chemical kinetics - Állatorvostudományi egyetem · chemical kinetics kinetics is thearea of...
TRANSCRIPT
1
Chemical Kinetics
Kinetics is the area of physical chemistry concerned with the
- rate which a given chemical reaction occurs
- investigation of the reaction mechanisms
Practical aspects: processes in the living organisms and industry
A B
2
Rate of Chemical Reactions
The reaction rate is the change in amount or concentration (at fixed volume)
of a reactant or product in a given unit of time, e.g.
H2(g) + I2(g) 2 HI(g)
v = rate (velocity) of the reaction in moldm3s1
(a function of time)
d[H2]dt
= d[I2]
dtd[HI]2 dt
=v(t) =
[A] – concentration of A in mol/dm3
At a constant volume:
[A] = [A]2 [A]1 and = d if 0.
‹v› = [H2]t
- an average rate (a number)
3
Reaction Rate and Concentration
e.g. NH4NO2.aq N2(g) + 2 H2O
Determining the volume of nitrogen formed within a unit time, V(N2) in cm3/s:
if [NO2] then V(N2) keeping [NH4
+] const. with high conc. of NH4Cl
if [NH4+] then V(N2) keeping [NO2
] const. with high conc. of NaNO2
In quantitative form:
v = k [NH4+][NO2
], where k is the rate constant
reactants products
mechanism
4
v = k[A]a[B]b[C]c…
a, b, c, … reaction order for a given reactant A, B, C, …
a + b + c +… overall reaction order: sum of the exponents that
occur in the rate law
Rate Law
The k rate constant
- characteristic for each reaction
- depends on the temperature exclusively
Rate law: must be determined experimentally, it cannot be predicted
from the stoichiometry of the chemical equation.
The reaction rate is proportional to the concentrations of reactants:
5
2 N2O5 = 4 NO2 + O2 v = k1.[N2O5] first order
2 NOBr(g) = 2 NO(g) + Br2(g) v = k2.[NOBr]2 second order
CHCl3(g) + Cl2(g) = CCl4(g) + HCl(g)
v = k.[CHCl3].[Cl2]1/2 fractional (1.5) order (indicates radical mechanism)
3 CH3OH + 2 H2CrO4 + 6 HCl = 3 CH2O + 2 CrCl3 + 8 H2O
v = k4.[CH3OH].[H2CrO4].[HCl]2 fourth order
2 N2O(g) = 2 N2(g) + O2(g) v = k0 zeroth order(on the solid Pt wire)
H2(g) + I2(g) = 2 HI(g) v = k2.[H2].[I2] k2
’.[HI]2
H2(g) + Br2(g) = 2 HBr(g) v = (k.[H2].[Br2]1/2)/(k’ + [HBr]/[Br2])
Often the order cannot be determined (i.e. it has not got sense):
Examples
6
First order reactions:
v = - = k1[A]d[A]
dt
integration ofd[A]/[A] = - k1dt
ln[A]t = ln[A]0 – k1t
k1 = — ln1
t
[A]0
[A]t
First and Second Order Reactions
t
ln[A]t
tg = - k1
(unit: 1/s)
Second order reactions:
v = - = k2[A][B]d[A]
dt
if [A] = [B], so
v = - = k2[A]2d[A]dt
1/[A]t = 1/[A]0 + k2t
1/[A]t
1/[A]0
tg = k2
t
k2 = — ( — - — )1
t [A]t [A]0
1 1
(unit: dm3/mols)
integration ofd[A]/[A]2 = - k2dt
7
is the time required for the concentration (with fixed volume) of the reactant to
decrease to halfway between its initial and final values (i.e. the time for [A]0 ½[A]0).
Half-life (t1/2) of the Reactions
First order reaction:
independenton the initial concentration
t1/2 = ln 2k1
Second order reaction:
reciprocal dependenceon the initial concentration
t1/2 = 1k2[A]0
Generally for r order reaction: ax = b (a > 1, b > 0)
x = logab (loga1 = 0)
a = 2 lb, e ln, 10 log
8
Effective collision: produces chemically new substance(s)
Ineffective collision: the molecules rebound unchanged (elastic collision)
Collision Theory and Transition State
A2 + B2
A A
B B
2 AB
reactants
transition state(activated complex)
product(s)
E
reaction coordinate (progress of rxn.)
A2 + B2
2 AB
H
Ea Ea = energy of activation
H = enthalpy of reaction
9
The Arrhenius-equation
The rate increases exponentially withincreasing temperature
The activation energy, Ea
can be determined
k - rate constant; e = 2.7182 …
Ea - energy of activation (J/mol); T - abs. temperature (K)
A - constant (characteristic for the given reaction)
R = 8.314 J/molK - universal gas constant
10
Classification of Reactions
single step
unimolecular(CH3NC CH3CN)
bimolecular(CH3Br + OH CH3OH + Br)
termolecular(very rare)
H + H + H H2 + H
Molecularity of a single step in a reaction refers to the number of
molecules that participate in the step.
multistep
11
Multistep Reactions
Some subsequent steps e.g.
CO(g) + NO2(g) CO2(g) + NO(g)
Rate equation determined by experiments as v = k [NO2]2 in NO2.
The proposed mechanisms with NO3 intermediate:
1) NO2 + NO2NO3 + NO v1 = k.[NO2]2
2) NO3 + CO NO2 + CO2 v2 = k’.[NO3].[CO]
1) rate-determining (slow) step, rds with Ea1
2) fast step with Ea2 and Ea1 > Ea2
The overall rate of the multistep reactions
is determined by the slowest step.
12
rds
RDS
13
Catalysts
A catalyst is a substance that increases the rate of a chemical reaction
without being used up in the reaction. The catalyst:
- may be recovered unchanged at the end of the reaction (theoretically)
- small amount is enough to accelerate a reaction
- cannot initiate thermodynamically not allowed reactions
- opens a new path by which the reaction can take place
- lowers the energy of activation, Ea
Sugar burns in the presence of LiCl
14
Catalytic Action
15
- homogeneous: 2 H2O2 2 H2O + O2
Catalyst: Br2 (l)
H2O2 + Br2 2 HBr + O2
2 HBr + H2O2 Br2 + 2 H2O
Steps of the catalysed decomposition of H2O2
Homogeneous and Heterogeneous Catalysis
- heterogeneous:
2 SO2 + O2 2 SO3 catalyst: V2O5 (s)
CH2=CH2 + H2 CH3–CH3 catalyst: Pt (s)
The reactants are adsorbed on the surface of the catalyst via physisorption and/or
chemisorption (e.g. H2 2 H on Pt). The catalysts are finely dispersed solids having a
large specific surface area (m2/g).
16
Inhibitor („negative catalysts”; increases the Ea) e.g. antioxidants like flavonoids
retard the decomposition of food by oxidants.
Catalytic poison is a substance that inhibits the activity of catalyst by blocking its
„active site” (e.g. small amount of arsenic destroys the power of platinum to
catalyze the formation of SO3 from SO2).
In autocatalysis the reaction is accelerated by one of the reaction products, e.g.:
2 KMnO4 + 5 (COOH)2 + 3 H2SO4 = 2 MnSO4 + K2SO4 + 10 CO2 + 8 H2O
Mn2+ ions formed work catalytically
Autocatalysis
17
Michaels-Menten Kinetics of Enzymes
The KM 1/KS is dependent on both the enzyme
and the substrate, as well as conditions such as
temperature and pH.
18
19
Chemical Equilibrium
Reversible reactions can proceed in both directions, e.g.
N2 + 3 H2 2 NH3
2 NH3 N2 + 3 H2
in one equation: N2 + 3 H2 ⇌ 2 NH3
The double arrow (⇌) indicates that the reaction can be read in either direction
(do not use , that is for mesomeric structures only).
The equilibrium composition is independent of the direction from which it is
approached. It is macroscopically static, but is microscopically dynamic.
20
In general for any reversible reaction:
a A + b B ⇌ c C + d D
K - equilibrium constant in (mol/dm3)n, where n = 0, 1, 2, …
- independent on the concentrations
- depends on the temperature
[C], [D], [A], [B] - concentrations are in equilibrium state in mol/dm3
by convention the concentrations of the
- products in numerator (right side)
- reactants in denominator (left side)
K = [C]c [D]d
[A]a [B]b
Law of Mass Action
21
All reversible processes tend to reach an equilibrium state and the
concentration of all substances involved remain constant.
rates of opposing (i.e. forward and reverse) reactions are equal: kfor = krev
phases of all reacting components can be same or different.
Homogeneous equilibria, e.g.
gas-phase reactions: H2(g) + I2(g) ⇌ 2 HI(g) at 440 oC
or the metal-complex formation in water (see Complex Compounds):
βn = K1. K2
. K3 ... KnMLn-1 + L ⇌ MLn
[MLn]
[MLn-1][L]Kn =
[MLn]
[M][L]n=
where n = 1 – 9 unit is dm3/mol unit is (dm3/mol)n
Homogeneous Equilibria
22
Equilibria between substances in two or more phases, e.g.
CaCO3(s) ⇌ CaO(s) + CO2(g)
Concentrations of pure solids and liquids are constant by definition:
[CaO] = a and [CaCO3] = b
K’ = [CO2] K = [CaO][CO2]
[CaCO3]=
a[CO2]
b
Irrespective the relative amounts of CaO and
CaCO3, at a given temperature the equilibrium
concentration of CO2 over a mixture of the solids is
a definite value.
Heterogeneous Equilibria
23
In saturated solutions with a solid substances a dynamic equilibrium is attained:
dissolution ⇌ precipitation (mostly applied for slightly soluble compounds), e.g.:
[AgCl] [Ag+][Cl]
K =
AgCl(s) ⇌ Ag+ + Clas [AgCl] is constant, K[AgCl] = [Ag+][Cl], so
Ksp = K[AgCl] = [Ag+][Cl] - solubility product of AgCl
Generally for a MxAy compound:
Ksp = [My+]x[Ax]y
in (mol/dm3)x+y
The Solubility Product
saturated solution of AgCl:Ag+ and CI ions
solid AgCl
24
Substance Ksp
AgCl 1.7 10-10
AgBr 5.0 10-13
AgI 8.5 10-17
Ag2CrO4 1.9 10-12
CaCO3 4.7 10-9
BaCO3 1.6 10-9
PbCl2 1.7 10-5
PbS 7.0 10-27
HgS 1.6 10-54
NaCl 37.2
The Solubility Product
Calculation of solubility, s from Ksp
PbCl2(s) ⇌ Pb2+ + 2 Cl
25
A system in equilibrium reacts to a change (stress) in conditions in a way that
counteracts the applied change and establishes a new equilibrium. Each change in
the conditions (concentration, temperature, etc.) should be considered a stress.
Henry Louis Le Chatelier(1850-1936)
Karl Ferdinand Braun(1850-1918)
The Le Chatelier - Braun Principle
26
Equilibrium Constant and Temperature
- exothermic forward reaction: N2 + 3 H2 ⇌ 2 NH3 ΔH = 92 kJ
[H2]3[N2]
[NH3]2
K =Temperature, oC
300 9.6400 0.5500 0.06600 0.014
If the temperature of the system
is raised, the position of the
equilibrium will shift to the left.
- endothermic forward reaction: H2 + CO2 ⇌ H2O + CO ΔH = + 41 kJ
[H2][CO2]
[CO][H2O] K =Temperature, oC
700 0.63800 0.93900 1.29
1000 1.66
If the temperature of the systemis raised, the position of the equilibrium will shift to the right.
27
System Change Result
N2 + 3 H2 ⇌ 2 NH3
4 moles → 2 moles
increase (partial) pressureby decreasing volume
Shift to the right. Counteracting the pressure increase by shifting to the side with fewer moles of gas that exert less pressure.
H2(g) + I2(g) ⇌ 2 HI(g) some argon gas is added No change since Ar is not a component of this reaction system.
NaCl(s) + H2SO4(l) ⇌ NaHSO4(s) +HCl(g)
reaction is carried out in an open container
Because HCl is a gas that can escape from the system, the reaction is forced to the right.
HCN(aq) ⇌ H+(aq) + CN–(aq)
HCN + H2O ⇌ H+(aq) + CN–(aq)
the solution is diluted Shift to right; the „reactant” concentration is increased
AgCl(s) ⇌ Ag+(aq) + Cl–(aq) some NaCl is added to the solution
Shift to left due to increase in Cl
concentration. This is known as the common ion effect on solubility.
2 H2O2 ⇌ 2 H2O + O2 a catalyst is added to speed up this reaction
No change. Catalysts affect only the rate of a reaction; the have no effect at all on the composition of the equilibrium state.