6.3 Measurements of Chemical Composition  6.2 Laboratory Measurements of Chemical Parameters  6.2.1 Absorption Cross Sections

6.2.2 Laboratory Measurements of Rate Constants

The chemical composition of the atmosphere is a continually changing entity and is controlled by a large number of elementary chemical reactions. In order to understand the chemical composition of the Earth's atmosphere and to predict future changes, it is important that laboratory experiments be conducted to determine the rate constants and mechanisms for all possible chemical reactions occurring in the atmosphere. These data are then used as input for chemical models.

Most of the chemical reactions of atmospheric interest are bimolecular - i.e., they involve the reaction of two species:

$$A + B \rightarrow C + D$$ (6.7)

 
In this case, the rate of loss of reactants and the rate of formation of the products is governed by the product of the rate constant, k, and the concentrations of the reactants:
 

$${-d[A]\over dt}={-d[B]\over dt}={d[C]\over dt}={d[D]\over dt}=k[A][B].$$ (6.8)

 
Usually, the concentrations of the chemical species (denoted by square brackets) are in units of molecules per cm³ and the rate constant has units of cm³ molecule^-1 s^-1. In general, the rate constant can vary with both pressure and temperature.

In order to make the determination of a rate constant in the laboratory simpler mathematically, the concentration of one of the two reactants (say B in the general example above) is made to be much larger than that of the other reactant, A. In this fashion, the concentration of B remains essentially constant during the study as A is consumed. This situation, referred to as "pseudo-first order conditions," allows the rate expression in equation (6.8) to be simplified as follows:
 
 

$${d[A]\over dt}=-k[A][B]=-k'[A].$$ (6.9)

 

This equation is usually used in its integrated form:
 
 

$$ln\left({[A]\over [A]_o}\right)=-k't.$$ (6.10)

 

One need only then monitor the relative concentration of A as a function of time in a given experiment to obtain the ``pseudo-first order rate constant," k'. This k' value can then be divided by the known, constant concentration of B to obtain k. In practice, k' is measured for a series of [B], and k is obtained as the slope of a linear plot of k' versus [B]. For more details the reader is referred to the book by Finlayson-Pitts and Pitts.

The two most common techniques employed for the determination of rate constants in the lab are the flow tube and flash photolysis systems. Flow tube experiments are generally conducted in cylindrical tubes, between 2 and 4 cm in diameter and 1 m in length as shown schematically in Figure 6.2:

 

 Figure 6.2:  Flow tube apparatus used to study reactions of the NO₃ radical using laser-induced fluorescence detection.

Gases are flowed rapidly at reduced pressure through the tube at linear velocities typically between 300 and 3000 cm s^-1. Most of the gas flow consists of an inert carrier gas, usually He or N₂. Usually a small concentration (10⁹-10¹² molecules cm^-3) of a reactive radical is added to the main tube at inlet X, while an excess (10¹²-10¹⁴ molecule cm^-3) of the other reactant is added through the movable inlet, Y. The radical of interest is usually created from the decomposition of a stable precursor either thermally or in a microwave discharge plasma. Atomic species (H, O, N, F, Cl) are produced from decomposition of the corresponding diatomic molecule, while more complex radicals can be generated from subsequent reactions of these atomic species. For example, the OH radical can be produced from the reaction of H atoms with NO₂,
 
 

$$H + NO_2 \rightarrow OH + NO$$ (6.11)

 

while the NO₃ radical can be produced from the reaction of F atoms with nitric acid,
 
 

$$F + HNO_3 \rightarrow NO_3 + HF.$$ (6.12)

 

The concentration of the reactive atomic species or radical is then monitored at the end of the flow tube using a detection system suitable to that species. For example, atomic species can be detected using resonance fluorescence (discussed later), while radical species can be detected by resonance or laser-induced fluorescence (see later), laser magnetic resonance, optical absorption, electron spin resonance, or mass spectrometry.

Kinetic information in a flow tube is obtained by measuring the relative concentration of the minor constituent (usually a free radical or atom) as a function of the position of the movable inlet. A knowledge of the linear velocity at which the gas is travelling provides a relationship between reaction time and distance, v = dz/dt. By combining this relationship with (6.10) above, one obtains the following relation: k' = -v (dln[A]/dz). The pseudo first-order rate constant, k', is thus obtained from the rate of change of the radical concentration with the position of the movable inlet. The bimolecular rate constant, k, is then obtained from the variation of k' with [B], as described above. In a special application of flow tube kinetics, the reactant B can be an aerosol particle, and the rate of uptake and reaction of A by the particle is measured. In this case the reaction probability, $\gamma$, is obtained from a plot of k' versus the total surface area, rather than the concentration of aerosol.

While flow tubes possess the advantage of being very versatile and relatively inexpensive, they do have limitations. Firstly, reactions must in general be carried out at low pressure (less than 10 torr) due to diffusion problems encountered at higher pressures. Also, this method is susceptible to complications due to heterogeneous reactions on the flow tube walls. These effects are particularly pronounced at low temperature, limiting the useful range of the flow tube to temperatures above 200 K. The major advantage of flow tubes is that highly reactive species can be prepared independently and mixed together in the flow tube. Also, since the reaction profile is frozen along the tube, a detector with a long time constant can be used.

The other common technique employed to determine a rate constant in the laboratory is a flash photolysis experiment. In a basic flash photolysis experiment, a reaction vessel is filled with gases and irradiated with light from a pulsed source (usually a flashlamp or pulsed laser system with a pulse duration of the order of ns to $\mu s$) to produce the radical of interest in the presence of a large excess of the other reactant. Kinetic information is obtained by measuring the temporal behavior of the radical concentration, which is monitored after the flash on timescales of $\mu s$ to ms using a fast detection system. Common detection methods include resonance fluorescence or absorption for atomic species, laser induced fluorescence for radicals such as OH, and absorption measurements for species such as NO₃. Again, pseudo first-order conditions are typically employed to allow a simpler study of the kinetics. The flash photolysis method offers the advantage of being less susceptible to heterogeneous effects, since the light pulse and subsequent reaction occur away from the walls of the reaction vessel, and the reaction is complete on a timescale shorter than that required for significant diffusion to occur. Since static, or slowly flowing mixtures of gases are used, pressure is not a limitation, and flash photolysis experiments have been carried out between a few torr and several hundred atmospheres. A flash photolysis experiment is, however, somewhat more expensive and less versatile than the flow tube in terms of the number of species that can be generated and detected.

Obtaining the rate constant for a particular reaction is only half the answer, as the products of the reaction must also be identified. A common method for determining the mechanism of a chemical reaction (or a small number of reactions) is using a chamber study. These experiments are generally conducted in large (50-5000 liter) vessels, filled with gases to pressures of typically 0.01 to 10 atmospheres. The vessel is irradiated continuously using either direct Sunlight or an artificial UV/visible light source. From an appropriate choice of gases in the cell, a reactive radical (such as OH) can be continuously generated in the presence of a reactant. The reactant is slowly consumed over time and new products are generated. The temporal behavior of the reactant and the products is monitored, usually using gas chromatography, infrared absorption, or occasionally UV/visible absorption. The quantitative yields of the various products obtained can then be used to elucidate the mechanism of the chemical reaction(s) occurring in the chamber. This technique has found wide application in the study of the complex chemistry involved in the oxidation of large hydrocarbons and sulfur-containing species found in the troposphere. Our overall understanding of a chemical process is thus derived from an amalgamation of direct measurements of the kinetics with product information from less direct bulk experiments.

Once kinetic parameters for a reaction have been determined, the lifetime of the species can be estimated. For reaction of a species with, say, the OH radical the lifetime is 1/k[OH], where [OH] is some OH concentration averaged over an appropriate spatial and temporal interval. The lifetime thus defined represents the time it would take for the concentration of the species to be reduced down by a factor of 1/e if there were no production in the atmosphere. It is a rough measure of the reactivity of a species. 

  
 6.3 Measurements of Chemical Composition  6.2 Laboratory Measurements of Chemical Parameters  6.2.1 Absorption Cross Sections 
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