reaction thermodynamics review
DESCRIPTION
Reaction Thermodynamics Review. D G rx – indicates direction of reaction given the current distribution of reactants and products. D G ˚ rx – indicates the free energy difference between reactants and products at their standard state concentrations). - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/1.jpg)
Reaction Thermodynamics Review
DGrx – indicates direction of reaction given the current
distribution of reactants and products. DG˚rx – indicates the free energy difference between reactants
and products at their standard state concentrations). The intrinsic ‘favorability’ of a reaction.
Q – indicates the current distribution of reactants and products. DG = DG˚ + RT ln Q
K – indicates the equilibrium distribution of reactants and products. DG˚ = -RT ln K
![Page 2: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/2.jpg)
Reaction Kineticsr – The rate of the reaction – M s-1
k – The rate constant for the reaction – Indicates the ‘intrinsic’ speed of a reaction.
Ea – The activation energy for a reaction – Indicates the free energy difference between the reactants
and the transition state. Rate law – Indicates the dependence of r on k and the concentrations of reactants and any other reagent that influences the rate of a reaction.
![Page 3: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/3.jpg)
Reaction Kinetics aA + bB cC + dD
Rate (r) = 1/ni dci/dt = -(1/a) (d[A]/dt) or ..... + (1/c) (d[C]/dt) etc.
rate = k [A]a [B]b [L]l
k = rate constant (if you determine k using the change in a reagent for which the stoichiometric coefficient ≠ 1 you must also adjust for this.
a/b/l = reaction orders with respect to A, B, L, respectively.
overall order, n = a + b + l.
A and B are reactants. L = catalyst, intermediate
![Page 4: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/4.jpg)
Elementary Reactions
1. Partial orders of reactants = stoichiometric coefficient i.e. a = a and b = b.
2. no catalysts or intermediates in rate law.
3. reverse reaction is also elementary
4. Represents the actual ‘collision’ that takes place resulting in the change in molecular arrangement.
5. Typically n will be 2 or less for an elementary reaction (and its reverse reaction).
A + B C + D and r = k [A] [B]
![Page 5: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/5.jpg)
Mechanism – A reaction is represented as a series of elementary steps that add up to overall stoichiometry and represent the actual collision order in the reaction.
e.g.... A + C I + D I + B F + C
stoichiometry: A + B D + FI is intermediate and C is catalyst r = k[A][C]
Experimental Goals1. Determine rate law – Find n and k e.g. r = k [A] [C], n = 2, and k = r/([A][C]).
2. Determine mechanism(s) consistent with rate expression
slowfast
3. Determine Activation energy by T dependence of k.
![Page 6: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/6.jpg)
Most Common Reaction Orders
1st order:
2nd order:
rate = k [A]rate = k [A]2 or....
rate = k [A][B]rate expression can include ......orders > 2, half-integral orders,inverse dependency – [X] in denominator
![Page 7: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/7.jpg)
1st Order Reactionsr = -d[A]/dt = k[A]
-d[A]/[A] = k dt
[Ao][A] d[A]/[A] = -k 0
tdtln [A] - ln[Ao] = ln ([A]/[Ao]) = -kt
[A] = [Ao] e(-kt)
Linear: ln [A] = -kt + ln [Ao]
half-life
if [A] = [Ao]/2 then t = t1/2 & .....
t½ is independent of [Ao]
t½ = 0.693/k
t½ = ln 2/k
ln ([A]/[Ao]) = -kt
ln 0.5 = -kt½
![Page 8: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/8.jpg)
2nd Order Reactions half-lifer = - d[A]/dt = k[A]2
1/[A] – 1/[A0] = k t linear 1/[A] = kt + 1/[A0]
[Ao][A] [A]-2 d[A] = -k 0
t dt
[A] = [Ao]/(1 + kt[Ao])
-d[A]/[A]2 = -k dt
t½ = 1/(k[Ao])
1/[A] – 1/[Ao] = kt
as [Ao] t½
2/[Ao] - 1/[Ao] = kt½
1/[Ao] = kt½
![Page 9: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/9.jpg)
0 Order Reactions (rare – some free radical reactions)
r = -d[A]/dt = k
∫AoA d[A] = k ∫0
t dt
[A] = kt + [Ao]
Plot [A] vs. t slope = k Yint = [Ao]
[A]
t
[Ao]
![Page 10: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/10.jpg)
0 50 100 150 200 250 300 350 400 450 5000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1st 2nd
115 (115) 230 (115) 345
167 (333) 500
1st order – t½ is constant regardless of [A]0.2nd order – t½ doubles as [A]0↓ by ½.plot ln t½ vs. ln [Ao] slope = 1-n
Determining Reaction Order, n
Half-life Method
Advantage: Single experimentDisadvantage: Requires reaction integrity over multiple half-lives unless ‘fraction’ < ½ used.
![Page 11: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/11.jpg)
Determining Partial Order (a) Initial rate method ― r = k [A]a [B]b
1. vary [Ao] while holding [Bo] etc. cst.
2. find initial rate r from plot of [A] vs. t
r2/r1 = ([A0,2]/[A0,1])a
log (r2/r1) = a log ([A0,2]/[A0,1])
Multiple data points: plot log (ro) vs. log [Ao]: slope = a
3. repeat for other reagents in rate expression
two data points: a = log(r2/r1)/log([A0,2]/[A0,1])
20.4 - p726
![Page 12: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/12.jpg)
G A + B
C + D
AB*
Ea determines rate - DG° determines Equil.
Ea
DG
where N2 = # collisions leading to reaction & N1 = total # collisions
Boltzmann Distribution N2/N1 = exp(-Ea/RT)
Transition State theory (collision theory) A + B → C + D
![Page 13: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/13.jpg)
Determining the Rate Law
F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2]x[ClO2]y
rate = k [F2] [ClO2] ― Note that partial orders ≠ reaction coefficients.
Problem 13.70
X = 1
r2 = k•(2[F2])x•[ClO2]y = k•2x•[F2]x•[ClO2]y = 2x = 2r1 k•[F2]x•[ClO2]y k• [F2]x•[ClO2]y
y = 1
r2 = k•[F2]x•(4•[ClO2])y = k•[F2]x•4y•[ClO2]y = 4y = 4r1 k•[F2]x•[ClO2]y k•[F2]x• [ClO2]y
![Page 14: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/14.jpg)
rate [A] [B] [L]1.00E-05 0.1 0.1 0.012.00E-05 0.2 0.1 0.011.00E-05 0.1 0.2 0.012.00E-05 0.1 0.1 0.02
![Page 15: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/15.jpg)
k = A exp(-Ea/RT)
ln k = (-Ea/R)(1/T) + ln A
Arrhenius Activation Energy
plot ln k vs. 1/T slope = -Ea/R Yint = ln A
The T dependence of reaction rates is due to the dependence of k on T. This in turn is due to the dependence of Ea on T. Through empirical observation Arrhenius determined that ….
or .. ln (k2/k1)/(1/T2 – 1/T1) = -Ea/R
![Page 16: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/16.jpg)
T (K) 103k 1/T ln k Fit
599 0.54 0.00167 -0.62 -0.63
629 2.5 0.00159 0.92 0.91
666 14 0.00150 2.64 2.63
683 25 0.00146 3.22 3.36
700 64 0.00143 4.16 4.05
H2 + I2 2HI
ln k = (-Ea/R)(1/T) + ln A
Ea = 160 kJ mol-1
![Page 17: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/17.jpg)
REACTION MECHANISM
1. List of Elementary Steps2. Must add to overall stoichiometry3. Must be “consistent” with Rate Law
2. Steady State Method (SS)
1. Rate Determining Step Method (RDS)
![Page 18: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/18.jpg)
C is an intermediateProduct in an early step, reactant in a later step. Doesn’t appear in stoichiometry. May appear in rate law
A + B C + DC + E B + FA + E D + F
B is a catalystReactant in an early step, product in a later step.Doesn’t appear in stoichiometry.Must appear in the rate law.
![Page 19: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/19.jpg)
Rate Law: r = k [H+] [HNO2] [Br-]
H+ + HNO2 + FNH2 FN2+ + 2H2O
Br- must be catalyst or intermediate and must show up in mechanism.
FNH2 is reactant that is not in the rate law.It must show up in the mechanism in a later step. If an RDS mechanism is sufficient to explain rate law then it must be a reactant in a step after the rate-determining step.
![Page 20: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/20.jpg)
Rate Law: r = k [H+] [HNO2] [Br-]
H+ + HNO2 + FNH2 FN2+ + 2H2O
k1
k-1
H+ + HNO2 H2NO2+ fast
k2H2NO2
+ + Br- ONBr + H2O slow k3
ONBr + FNH2 FN2+ + H2O + Br- fast
r = k2 [H2NO2+] [Br-]
[H2NO2+] = k1/k-1 [H+][HNO2]
r = k [H+][HNO2][Br-] k = (k2k1/k-1)
![Page 21: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/21.jpg)
Rate Law: r = k [H+] [HNO2] [Br-]
H+ + HNO2 + FNH2 FN2+ + 2H2O
k1
k-1
H+ + HNO2 H2NO2+
k2
H2NO2+ + Br- ONBr + H2O
k3ONBr + FNH2 FN2
+ + H2O + Br-
r = k3 [ONBr][FNH2] d[ONBr]/dt = 0
k2 [H2NO2+][Br-] = k3 [ONBr][FNH2]
r = k3 k2 [H2NO2+][Br-] [FNH2]/(k3[FNH2])
apply ss assumption to H2NO2+
[ONBr] = k2 [H2NO2+][Br-]/(k3[FNH2])
![Page 22: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/22.jpg)
Rate Law: r = k [H+] [HNO2] [Br-]
H+ + HNO2 + FNH2 FN2+ + 2H2O
k1
k-1
H+ + HNO2 H2NO2+
k2
H2NO2+ + Br- ONBr + H2O
r = k2 [H2NO2+][Br-]/[FNH2]
apply ss assumption to H2NO2+
r = k1[H+][HNO2] = k-1[H2NO2+] + k2 [H2NO2
+][Br-]
[H2NO2+] = k1[H+][HNO2]
k-1 + k2[Br-]r = k2k1 [Br-][H+][HNO2] k-1 + k2[Br-]
![Page 23: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/23.jpg)
same as RDS mech. when ... k2[Br-] << k-1
RDS r = k [H+][HNO2][Br-] k = (k2k1/k-1)
r = k2k1 [Br-][H+][HNO2] k-1 + k2[Br-]
SS
Rate Law: r = k [H+] [HNO2] [Br-]
H+ + HNO2 + FNH2 FN2+ + 2H2O
![Page 24: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/24.jpg)
Half Orders in Rate Law .....
Reactant split in first step - prior to RDS D + 2B 2P
D 2M2 (M + B P) RDS
r = k2[M][B] & [M] = (k1/k-1 [D])1/2
r = k[B][D]1/2
![Page 25: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/25.jpg)
Look for P that is co-product prior to RDS… or I that is P in first step & R after RDS
Term in denominator of rate lawHg2
2+ + Tl3+ 2Hg2+ + Tl+
Hg22+ Hg2+ + Hg fast
k1
k-1
Hg + Tl3+ Hg2+ + Tl+ slow k2
r = k2 [Hg][Tl3+]
[Hg] = k1[Hg22+]/(k-1[Hg2+])
r = k [Hg22+][Tl3+]/[Hg2+]
![Page 26: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/26.jpg)
A B (+ C)
Unimolecular ReactionsStill involve some type of collision.
A + M A* + M
A* B (+ C)
r = k[A]
![Page 27: Reaction Thermodynamics Review](https://reader035.vdocuments.us/reader035/viewer/2022081420/56816021550346895dcf23cf/html5/thumbnails/27.jpg)
Enzyme Kinetics Mechanism:
k1
1. E + S ES k2
k3
2. ES E + P
r = k3 [ES] k1[E][S] = (k2 + k3) [ES][ES] = k1/(k2 + k3) [E][S] [ES] = [E][S]/KM (KM = (k2+k3)/k1
r = k3/KM [E][S]If [S] >> KM then [ES] = [E]tot and …..
r = k3 [E]tot