This document contains detailed design procedure for a RCC frame building. Analysis and design has been carried out for gravity loading as well as earthquake loading.Descripción completa
This document contains detailed design procedure for a RCC frame building. Analysis and design has been carried out for gravity loading as well as earthquake loading.Full description
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GENERAL CHEMISTRY Principles and Modern Applications PETRUCCI
HERRING
MADURA
Chemical Kinetics PHILIP DUTTON UNIVERSITY OF WINDSOR DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY
TENTH EDITION
BISSONNETTE
14
Chemical Kinetics
Chemical Kinetics
Chemical Kinetics
14-1 The Rate of a Chemical Reaction
Rate of change of concentration with time. 2 Fe3+(aq) + Sn2+ → 2 Fe2+(aq) + Sn4+(aq) [Fe2+] = 0.0010 M
t = t = 38.5 s Δt = t =
38.5 s
Δ[Fe2+]
Rate of formation of Fe2+=
= (0.0010 – 0) M
Δ[Fe2+] Δt
=
0.0010 M 38.5 s
= 2.6×10-5 M s-1
2 Fe3+(aq) + Sn2+ → 2 Fe2+(aq) + Sn4+(aq)
Δ[Sn4+] Δt
=
1
Δ[Fe2+]
2
Δt
= -
1
Δ[Fe3+]
2
Δt
General Rate of Reaction a A + b B → g G + h H Rate of reaction = negative of rate of disappearance of reactants =-
1 a
Δ[A] Δt
=-
1 b
Δ[B] Δt
= rate of appearance of products 1 = g
Δ[G] Δt
1 = h
Δ[H] Δt
14-2 Measuring Reaction Rates
H2O2(aq) → H2O(l) + ½ O2(g) Measure the rate by monitoring O 2 volume or by chemical analysis of aliquots
Initial Rate of Reaction -(-2.32 M / 1360 s) = 1.71
× 10 M s -3
-1
Rate =
-Δ[H2O2] Δt
-(-1.7 M / 2800 s) =
Rate of Reaction at time t
6.1 × 10-4 M s-1
FIGURE 14-2 Graphical representation of kinetic data for the reaction H 2O2(aq)
→
H2O(l) + ½ O2(g)
14-3 Effect of Concentration on Reaction Rates: The Rate Law
a A + b B …. → g G + h H ….
rate of reaction = k [A]m[B]n …. Rate constant = k Overall order of reaction = m + n + ….
Method of Initial Rates 2 HgCl2(aq) + C2O42-(aq)
2 Cl-(aq) + 2 CO2(g) + Hg2Cl2(s)
rate of reaction = k[HgCl 2]m[C2O42-]n
General effect of doubling the initial concentration of a particular reactant (with other reactant concentrations held constant). • Zero order in the reactant —there is no effect on the initial rate of reaction. • First order in the reactant —the initial rate of reaction doubles. • Second order in the reactant —the initial rate of reaction quadruples. • Third order in the reactant —the initial rate of reaction increases eightfold.
FIGURE 14-5 Decomposition of di-t-butyl peroxide (DTBP) at 147°C
14-6 Second-Order Reactions Rate law where sum of exponents m + n +… = 2 A → products d[A] dt
= -k [A]2 [A]t
∫ [A]0
d[A] [A]2
[k ] = M-1 s-1 = L mol-1 s-1 t
= - ∫ k dt 0
1 1 = kt + [A]t [A]0
FIGURE 14-6 A straight-line plot for the second order reaction A
products
Pseudo First-Order Reactions Simplify the kinetics of complex reactions. Rate laws become easier to work with. CH3CO2C2H5 + H2O → CH3CO2H + C2H5OH
• If the concentration of water does not change appreciably during the reaction. Rate law appears to be first order.
• Hold one or more reactants constant by using high concentrations use a low concentration of the reactant under study.
14-7 Reaction Kinetics: A Summary Calculate the rate of a reaction from a known rate law using: Rate of reaction = k [A] m[B]n ….
Determine the instantaneous rate of the reaction by: Finding the slope of the tangent line of [A] vs t or, Evaluate – Δ[A]/Δt , with a short Δt interval.
Determine the order of reaction by: Using the method of initial rates. Find the graph that yields a straight line. Test for the half-life to find first order reactions. Substitute data into integrated rate laws to find the rate law that gives a consistent value of k.
Find the rate constant k by: Determining the slope of a straight line graph. Evaluating k with the integrated rate law. Measuring the half life of first-order reactions. Find reactant concentrations or times for certain conditions using the integrated rate law after determining k.
14-8 Theoretical Models for Chemical Kinetics Collision Theory Kinetic-Molecular theory can be used to calculate the collision frequency. In gases 1030 collisions per second. If each collision produced a reaction, the rate would be about 106 M s-1. Actual rates are on the order of 10 4 M s-1. Still a very rapid rate. Only a fraction of collisions yield a reaction.
FIGURE 14-8 Distribution of molecular kinetic energies
Collision Theory If activation barrier is high, only a few molecules have sufficient kinetic energy and the reaction is slower. As temperature increases, reaction rate increases. Orientation of molecules may be important.
FIGURE 14-9 Molecular collisions and chemical reactions
For a reaction to occur there must be a redistribution of energy sufficient to break certain bonds in the reacting molecule(s). Activation Energy: The minimum energy above the average kinetic energy that molecules must bring to their collisions for a chemical reaction to occur.
FIGURE 14-11 An analogy for a reaction profile and activation energy
Transition State Theory
FIGURE 14-10 A reaction profile for the reaction N 2O(g) + NO(g)
N 2(g) + NO 2(g)
14-9 Effect of Temperature on Reaction Rates
Svante Arrhenius
k = Ae-E a /RT ln k = - Ea 1 + ln A R T
ln k =
k = Ae-E a /RT
ln k 2 – ln k 1 =
ln
k 1 k 2
- E a
1
R
T 2
=
- E a
1
R
T
+ ln A -
- E a
1
R
T 2
-
+ ln A
- E a
1
R
T 1
1 T 1
- ln A
N2O5(CCl4) → N2O4(CCl4) + ½ O2(g)
- E a
= -1.2×104 K
R - E a = 1.0×102 kJ mol-1
FIGURE 14-12 Temperature dependence of the rate constant k for a reaction
14-10 Reaction Mechanisms
Step-by-step description of a reaction. Each step is called an elementary process. Any molecular event that significantly alters a molecules energy of geometry or produces a new molecule.
Reaction mechanism must be consistent with: Stoichiometry for the overall reaction. The experimentally determined rate law.
Elementary Processes Unimolecular or bimolecular. Exponents for concentration terms are the same as the stoichiometric factors for the elementary process.
Elementary processes are reversible. Intermediates are produced in one elementary process and consumed in another.
One elementary step is usually slower than all the others and is known as the rate determining step.
A mechanism with a Slow Step Followed by a Fast Step H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g)
d[ P ] dt
= k [H2][ICl]
Postulate a mechanism: H2(g) + ICl(g) HI(g) + ICl(g)
slow
fast
d[HI] HI(g) + HCl(g) I2(g) + HCl(g)
H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g)
dt d[I2] dt d[P] dt
= k [H2][ICl] = k [HI][ICl]
= k [H2][ICl]
FIGURE 14-14 A reaction profile for a two-step mechanism
A Mechanism with a Fast Reversible First Step Followed by as Slow Step 2NO(g) + O2(g) → 2 NO2(g)
d[ P ] dt
= -k obs[NO]2[O2]
Postulate a mechanism: fast
2NO(g) K =
slow
k 1 k -1
k 1 k -1
=
N2O2(g)
[N2O2] =
k 1 k -1
[NO]2 = K [NO]2
[N2O2] [NO]
N2O2(g) + O2(g)
k 2
2NO2(g)
2NO(g) + O2(g) → 2 NO2(g)
d[NO2] dt
= k 2[N2O2][O2]
d[NO2] k = k 2 1 [NO]2[O2] dt k -1
The Steady State Approximation 2NO(g)
k 1
2NO(g)
k -1
N2O2(g) + O2(g)
N2O2(g)
2NO(g)
N2O2(g)
N2O2(g)
k 3
2NO2(g)
d[NO2] dt d[N2O2] dt
k 1 k -1
N2O2(g) + O2(g)
N2O2(g) 2NO(g) k 3
2NO2(g)
= k 3[N2O2][O2]
= k 1[NO]2 – k -1[N2O2] – k 3[N2O2][O2] = 0
The Steady State Approximation d[N2O2] dt
= k 1[NO]2 – k -1[N2O2] – k 2[N2O2][O2] = 0 k 1[NO]2 = [N2O2](k -1 + k 2[O2])
[N2O2] =
d[NO2] dt
k 1[NO]2 (k -1 + k 2[O2])
= k 2[N2O2][O2] =
k 1k 2[NO]2[O2] (k -1 + k 2[O2])
Kinetic Consequences of Assumptions 2NO(g)
d[NO2] dt
=
k 1k 2[NO]2[O2]
N2O2(g)
k 1 k -1
(k -1 + k 2[O2]) N2O2(g) + O2(g)
Let k -1 << k 2
d[NO2] dt
=
k 1k 2[NO]2[O2] ( k 2[O2])
N2O2(g) 2NO(g) k 3
2NO2(g)
= k 1[NO]2
Or Let k -1 >> k 2
d[NO2] dt
=
k 1k 2[NO]2[O2] ( k -1)
=
k 1k 2 k -1
[NO]2[O2]
Smog-An Environmental Problem with its Roots in Chemical Kinetics .
FIGURE 14-16 Smog component profile
Smog N2 + O2 NO2 + h ν O2 + O
2 NO NO + O O3
Where does the NO2 come from? 2 NO + O2 NO + O3
slow fast
2 NO2
NO2 + O2
But this would not account for the buildup of ozone in the smog. There must be another way to make NO2.
Smog Unburned hydrocarbons provide a pathway to NO 2. RH +
•O•
R•
+
•OH
RH + •OH
R•
+
H2O
R• + O2
RO2•
RO2• + NO O CH3C-O-O• + NO2
RO• + NO2 O CH3C-O-O-NO2 PAN
Catalytic Converters
Dual catalyst system for oxidation of CO and reduction of NO. cat CO +
NO
CO2 +
N2
14-5 Catalysis • Alternative reaction pathway of lower energy. • Homogeneous catalysis. • All species in the reaction are in solution. • Heterogeneous catalysis. • The catalyst is in the solid state. • Reactants from gas or solution phase are adsorbed. • Active sites on the catalytic surface are important.
14-5 Catalysis
FIGURE 14-17 An example of homogeneous catalysis
Catalysis on a Surface
Figure 14-18 Heterogeneous catalysis in the reaction 2 CO + 2 NO 2 CO 2 + N2
Figure 14-19 Reaction profile for a surface-catalyzed reaction
Enzymes as Catalysts
E+S
k 1 k -1
ES
FIGURE 14-20 Lock-and-key model of enzyme action
ES
k 2 →
E+P
E+S
k 1 k -1
ES
k 2 →
E+P
d[ P ] dt d[ P ] dt
= k 2[ES]
= k 1[E][S] – k -1[ES] – k 2[ES]= 0 k 1[E][S] = (k -1+ k 2 )[ES] [E] = [E]0 – [ES]
k 1[S]([E]0 –[ES]) = (k -1+ k 2 )[ES] [ES] =
k 1[E]0 [S] (k -1+ k 2 ) + k 1[S]
FIGURE 14-21 Effect of substrate concentration on the rate of an enzyme reaction.
