How fast can a reaction go
Four things that affect ratea. concentration b. temperaturec. catalystd. surface area
Chemical KineticsChemical Kinetics
Average rateAverage rate
Instantaneous rateInstantaneous rate
NH4+ + NO2
- N2 + 2H2O
R = k [NH4+]m [NO2
-]n •k = rate proportionality constant•m = reaction order for the
•ammonium ion•n = reaction order for the nitrite
• ion
Rate Laws
Rate
N2 + 3H2 → 2NH3
R or rate = -Δ[N2] = M/s
Δt
How do the three chemicals compare?
NH4+ + NO2
- N2 + 2H2O
indep. var control Dep. var
indep. var control Dep. var
R = k [NH4+]m [NO2]n
2x
Skeleton rate law
R = k [NH4+]1 [NO2]1
10.8 x 10-7M/s = k [0.02M]1[0.200M]1
10.8 x 10-7M/s = k[0.02M]1 [0.200M]1
k= 10.8 x 10-7 M/s /[0.02M]1[0.200M]1
k = 10.8 x 10-7 M/s / 0.004M2
k = 2.7 x 10-4 1/M • s
M = ? M1 M1
s ?
Suppose the concentrations for NH4
+ and NO2- are
0.15 M and 0.20 M, respectivelySince R = k[NH4
+]1 [NO2]1
where k = 2.7 x 10-4 1/M - s at 25 C
then R = 2.7 x 10-4 1/M - s [0.15 M] [0.20 M]
R = 8.1 x 10-6 M/s
1 0.0160 0.0120 3.24 x 10-4
2 0.0160 0.0240 6.38 x 10-4
3 0.0320 0.0060 6.42 x 10-4
Initial [NO] Initial [Br2] Rate of appearance NOBr (M/s)
(M/L)(M/L)
2NO(g) + Br2(g) 2NOBr
R = k[NO]m [Br2]n
3.24 x 10-4
6.42 x 10-4=
k(0.0160)x (0.0120)1
k(0.0320)x (0.0060)1
12
=(0.0160)x
(0.0320)x
2 1
4= .5x x = 2x = 2
R = k[NO]2 [Br2]1
CH3NC1 Time (sec)
1 mm Hg
15014013011890705535
0900
2,5005,000
10,00015,00020,00030,000
H3C N C: H3C C N:
Using the calculator to find order
H3C N C: H3C C N:
CH3NC1
1 mm Hg
15014013011890705535
Ln CH3NC2
5.024.944.864.774.494.244.003.55
2 r = 0.98
ln [A]t = - k t + ln [A]0
y = m x + b
H3C N C: H3C C N:
CH3NC1
1 mm Hg
15014013011890705535
1/ CH3NC3
.0067
.0071
.0076
.0084
.0111
.0142
.0182
.0286
3 r = 0.92
y = mx + b
1
= kt + [A]t
1
[A]0
H3C N C: H3C C N:
CH3NC1 Time (sec)
15014013011890705535
0900
2,5005,000
10,00015,00020,00030,000
H3C N C: H3C C N:
1/ CH3NC3
.0067
.0071
.0076
.0084
.0111
.0142
.0182
.0286
ln CH3NC2
5.024.944.864.774.494.244.003.55
zero order Rate = k[A]o
plot concentration [A] vs. time (t) – linear, negative slope integrated rate law - [A]t = -kt + [A]0
half life – t1/2 = [A]0/2k [A]
1st order Rate = k[A]1 t
plot of ln conc. vs. time is linear, negative slope integrated rate law - ln[A]t = -kt + ln[A]0
half life – t1/2 = .693/k ln[A]
2nd order Rate = k[A]2 tplot inverse of conc. vs. time is linear, positive slope integrated rate law - 1/[A]t = kt + 1/[A]0
half life – t1/2 = 1/k[A]0 1/[A] t
Using Rate Law Equations to Determine Change in Concentration Over Time
The first order rate constant for the decomposition of a certain insecticide in water at 12 C° is 1.45 yr1-. A quantity of insecticide is washed into a lake in June leading to a concentration of 5.0 x 10-7 g/cm3. Assume that the effective temperature of the lake is 12 C°. (a)What is the concentration of the insecticide in June of the following year? (b) How long will it take for the concentration of the insecticide to drop to 3.0 x 10-7 g/cm3?
R = - [A] = k[A]t
ln [A]t = - k t + ln [A]0
ln [A]t = - (1.45 yr.-1)(1.00 yr.) + ln( 5.0 x 10-7 g/cm3)
ln [A]t = - 15.96, [A]t = e -15.96 [A]t = 1.2 x 10-7 g/cm3
Using Rate Law Equations to Determine the Half-Life of a Reaction
Let’s begin with ln[A]t - ln[A]0 = ln[A]t
[A]0
= - kt
ln[A]t
[A]0
= - kt,
let [A]t = ½ [A]0given
ln½ [A]0
[A]0
= - kt,then and ln ½ = -kt ½
t ½ = -ln ½ = 0.693
k k
Using Rate Law Equations to Determine the Half-Life of a Reaction
The concentration of an insecticide accidentally spilled into a lake was measured at 1.2 x 10-7 g/cm3. Records from the initial accident show that the concentration of the insecticide was 5.0 x 10-7 g/cm3. Calculate the 1/2 life of the insecticide.
ln 1.2 x 10-7 g/cm3
5.0 x 10-7 g/cm3= - k (1.00 yr.)
k = 1.43 yr-1 t ½ = 0.693 = 0.484 yr.1.43 yr-1
Examining the Relationship Between the Rate Constantand Temperature
Why does Temperature Have an Effect on Rate?
..it’s because ofCollision Theory
It’s All About Activation Energy and Getting overthe HUMP!!
1010 collisions/sec occur 1 in 1010 collisions succeeds
...And What Do the Mathematicians Have to Say AboutCollision Theory?
k = Ae-Ea/RT
k = Ae-Ea/RT
ln k1 = -Ea/RT1 + ln Ae
ln k2 = -Ea/RT2 + ln Ae
lnk1 - ln k2 = (-Ea/RT1 + ln Ae) - (Ea/RT2 + ln Ae)
ln k1
k2
=Ea
R1
T2
1T1
-
Rewriting the Arrhenius Equation
ln k1 = -Ea/RT1 + ln Ae
y = m x + bln
k
1/T
Slope = -Ea/R
R (ideal gas constant) 8.31 J/K-mol
Getting a Line on the Arrhenius Equation
ln k1 = -Ea/RT1 + ln Ae
y = m x + b
L1 L2 L3 L4 L5
T(°C) L1 + 273 1/L2 k ln L4
ln k
(L
5)
1/T (L3)
Slope = -Ea/R*
Mastering the Arrhenius Equation with your TI
The following table shows the rate constants for the rearrangement of CH3CN (methyl isonitrile) at various temperatures
Temperature (°C) k (s-1)
189.7198.9230.3251.2
2.52 x 10-5
5.25 x 10-5
6.30 x 10-4
3.16 x 10-3
From these data calculate the activation energy of this reaction
Mastering the Arrhenius Equation with your TI
The following table shows the rate constants for the following reaction at varyingtemperatures: CO(g) + NO2(g) CO2(g) + NO(g)
Temperature (°C) k (M-1 s-1)600650700750800
0.0280.221.3623
From these data calculate the activation energy for this reaction
Reaction Mechanisms A Reaction Mechanism is the process which describes in great detail the order in which bonds are broken and reformed, changes in orientation and the energies involved during those rebondings, and changes in orientationsNO(g) + O3(g) NO2(g) + O2(g)
A single reaction event is called an elementary reactionelementary reactionNO2(g) + CO(g) NO(g) + CO2(g)
While this reaction looks like an elementary reaction, elementary reaction, it actually takes place in a series of steps
NO2(g) +NO2(g) NO3(g) + NO(g)
NO3(g) + CO(g) NO2(g) + CO2(g)NO2(g) + CO(g) NO(g) + CO2(g)
Reaction MechanismsNO2(g) +NO2(g) NO3(g) + NO(g)
NO3(g) + CO(g) NO2(g) + CO2(g)
NO2(g) + CO(g) NO(g) + CO2(g)
Slow step
Fast step
Rate Determining step
The rate law is constructed from the rate determining step
Rate = k1[NO2]2
Reaction Mechanisms: Catalysts
NO + O3 → NO2 + O2
O + NO2 → NO + O2
O + O3 → 2O2
NO(g) +Br2(g) NOBr2(g)
NOBr2(g) + NO(g) 2NOBr(g)
2NO(g) + Br2(g) 2NOBr(g)
Slow step
Fast stepRate Determining step
If step 2 is the rate determining step, then R = k[NOBr2][Br2]. Keep in mind, however, that one cannot include an intermediate in the rate determining step.
We can substitute for NOBr2 using the previous equation NO(g) and Br2(g) which are not intermediates
rate = k [NO]2[Br2]
Prove that the following mechanism is consistent with R = k[NO]2[Br2], the
rate law which was derived experimentally:
NO(g) +NO(g) N2O2(g)
N2O2(g) + Br2(g) 2NOBr(g)
2NO(g) + Br2(g) 2NOBr(g)
Catalyst: a substance that changes the speed of a chemical reaction without it self undergoing a
permanent chemical change in the process or it is reconstituted at the end.
Br - is a homogeneous catalyst
This metallic substrate is a heterogeneous catalyst
Heterogeneous Catalysts
Ethylene
Ethane