kinetics and atmospheric chemistry nc a&t lecture february 1, 2011 john orlando orlando@ucar

KINETICS AND ATMOSPHERIC CHEMISTRY

NC A&T Lecture

February 1, 2011John Orlando

[email protected]

What is KINETICS?From Wikipedia, the free encyclopedia

Boulder Kinetics

“… a race from the banks of Boulder Reservoir and back by human-powered vehicles timed on speed and judged for style.”

The Kinetics, a rock band

Kinetics (physics), the study of motion and its causes

What is KINETICS?

Chemical kinetics - the study of chemical reaction rates

Oxford English Dictionary – “A field of study concerned with the mechanisms and rates of chemical reactions or other kinds of process;

But first, let’s review a little !!

What do we know so far?Macroscopic properties of gases:

For atmospheric T and P, the atmosphere is an ideal gas. PV = nRT

Scale Height:

Lapse Rate:

This is the Dry Lapse Rate, ≈10 K/kmIn practice, air contains humidity → 7 K/km

What do we know so far?Structure of the atmosphere

From Lutgens and Tarbuck, 2001

What do we know so far?General Motions of Air:

What do we know so far?Atmospheric Composition

Mostly ‘inert’ species – N2, O2, H2O, CO2, Ar

Not much chemistry?

What do we know so far?Atmospheric Composition

Mostly ‘inert’ species – N2, O2, H2O, CO2, Ar

LOTS OF REACTIVE TRACE GASES !! So, Actually, Lots of Chemistry!

Natural sources – NO from soil, many hydrocarbons (isoprene) from plants

Anthropogenic sources – hydrocarbons, NO, …

What do we know so far?Atmospheric Composition (besides the basic N2, O2, H2O, etc.)Emissions – Lots of “stuff” out there.

Urbanski et al., Wildland Fires and Air Pollution, 2009

What do we know so far?Atmospheric Composition (besides the basic N2, O2, H2O, etc.)Emissions – Lots of “stuff” out there.

Urbanski et al., Wildland Fires and Air Pollution, 2009

The atmosphere needs a way to remove these species.

GENERAL DESCRIPTION:

The atmosphere (particularly the troposphere) acts as a low-temperature, slow-burning combustion engine.

Takes all the emissions (reduced compounds) and ‘burns’ (oxidizes) them:

CH4 CO2 + H2O

Isoprene Other by-products, such as O3, particles, acids,

DMS, NH3 nitrates, etc. (2ry POLLUTANTS)

GENERAL DESCRIPTION:



OH HO2

CH4 CO2 + H2O



NO NO2

MACROSCOPIC : (1044 molecules in the atmosphere)

MICROSCOPIC : (about 25 molecules in a 10 nm cube)

KINETIC THEORY OF GASES

KINETIC THEORY OF GASES: (most any Physical Chemistry text, including Adamson, 1979; Atkins, 1986).

1) Molecules Move !! (they have kinetic energy):

Average Velocity:

For N2, can show that c is about 4 x 104 cm/sec at 298 K


2) Molecules bump into walls!! (pressure on wall of a vessel)

Pressure:


3) Molecules collide with each other!!

Frequency of collisions is about 5 x 109 sec-1 / atm at 298 K.

With velocity of 4 x 104 cm/s, Mean Free Path = 7 x 10-6 cm at atmospheric P.


3) Molecules collide with each other!!


With velocity of 4 x 104 cm/s, Mean Free Path = 7 x 10-6 cm at atmospheric P.

4) Molecules can react with each other when they collide !

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) First, a couple of definitions.

ELEMENTARY REACTION

From Wikipedia - An elementary reaction is a chemical reaction in which one or more of chemical species react directly to form products in a single reaction step.

Usually involves 1-3 molecules, with bimolecular most common:

e.g., OH + CH4 CH3 + H2O

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.)

COMPLEX REACTION SCHEME OR MECHANISM

- Made up of a bunch of elementary reactions

- e.g., the oxidation of CH4 to CH2O in the polluted troposphere leads to the following net effect:

CH4 + 4 O2 CH2O + H2O + 2 O3

OH + CH4 CH3 + H2OCH3 + O2 CH3O2

CH3O2 + NO CH3O + NO2

CH3O + O2 CH2O + HO2

HO2 + NO OH + NO2

NO2 + h NO + ONO2 + h NO + O

O + O2 O3

O + O2 O3


COMPLEX REACTION SCHEME OR MECHANISM

- Explicitly describing the chemical mechanism occurring in the troposphere would probably require > millions of reactions.

- e.g., Aumont et al., ACP 2005.

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) ELEMENTARY REACTIONS (BIMOLECULAR)

What determines the value of the rate constant???

Recall:




So, let’s say that OH and CH4 are the two reactants:

OH + CH4 H2O + CH3

In the troposphere, typically daytime [OH] = 4.1 x 10-14 atm[CH4] = 1.86 x 10-6 atm

So, IF REACTION OCCURRED ON EVERY COLLISION,

Rate = k [OH] [CH4] = (5e9 sec-1/atm-1) * (4.14e-14 atm) * (1.86e-6 atm) = 3.8e-10 atm sec-1


So, IF REACTION OCCURRED ON EVERY COLLISION,

Rate = (5 x 109 sec-1/atm-1) * (4.1 x 10-14 atm) * (1.86 x 10-6 atm) = 3.8x 10-10 atm sec-1

Usually, we work in molecules cm-3, rather than in atmospheres

So, given that there are 2.45 x 1019 molecule cm-3 in 1 atm of gas at 298 K:

Rate = (2 x 10-10 cm3 molecule-1 s-1) * (1 x 106 molecule cm-3) * (4.56 x 1013 molecule cm-3) = 9.1 x 109 molecule cm-3 s-1

BUT IN REALITY, REACTION DOES NOT OCCUR ON EVERY COLLISION!!!

Why NOT? – any ideas?



Two main reasons:

1)There are energetic limitations. Colliding molecules must possess sufficient energy to overcome an ‘activation energy’ that typically exists.

2)Also, there may be ‘geometrical limitations’. Molecules must approach each other in such a way that the appropriate bonds can break / form.



Ea

k = A * exp(-Ea/RT)

A is the pre-exponential factor, and accounts for the geometry limitations.Ea is activation energy.

From Wikipedia


k = A * exp(-Ea/RT)

So, Let’s go back to the OH / CH4 reaction.

IF REACTION OCCURRED ON EVERY COLLISION,

k = 2 x 10-10 cm3 molecule-1 s-1

Turns out that k = 2.45 x 10-12 * exp(- 3525 cal / RT)

k = 6.3 x 10-15 cm3 molecule-1 s-1 at 298 K

k = 5.2 x 10-16 cm3 molecule-1 s-1 at 210 K

Only about 1 in 30000 OH/CH4 collisions results in reaction at 298 K.


Another example HO2 + NO OH + NO2

– two radical species; no barrier to reaction (attractive forces).

HO2 + NO

HOO-NO

OH + NO2

Reaction turns out to have a “negative activation energy”.k = 3.5 x 10-12 exp(500 cal / RT) cm3 molecule-1 s-1

(Colder molecules more likely to react – less able to overcome attraction).


REACTION A-Factor(cm3 molecule-1 s-1)

Activation Energy (cal.)

Rate constant k at 298 K

(cm3 molecule-1 s-1)

•OH + CH4 •CH3 + H2O 2.45e-12 3525 6.3e-15

•OH + H2 H• + H2O 5.5e-12 3975 6.7e-15

•OH + CH3OH •CH2OH + H2O 6.7e-12 1200 8.9e-13

NO3• + CH3CHO HNO3 + CH3CO• 1.4e-12 3800 2.4e-15

HO2• + CH3O2• O2 + CH3OOH 3.8e-13 -1600 5.6e-12

NO + CH3O2• NO2 + CH3O• 4.2e-12 -360 7.7e-12

CH3C(O)OO• + CH3C(O)OO•

CH3C(O)O• + CH3C(O)O• + O2

2.9e-12 -1000 1.5e-11

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) EQUILIBRIUM – All elementary reactions are reversible. At equilibrium, rate of forward and reverse reactions must be equal.

[ HO…H-CH3 ]

Ea = 3525 calories Ea = 17450 calories

OH + CH4

kf [OH] [CH4] = kr [CH3] [H2O]

HOH + CH3

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) EQUILIBRIUM – All elementary reactions are reversible. At equilibrium, rate of forward and reverse reactions must be equal.

[ HO…H-CH3 ]

Ea = 3525 calories Ea = 17450 calories kf = 6.3e-15 cm3 molec-1 s-1 kr = 1.2e-25 cm3 molec-1 s-1

OH + CH4

kf [OH] [CH4] = kr [CH3] [H2O]

HOH + CH3

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) “Equilibrium” and “Steady-State” are different:

Equilibrium is a very precise, physical concept - established when forward and reverse rates of all reactions in a system are equal.

Steady-State is more conceptual and approximate- A (short-lived) species, often an intermediate in a chemical

scheme, is being produced and destroyed at roughly the same rate.

Production Rate = Loss Rate

O(1D) + H2O OH Reaction with CH4

HO2 + NO

Reaction with CO Reaction with Isoprene

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) Let’s look at this in more detail.

Consider a reaction scheme like this:




HO2 + NO OH + NO2


O + O2 O3

O + O2 O3

Can assume CH3 to be in ‘steady-state’. (CH3O, CH3O2, OH, HO2, NO, NO2 too).

What is the steady-state [CH3]? (What do we need to know?)





HO2 + NO OH + NO2


O + O2 O3

O + O2 O3


Assume [OH] = 106, [CH4] = 4.6 x 1013, [O2] = 5 x 1018, all in molecule cm-3

Appropriate rate constants:

k1 = 6.3 x 10-15 cm3 molecule-1 s-1 k2 = 1 x 10-12 cm3 molecule-1 s-1





HO2 + NO OH + NO2


O + O2 O3

O + O2 O3





k1[OH][CH4] = k2[O2][CH3]ss





HO2 + NO OH + NO2


O + O2 O3

O + O2 O3





k1[OH][CH4] = k2[O2][CH3]ss [CH3]ss = 0.06 molecule cm-3 (Very small !!)

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) Termolecular reactions (three-body reactions).

(Strangely enough, closely related to “unimolecular reactions” as we will see in a minute or two).

e.g., NO3 + NO2 N2O5

N2O5 NO3 + NO2 - not as simple as they look (not elementary reactions)

So, what is actually going on?



NO3 + NO2 (N2O5) * (N2O5) * has a choice – forwards or backwards

N2O5

NO3 + NO2 = (N2O5) * (N2O5) * = NO3 + NO2 (N2O5) * + M = N2O5 + M where “M” = N2, or to a lesser extent, O2


NO3 + NO2 = (N2O5) * ka

(N2O5) * = NO3 + NO2 kb

(N2O5) * + M = N2O5 + M kc, where “M” = N2 or O2

Interested in the rate of formation of (stabilized) N2O5:

Assume steady-state for (N2O5)* : ka [NO3] [NO2] = { kb + kc [M] } [(N2O5)*]

Or [(N2O5)*] = { ka [NO3] [NO2] } / { kb + kc [M] }

Substitution yields


NO3 + NO2 = (N2O5) * ka

(N2O5) * = NO3 + NO2 kb


Substitution yields:

Consider low-pressure limit, [M] 0 (termolecular)

And high-pressure limit [M] (bimolecular)


NO3 + NO2 = (N2O5) * ka

(N2O5) * = NO3 + NO2 kb


Unfortunately, life is even more complicated. AHHH!!!

Jurgen Troe:

where Fc is the “broadening factor”.


NO3 + NO2 = (N2O5) * ka

(N2O5) * = NO3 + NO2 kb


PRESSURE (Torr)

0.1 1 10 100 1000 10000

RA

TE

CO

EF

FIC

IEN

T (

cm

3 m

ole

cu

le-1 s

-1)

0.0

2.0e-13

4.0e-13

6.0e-13

8.0e-13

1.0e-12

Fc = 0.6 Fc = 1


(Strangely enough, closely related to “unimolecular reactions”)


N2O5 NO3 + NO2 - not as simple as they look (not elementary reactions)

N2O5 + M (N2O5) * + M(N2O5) * + M N2O5 + M(N2O5) * NO2 + NO3 + M

Analogous treatment:

Consider low-pressure limit, [M] 0 (bimolecular)

And high-pressure limit [M] (unimolecular)

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) Termolecular reactions (three-body reactions) / Unimolecular reactions:

Main “Take-home” Message: Set of chemical reactions that lead to recombination of reactive species (radicals), and formation of reservoirs:

NO3 + NO2 + M N2O5 + MOH + NO2 + M HNO3 + MHO2 + NO2 + M HO2NO2 + MCH3C(O)OO + NO2 + M CH3C(O)OONO2 + MClO + NO2 + M ClONO2 + MClO + ClO + M ClOOCl + M

Often reversible (equilbrium).

Even though the formation of the reservoir is exothermic, the reverse reaction results in a gain in entropy to compensate.

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) Photolysis reactions: (brief introduction to next week).

Some generalities:

- Sunlight provides energy across the electromagnetic spectrum, which can be absorbed by molecules.

- Energies of chemical bonds typically correspond to UV photons.

- Thus, absorption of UV sunlight can lead to photolytic destruction of certain molecules.

e.g., NO2 + h NO + O(3P)

“j-value” – unimolecular ‘rate constant’. Vary with spectral properties of the molecule of interest, but also with solar intensity (as a fn of wavelength)


e.g., NO2 + h NO + O(3P)

Assume constant solar intensity (j-value is constant), and assume no production of NO2:

Then, rearrangement and integration leads to:

[NO2]t = [NO2]o exp -(j*t) (exponential decay of NO2)


e.g., NO2 + h NO + O(3P)

O2 + h O(1D) + O(3P), upper stratosphere and aboveO2 + h O(3P) + O(3P), stratosphere and above

O3 + h O(1D) + O2

O3 + h O(3P) + O2

NO3 + h NO2 + O(3P)NO3 + h NO + O2 Important at all altitudesCH2O + h HCO + HCH2O + h CO + H2

HONO + h OH + NO

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) HOW DO WE MEASURE RATE CONSTANTS IN THE LAB???

TWO BASIC METHODS:

TIME–RESOLVED METHODS (includes “Flash Photolysis” and “Flow Tube”)

INDIRECT METHODS (“Relative Rate” method)


“Flash Photolysis” – e.g., Bryukov et al., J. Phys. Chem. A., 2004, v. 108, 10464-10472.

OH + CH4 H2O + CH3

Basic requirements:

A method for getting CH4 in the vessel, and knowing its concentration.

A method of generating reactive radicals (in this case, OH) ‘instantaneously’.


“Flash Photolysis” – e.g., Bryukov et al., J. Phys. Chem. A., 2004, v. 108, 10464-10472.

OH + CH4 H2O + CH3

Basic requirements:

A fast (s to ms) method for detecting andquantifying [OH], as it decays via reactionwith CH4.

Generally, detection is via absorption orfluorescence-based methodologies. In thiscase, Laser-Induced Fluorescence (LIF) is used.


Looking at an elementary bimolecular reaction, so:

To simply measurement, often use “Pseudo-First-Order” conditions. Keep [OH] produced in the flash small compared to amount of CH4 present.

Then, [CH4] remains essentially constant (change due to reaction with OH very small), and :


IDEALIZED OBSERVED OH TEMPORAL PROFILE

TIME (ms)

-4 -2 0 2 4 6 8 10 12

LIF

SIG

NA

L (

pro

po

rtio

na

l to

[O

H])

0.0

0.2

0.4

0.6

0.8

1.0

1.2



TIME (ms)

-4 -2 0 2 4 6 8 10 12

LIF

SIG

NA

L (

pro

po

rtio

na

l to

[O

H])

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Col 1 vs Col 2

TIME (ms)

0 2 4 6 8 10 12

Ln

{ [

OH

] t/[O

H] o

}-2.5

-2.0

-1.5

-1.0

-0.5

0.0



TIME (ms)

-4 -2 0 2 4 6 8 10 12

LIF

SIG

NA

L (

pro

po

rtio

na

l to

[O

H])

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Col 1 vs Col 2

TIME (ms)

0 2 4 6 8 10 12

Ln

{ [

OH

] t/[O

H] o

}-5

-4

-3

-2

-1

0


k = k [CH4]

Col 1 vs Col 2

TIME (ms)

0 2 4 6 8 10 12

Ln

{ [

OH

] t/[O

H] o

}

-5

-4

-3

-2

-1

0

PLOT OF k' VERSUS METHANE (Slope give the value for k)

[CH4]

0 1 2 3 4 5

k'

0.0

0.1

0.2

0.3

0.4

0.5


“Flow Tube” e.g., Vaghjiani, J. Chem. Phys., 104, 5479 (1996).

O(3P) + N2H4

Basic concept:

Gases flow through a tube at a precisely-known velocity.

Concentration of reactive radical is made at the bottom of the tube.

Because velocity known, exact reaction time is known. Make measurements of [O(3P)] as a function of reaction distance, which can be converted to reaction times.

Again use pseudo-first order conditions, so that decay is logarithmic with time.


RELATIVE RATE METHOD:

-Basic concept – measure an unknown rate coefficient relative to a known one.

- e.g., if want to measure k for reaction of OH with “X” relative to “Y”, expose X and Y simultaneously to OH, and measure relative rate of decay of the two species.

and

Because both X and Y exposed to sameOH ‘field’,

REACTION KINETICS: (follows Brasseur, Orlando and Tyndall, pp. 95-114.) One More Concept – Atmospheric lifetime.

If a compound is emitted into the atmosphere, how long (on average) will it take to remove it (assuming no other production or emission).

Consider CH4 and its reaction with OH:

OH + CH4 CH3 + H2O

Let’s assume that, on average, [OH] = 106 molecule cm-3. Then k [OH] = k

And

The atmospheric lifetime is then defined as the inverse of this k value.

In this particular case, with k = 3.7 x 10-15 cm3 molecule-1 s-1 at 273 K (roughly the average tropospheric temperature), k = 3.7 x 10-9 s-1.

The inverse of this quantity is the lifetime, = 2.7 x 108 s, or about 8.5 years.


One more example – Isoprene, C5H8.

Reacts with OH (daytime only), O3 (day and night) and NO3 (nighttime only).

Calculate isoprene lifetime during daylight hours and during nighttime hours, assuming the following rate constants and concentrations:

[OH] = 106 molecule cm-3, 12-hr daylight; k(OH+Isoprene) = 1 x 10-10 cm3 molecule-1 s-1

[NO3] = 108 molecule cm-3, 12-hr nighttime; k(NO3+Isoprene) = 7 x 10-13 cm3 molecule-1 s-1

[O3] = 1012 molecule cm-3, 24-hr average; k(O3+Isoprene) = 1.3 x 10-17 cm3 molecule-1 s-1




Daytime loss via OH and O3 reactions.

[OH] = 2 x 106 molecule cm-3, 12-hr daylight; k(OH+Isoprene) = 1 x 10-10 cm3 molecule-1 s-1


Then Isoprene Loss Rate = kOH [OH] + kO3[O3] = 2 x 10-4 s-1 + 1.3 x 10-5 s-1 = 2.13 x 10-4 s-1.

Then, lifetime t = 1/ (Loss Rate) = 4700 sec. = 1.3 hrs.




Nighttime loss via NO3 and O3 reactions.

[NO3] = 108 molecule cm-3, 12-hr nighttime; k(NO3+Isoprene) = 7 x 10-13 cm3 molecule-1 s-1


Then Isoprene Loss Rate = kNO3 [NO3] + kO3[O3] = 7 x 10-5 s-1 + 1.3 x 10-5 s-1 = 8.3 x 10-5 s-1.

Then, lifetime t = 1/ (Loss Rate) = 12000 sec. = 3.3 hrs.

A LITTLE BIT OF REVIEW:

Spent the last while talking about kinetic theory of gases, and elementary reactions.

Molecules move, collide with each other, and (when possible) react with each other!

Talked about how to look at individual elementary reactions – bimolecular, termolecular/unimolecular, photolysis reactions.

What is the rate of these reactions? Rate constant? How do we measure rate constants, etc?

A LITTLE BIT OF REVIEW:



OH HO2

CH4 CO2



NO NO2

OH HO2

CH4

IsopreneNMHC CO2, Ozone, otherDMS, NH3 secondary pollutantsetc.

NO NO2

So, how do these elementary reactions come together to create the engine?

Consider a very simplified atmosphere, for illustrative purposes.

Use CO to represent all the ‘fuel’, combine with NO, NO2, OH, HO2, and see what happens.

THE TROPOSPHERIC “ENGINE”: Start with “Odd Nitrogen” Family:

“Active Species” : NO and NO2, collectively called NOx

“Reservoir Species” : HNO3, (HO2NO2, HONO, many others)

Consider first NO and NO2: Present in the atmosphere mainly due to emissions from anthropogenic activity, but also from soils and lightning.

NO + O3 NO2 + O2, k = 2 x 10-14 cm3 molecule-1 s-1

NO2 + h NO + O, j = 8 x 10-3 s-1

O + O2 + M O3 + M, (very fast, assume instantaneous)

Assume [O3] = 1 x 1012 molecule cm-3, and assume ‘photo-stationary state’

Then: k [NO] [O3] = j [NO2]

Rearrange: [NO2] / [NO] = k [O3] / j = 2.5

Loss is often via reaction of OH with NO2, OH + NO2 + M HNO3 + M

THE TROPOSPHERIC “ENGINE”: Now the “Odd Hydrogen” Family:

“Active Species” : OH and HO2, (CH3O2, …), called HOx

“Reservoir Species” : H2O2, HNO3, (HO2NO2, HONO, many others)

THE TROPOSPHERIC “ENGINE”: Now the “Odd Hydrogen” Family: Consider first OH and HO2:

Production: O3 + h O(1D) + O2 O(1D) + H2O OH + OH

Conversion of OH to HO2:

OH + CO (+O2) HO2 + CO2 dominant (when all ‘fuel’ considered)OH + O3 HO2 + O2, usually minor

Conversion of HO2 back to OH:

HO2 + O3 OH + 2 O2 HO2 + NO OH + NO2, (followed by NO2 + h NO + O, O + O2 + M O3 + M,

which generates O3 !!)

Losses of HOx via two processes:

HO2 + HO2 + M HOOH + O2 + M OH + NO2 + M = HNO3 + M

kinetics and atmospheric chemistry nc a&t lecture february 1, 2011 john orlando orlando@ucar

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