol Bq) S
Other units: Curie (Ci) 1Ci = 3.7 × 1010dps. r :
o
t
(cid:1) c
e
Half life (t ) The time taken by half the nuclei (originally present) to decay. t = 0.693/λ r
½ ½ Di
1
Note : After n half−lives have passed, activity is reduced to of its initial value. S,
2n E
(cid:1) S
Average life (t ) t = 1/λ = 1.44 t S
av av ½ A
L
Isotopes : Nuclei with same atomic number but different atomic mass number. C
Isobars : Nuclei with different atomic number but same atomic mass number. O
K
Isotones : Nuclei with same number of neutrons but different number of protons. E
T
THE ATLAS
M
U
RI
B
I
L
I
U
Q
E
M.
E
H
C
2
3
of
7
e
g
a
P
L
A
m P
O
o H
s.c B
sse 1 ,
a 8
l 8
c 8
o 5
k 0
e 3
w.t 89
w 9
w 0
0,
e: 0
t 0
si 0
b 0
we 2
3
m )-
5
o 5
r 7
f 0
ge H: (
a
k P
c )
Pa Sir
y K.
ud R.
St S.
d A (
a Y
o I
l R
n
A
w
K
Do R.
E G
E A
H
R U
F S
r :
o
t
c
e
r
Di
S,
E
S
S
A
L
C
O
K
E
T
GLOSSARY
M
U
IMPORTANT TERMS AND DEFINITIONS RI
B
1. Rate of reaction. It is defined as the change in concentration of reactant (or product) in a particular I
L
I
time interval. Its unit is mol L–1s–1. If time is in minutes, then units are mol L–1 min–1 and so on. U
Q
2. Average rate. The rate of reaction measured over a long time interval is called average rate of reaction. E
M.
It is equal to ∆x/∆t as shown in fig.(a) and (b). E
H
C
2
3
of
8
e
g
a
P
L
A
m P
O
o H
s.c B
sse 1 ,
la Instantaneous and average rate of reaction 88
c 8
o3. Instantaneous rate. It is the rate of reaction when the average rate is taken over a very small interval of 5
k 0
e time. It is equal to dx / dt as shown in fig. (a) and (b). 3
w.t4. Rate law or rate equation. It is the expression which relates the rate of reaction with concentration of 89
w 9
w the reactants. The constant of proportionality 'k' is known as rate constant. 0
5. Rate constant. When concentration of both reactants are unity, then the rate of reaction is known as 0,
e: 0
t rate constant. It is also called specific reaction rate. 0
si 0
b6. Molecularity. Total number of molecules of the reactants involved in the reaction is termed as its 0
we molecularity. It is always in whole number, It is never more than three. It cannot be zero. 32
m 7. Order of a reaction. The sum of the powers of the concentration of reactants in the rate law is termed 5)-
o 5
r as order of the reaction. It can be in fraction. It can be zero also. 7
f 0
ge 8. Zero order reaction. The rate of reaction does not change with the concentration of the reactants, H: (
a
k i.e., rate = k[A] ° P
c )
Pa9. First order reaction. The reaction in which the rate of reaction is directly proportional to the concentration Sir
y of reacting substance. Rate constant of first order reaction is K.
ud R.
St 2.303 a 2.303 [A0] S.
d k = t log a−x or k = t log [A] A (
a Y
lo where 'a' is initial concentration, (a–x) is the conc. of reactants after time 't'. The unit of 'k' is s–1 or RI
n
A
w min–1. A plot between ln [A] vs. t is a straight line with slope equal to –k. [A] is concentration of reactants K
Do after time t. R.
E G
E10. Half–life of a reaction. The time taken for a reaction when half of the starting material has reacted is A
H
R called half–life of a reaction. For first order reaction U
F S
t = 0.693, where k is rate constant. or :
1/2 k ct
e
11. Second order reaction. The reaction in which sum of powers of concentration terms in rate law or rate r
Di
equation is equal to 2, e.g., S,
E
dx S
=k[A]1[B]1 AS
dt L
C
O
K
E
T
12. Third order reaction. The reaction in which sum of powers of concentration terms in rate law or rate
M
equation is equal to 3, e.g.,
U
RI
dx B
=k[A]x[B]y where x + y = 3 LI
dt UI
Q
13. Specific rate constant (k). It is defined as equal to rate of reaction when molar concentration of E
reactant is unity. M.
E
14. Activation energy. It is extra energy which must be possessed by reactant molecules so that collision H
C
between reactant molecules is effective and leads to formation of product molecules. 2
3
15. Initial rate. The rate at the beginning of the reaction when the concentrations have not changed 9 of
e
appreciably is called in initial rate of reaction. g
a
P
16. Arrhenius equation of reaction rate. It gives the relation between rate of reaction and temperature.
K =Ae−Ea/RT
where k = rate constant A = frequency factor, E = energy of activation L
A
m R = gas constant, T = temperature in kealvin. OP
o H
s.c ln k = ln A – Ea/RT B
sse E 1 ,
a log k = log A – a 8
cl 2.303RT 88
o 5
ek17. Photochemical reactions. Those reactions which take place in the presence of light are called 30
w.t photochemical reactions. Photosynthesis is an example of photochemical reaction. 89
w 9
w18. Photosensitization. The process in which a molecule that absorbs light transfers its extra energy to 0
another molecule which may undergo a reaction. This process is called photosensitization. 0,
e:19. Chain reaction. The sequence of reactions, where a reactive species produces more reactive species is 0
t 0
si called chain reaction. It involves free radicals. 0
b 0
we20. Elementary processes. Some reactions occur by a series of elementary steps and such simple steps 2
3
m are called elementary processes. )-
5
ro21. Mechanism of reaction. The sequence of elementary processes leading to the overall stiochiometry of 75
f 0
ge a chemical reaction is known as mechanism of a reaction. H: (
a22. Slow reaction. Those reactions which take place very slowly are called slow reactions, e.g., rusting of
k P
y Pac23. Liroifne atnimd ere. aTchteio tnim oef oinx awlihci cahc i9d8 w%it oh fa tchied irfeieadc tKioMn insO co4 amt prloeotem i st ecmalpleedr alitfuerteim aere. slow reactions. K. Sir)
ud24. Threshold energy. The minimum energy that reacting species must possess in order to undergo effective R.
St collision to form product molecules is called threshold energy. S.
d 25. Effective collision (f). Those collisions which lead to the formation of product molecules are called A (
a Y
o effective collisions. Rate of reaction = f × z where 'z' is collision frequency and 'f' is fraction of collisions, I
l R
n
w which are effective. A
K
Do26. Collision frequency (z). It is defined as total number of collisions per unit volume per unit time. R.
E 27. Activated complex. It is defined as unstable intermediate formed between reacting molecules which is G
E A
highly unstable and readily changes into product. H
R U
F28. Thermodynamic stability. A mixture of substances may not undergo reaction although thermodynamic S
predict the reaction to be spontaneous. Such substances are thermodynamically unstable at ordinary r :
o
temperature but may not be kinetically unstable. ct
e
29. Kinetic stability. The reaction occurs only when the reactant crosses energy–barrier. Once it occurs, it Dir
becomes kinetically unstable because the reaction is spontaneous. The energy evolved helps the other S,
E
reactants to cross energy–barrier. Thus, reactants should be thermodynamically as well as kinetically S
S
unstable so as to change into products at a particular temperature. A
L
C
O
K
E
T
30. Rate determining step. The slowest step in the reaction mechanism is called rate determining step.
M
U
I
31. Temperature coefficient. It is the ratio of rate constant at temperature 308 K to the rate constant at R
B
temperature 298 K. LI
I
U
Rate constant 'k'at 308 K Q
E
Temperature coefficient = Rate constant 'k'at 298 K M.
E
H
It lies between 2 and 3. C
2
32. Pseudo first order reaction. The reaction in which one reacted is in excess so order is one is called 3
of
Pseudo first order reaction, e.g., acidic hydrolysis of ester. 0
1
e
CH COOC H + H O (excess) CH COOH + C H OH ag
3 2 5 2 3 2 5 P
33. Einstein's law of photochemical equivalence. Each atom or molecule is activated by 1 photon (quantum
of light).
34. Chain initiation step. The step in which neutral molecule changes into free radicals by absorbing L
A
m photons is called chain initiation step. OP
o H
s.c35. Chain propagation step. The step in which free radical reacts with neutral molecule to form a neutral B
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a36. Chain termination step. The step in which radicals combine to form neutral molecules. 8
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o37. Fast reactions. Those reactions which occur instantaneously and is complete in fraction of seconds are 5
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w.t38. Thermochemical reactions. Th3ose reactions initiated by heat energ3y are called thermochemical 89
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