3 Environmental Chemical Kinetics

Prof. K.S. Gupta

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Contents

  1. Introduction
  2. Reaction Rate and Rate Constant
  3. Reaction Order
  4. Molecularity of the Reaction
  5. Kinetics of Reactions of Different Orders
  6. Methods of Studying of Chemical Reactions
  7. Determination of Rate Constants and Establishing the Rate Law
  8. Halflife, Lifetime, Average Life and  Residence Time
  9. lReaction Mechanism
  10. Temperature Dependence of Reaction Rates/Energy of Activation
  11. Photochemical Reactions
  12. Catalysis
  13. Suggesting Reading

Introduction

Chemical kinetics is the study of the rates and the mechanisms of chemical processes. It is of great practical value. It is often necessary to know under what conditions a slow but useful reaction can be made to proceed rapidly to yield a desired product in high yield. For environmental chemistry, it has great predictive value. By studying the kinetics and mechanisms of environmental reactions, we can at least roughly estimate the residence times of polluting and non-polluting species both. Our knowledge of several pollution and atmospheric phenomena such as ozone depletion, acid rain, photochemical smog etc rests mainly on the study of the kinetics of individual rate constants of the thermal and photochemical reactions involved. Rate data and mechanisms are useful in designing pollution- mitigation steps.

 

Reaction Rate and Rate Constant

During the progress of a chemical reaction, the concentrations of the reactants decrease and those of the products increase as the time passes. The rate of a chemical reaction is the rate of decrease in the concentration of the reactant per unit time or the increase in the concentration of the product per unit time. Mathematically, the rate of the reaction in Eq. 1 may be expressed using the differential Eq. 2, both in the form of the disappearance of reactant A or the appearance of B.

The unit of rate is mol L-1 s-1 (in chemistry) and molecule cm-3 s-1 (in atmospheric chemistry). Other units corresponding to dimension concentration time-1 are also be used.The change in the concentration of a reactant, A, is shown in Fig. 1. The rate of the reaction at any instant is determined by drawing a tangent on the concentration versus time curve at the desired instant, as shown in Fig 1.

 

 

Fig. 1 Change in the concentration of the reactant (y-axis) with time(x-axis).

 

The slope of the tangent is the rate. The rate is seen to decrease with time. This is due to decrease in the concentration of the reactant(s). Thus, at any instant the rate of a reaction is the function of the concentration of the reactants at that instant. The rate of the reaction at the very beginning of the reaction is known as initial or instantaneous rate and determined by drawing tangent at t = 0.

The dependence of the rate of a hypothetical reaction (Eq. 6) on the concentration of the reactants can be expressed as in Eq. 6.

where k is rate constant, rate coefficient or velocity constant, [A] and [B] are the concentrations of the reactants A and B, respectively. The terms a and b are orders of reaction with respect to A and B, respectively. When the concentration of each reactant in the rate expression (say Eq. 6) is unity then rate becomes equal to rate constant, k. Thus, the rate constant is equal to reaction rate when all reacting species are at unit concentration.

 

Reaction Order

The order with respect to a chemical species is defined as the order of the concentration of that species in the differential form of the rate law, and the order of a reaction is defined as sum of the powers of the all the concentration terms that occur in such a rate law. The experimental kinetics rate law for the important atmospheric reaction (7) is Eq. 8.

The Eq. 8 shows the order with respect to NO is two and with respect to O2 is one, and the order of reaction to be three ( i. e., the sum of the orders of NO and O2).

 

Consider the aqueous phase atmospheric Fe3+- catalyzed oxidation of dissolved sulfur dioxide, generally written as sulfur(IV), by O2. It obeys the rate law:

This reaction is first order in each of Fe(III) and S(IV) and of negative first order in [H+]. So order can be negative, fractional and also zero.

 

Molecularity of the Reaction

In general, reactions occur in more than one step, so each reaction comprises a sequence of elementary reactions. The molecularity is the number of reactant molecules, ions, radicals or any other chemical species in an elementary step. A reaction may have two or more steps and then the molecularity of each step would depend on the number of reactant molecules involved in that step.

 

Bimolecular Reactions involve two reactant species. These are actually two-body reactions.

The formation of the hydroxyl radical, OH, is an example of this type. OH radical is most import in atmospheric chemistry.

Kinetics of Reactions of Different Orders

Zero order reactions occur at a constant rate, and the magnitude of the rate does not change with time. The plot of concentration versus time is linear and the slope of this line equal to zero order rate constant as in Fig. 2.The differential rate equation and its integrated forms are in Eq13.

 

                                                                                             time, (min.)

Fig, 2. Plot of concentration versus time for a zero order reaction

For a first order reaction, the rate depends on the reactant concentration raised to first power.

Consider the rate of a first order reaction, defined by Eq. 14.

On integrating Eq. 14, we obtain the following forms of rate law for a first order reaction.

 

(i)   log {[A]o/[A]t}= 2.303kt (ii) [A]t = [A]o e-kt.                    (iii) log {a/(a–x)}= 2.303kt                 (15)

 

where [A]o = initial concentration of the reactant, A = a and [A]t = concentration at time t = (a–x), and concentration of the reactant reacted in t time = x.

The unit of the first order rate constant is s-1; it is independent of the unit of concentration used.

A second order reaction is one in which the rate depends on (i) the concentration of one reactant raised to power two or (ii) on the concentrations of two reactants each raised to the first power as shown in the rate laws (116) and (17).

The Eq.17 changes into Eq. 16, if the initial concentrations of both A and B are taken equal. So when

[A]= [B], Eq. 17 becomes same as Eq. 16: rate = k[A][A] =

k[A]2. On integrating Eq. 16, we get

(i)           k = (1/[A]t – 1/[A]o)                                          (ii) k = (1/t)( x/{a(a-x)}             (18)

 

In Eq. 18, the symbols have same meaning as in case of first order reaction. The unit of a second order rate constant is L mol-1 s-1.

In third order reactions, the rate expressions are of the type: (i) Rate = k [A]3 (ii) Rate = k[A][B]2 and (iii) Rate = k [A] [B] [C]. Under the condition, [A] = [B] = [C], rate laws (ii) and (iii) will also

The atmospheric oxidation of nitrous acid by O2 (2HNO2 + O2  2HNO3) obeys the third order rate law: – d[O2]/dt = k [HNO2][O2]2. The unit of a third order rate constant is L2 mol-2 s-1.

In Pseudo order reactions the order of chemical reaction appears to be less than the true order because of the experimental conditions used. Pseudo orders occur when one or more reactants are present in large excess as compared to others. For example, the atmospheric reaction: NO + O3

NO2 + O2, obeyed the rate law:

Under the condition [O3] in large excess ( ≥ 10 times) over [NO], up to the end of reaction there would hardly be any significant change in [O3] and so [O3] would remain virtually constant. The kinetics will then obey the rate law

where k1 = k [NO]. So the apparent order in O3 during the reaction will be zero. The reaction will, therefore, will follow a first order kinetics in [NO].

 

Methods of Studying    of Chemical Reactions

Gas Phase Reactions- The major techniques used are: fast flow systems, flash photolysis systems, pulse radiolysis, cavity ring down systems. For example laser- flash photolysis resonance fluorescence technique was used in studying the atmospheric reactions of H, O, Cl, Br , OH radicals etc with atmospheric trace gases.

Reaction in Solutions– The UV-visible spectrometry is the primary tool. It can be combined with stop-flow system for relatively fast solution reactions. Flash photolysis with lasers or lamps, and pulse

radiolysis using high energy ionizing radiation are techniques for studying reactions of radicals and transient species. Electron spin resonance spectroscopy is for detection of radicals.

Determination of Rate Constants and Establishing the Rate Law

The nature of kinetics is determined from appropriate plots such as between log (a – x) vs. t for first order, 1/(a-x) vs. t for second order. The values of rate constants are determined from such plots. It may be pointed out that in environmental chemistry, most of the reactions follow a first- order or pseudo –first- order kinetics.

Kinetics as far as possible is studied under pseudo order conditions. As an example, consider the reaction: HNO2 + O2  2HNO3. The kinetics of this reaction was studied under pseudo order conditions by keeping [HNO2] > [O2]. Kinetics was followed by measuring [O2] periodically with the help of a DO-meter. The disappearance of [O2] was found to be second order and 1/(a-x) vs. t plots were straight lines. The values of second order rate constants determined from these plots at different initial concentrations of [O2] were same within experimental error confirming second order in [O2]. These second order rate constants were proportional to [HNO2], which indicated a first order in [HNO2]. Thus the rate law for this reaction is:

 

At first, the kinetics runs are performed at different concentrations of A by keeping the concentrations of all other reactants constant. From the plot of log rate vs. log [A], which should be linear, the value of the slope, which is equal to a, the order of [A], is determined. Likewise, the orders in B and C are also determined and the experimental rate law is thus established.

 

Half life, Lifetime, Average Life and Residence Time

Half life is the time during which the concentration of a species is reduced to half its initial value. If a be the initial concentration the time required it to decrease up to a/2 is half life, t1/2. For a first order reaction from the rate equation: log {a/(a–x)}= 2.303kt by substituting (a–x) = a/2 and t = t1/2 it can be shown that

The removal of the species may involve several pathways, viz., physical and chemical. Hence, the rate constant k in Eq 26 is sum of rate constants of all the removal processes, assuming these all are of first order. From Eqs. 25 and 26, we get:

Half life = 0.693 × Residence time

Some selected values of residence times are in the Table 1.


 

A reaction mechanism is the description of all the reactants, products, intermediates, transition states and elementary reactions comprising a chemical reaction. Consider the mechanism of the aqueous phase atmospheric oxidation of HNO2 by O2, which comprises two intermediates.


Reaction Mechanism

 

In a multistep reaction, the rate of the reaction is determined by the rate of slowest step, which is known as rate determining or rate controlling step. The fast reactions following slow step have no influence on the rate of the reaction. In the above mechanism, the rate determining step is (C) . Based on steps (A) and (B), at fixed pH the rate law (D) can be derived:

      -d[O2] /dt = k [HNO2]2 [H+]2 [O2]

 

Temperature Dependence of Reaction Rates/Energy of Activation

In general, a 10oC rise in temperature results in ~2-3 times increase in the rate of a reaction.

This is expressed by Arrhenius equation:

               k = A e-Ea/RT

where k is the rate constant , A is pre-exponential or frequency factor, Ea is the Energy of Activation and T is the temperature in K. Ea is defined as the minimum or threshold energy, which molecules must possess in order to react. In modern terms, it is defined as the difference between the energy of the transition state and the average energy of the reactants.

A more useful form of the equation is given below which generally used for the calculation of Ea.

For determination of Ea, the values of rate constants at different temperatures are determined and the plot between log k and 1/T is drawn. The slope of this plot is equal to Ea/2.303R from which Ea can be obtained

 

From the values of rate constants at two different temperatures, Ea can be obtained from the following Eq(30).

where k1 and k2 are the values of rate constants at temperatures at T1 and T2, respectively.

In general, slow reactions have high Ea and fast reactions of low Ea.

 

Problem : The values of rate constants for a reaction were found to be 1×10-3 and 2×10-2 at 27 and 37 OC, respectively. Calculate the value of Ea of the reaction. Given that R = 1.98 cal mol-1.

Solution : Given that k1 = 1×10-3, k2 = 1×10-2 , T1 = 27 + 273= 300 K , T2 = 37 + 273 = 310 K and R = 1.98 cal mol-1. On substituting these values in Eq.(30), we get:

log (1×10-2/1×10-3) = (Ea/2.302×1.98)(1/300-1/310).

On solving the above Eq. Ea =   4.24 × 104 J

 

Photochemical Reactions

When a molecule interacts with the electromagnetic radiation of the appropriate energy, the photon is absorbed and the molecule is raised to an excited state of higher energy. The excited state so formed, depending up on the energy, may undergo variety of photophysical and/photochemical processes. The energy of photon is given by the Eq.(31)

where ʋ is frequency of radiation and h = Planck’s constant. Frequency is related to velocity of the radiation (light), c, and wavelength, λ, by c = ʋ λ.

It may be pointed out that the atmospheric chemistry is driven principally by photochemistry initiated by solar radiation and so the number of important photochemical reactions is large. For example when the radiation of wavelength 390 nm interacts with NO2 the following photochemical reaction occurs. Since NO2 dissociates, it is called photolysis. This reaction generates tropospheric ozone.

 

               NO2 + hט,(λ = 390 nm)    NO + O(3P)

 

Another important reaction is the photolysis of O2 in stratosphere for the formation of ozone.

O2 + hט(λ = 242 nm)       O + O.

There are many photophysical processes, which an excited molecule may undergo without undergoing any chemical reaction, such as luminescence, fluorescence, phosphorescence etc.

 

Catalysis

The catalysts are the substances which accelerate the rate of a reaction without being consumed and undergoing any chemical change. However, the catalysts take part in the reaction and acts through providing a path of lower activation energy. The catalysts are regenerated at the end of the reaction.

For example, the stratospheric ozone depletion is due to catalytic action of species such as Cl, NO etc., as in the reactions:

In the above cycle, a single Cl is able to destroy thousands of O3 molecules. Another important example is the iron-catalyzed oxidation of dissolved SO2 in rainwater.

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Reference

  1. K. J. Laidler, Chemical Kinetics, Harper & Row ,1987.
  2. M. J. Pilling and P. W. Seakins, Reaction Kinetics, Oxford, 1996.
  3. P. W. Atkins, Physical Chemistry, Oxford, 2009.
  4. A. Cornish-Bowden, Fundamentals of Enzyme Kinetics, Wiley-VCH Verlag GmbH & Co., 2012.
  5. James F. Pankow and James J. Morgan, Kinetics for the aquatic environment, Environ. Sci
  6. A Bahl, B. S. Bahl and G. D. Tuli(2012), Essentials of Physical Chemistry, S. Chand, New Delhi
  7. Philip Matthews(2013), Advanced Chemistry, Cambridge, New Delhi
  8. V. Hobbs(2000), Basic Physical Chemistry for the Atmospheric Sciences, Cambridge, UK
  9. Chemosphere; Special issue Thermodynamics and Kinetics of Emerging Contaminants in the Environment, 2015, Elsevier
  10. Chemistry I for Class XII, NCERT, New Delhihttp ://www.answers.com/topic/pseudo-order-1#ixzz2NPBiBpGTcires.colorado.edu/jimenez/…/CHEM-5151_S05_Kinetics_class.pdfhttp://ua.acd.ucar.edu/Presentations/lecture1.pdf