Second order reaction, rate expression, characteristics

Problem 7 What is a second order reaction Derive the rate expression for a second order reaction. Discuss the characteristics of a second order reaction. Write some examples of second order reactions and study the kinetics of any one reaction. (Meerut 2002,2000) 

Or What is the unit of k in a second order reaction (Meerut 2006) 

A reaction is said to be of the second order if its reaction rate depends on two concentration terms of reactants. 

Let a be the initial concentration of each of the two reactants and (a - jc) be their concentration after any time t. Then, according to the law of mass action, the reaction rate is given by 

Equation (2) is known as second order rate expression. 

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Even for more complicated reactions, the linear half-life expression is a good approximation for short times. Second-order reactions have a characteristic time of 1/kC, and a general time constant for higher-order reactions can be defined l/kC" . The concepts of rate and characteristic time are used interchangeably throughout the chapter. 

The mass transfer characteristics obtained on packings are reported in several different ways. At the more fundamental level, we extract volumetric mass transfer coefficients from the experimental performance data. These coefficients, which we encountered in Illustrations 2.2 and 2.3, consist of the product of a film coefficient and the nominal specific surface area a (in w /m ) of the packing, expressed in units of square meter (m ) per cubic meter (m ) of packing. If we use the molar concentration-based coefficient or /cl that has units of meter per second (m/s), then the volumetric coefficient given by the product k a or ki a will have units of reciprocal seconds, which is the same as that of a first-order reaction rate constant. Specific surface areas of packings span the range of 100 to 1000 m /m. ... 

Although Diels-Alder polymerizations involve a reaction of an unsaturated molecule, and the polymer does not have a structure typical of a condensation polymer, the characteristics of the polymerization reaction are those of a condensation polymerization. The kinetics of a Diels-Alder polymerization should be those of a typical condensation polymerization and involve a series of individual reactions, and not a chain type mechanism. A typical second-order rate expression, -dC/dt = kC2 should hold for a good portion of the polymerization reaction, where C is the concentration of both diene and dienophile ends. Typically, this rate would break down only when the molecular mobility is extremely low or when shielding of functional groups occurs in dilute solutions. 

For first-order reactions in closed vessels, the half-life is independent of the initial reactant concentration. Defining characteristic times for second- and third-order reactions is somewhat complicated in that concentration units appear in the reaction rate constant k. Integrated expressions are available in standard references (e.g., Capellos and Bielski, 1980 Laidler, 1987 Moore and Pearson, 1981). 

The rate constant expresses the proportionality between the rate of formation of B and the molar concentration of A and is characteristic of a particular reaction. The units of k depend on the order of the reaction. For zero order, they are moles liter" time" (time is frequently given in seconds). For first order, they are time" , and for second order, liters moles" time" , etc. The units of k are whatever is needed for zero order reaction, [B] changes at a constant rate independent of the concentration of reactants, which is especially important in enzyme kinetics. A plot of [B] versus t for such a reaction is a straight line. A somewhat more complicated example is... 

The N02" ion can be detected in such solutions by the observation of characteristic Raman absorption bands. Two kinds of rate laws have been found to describe the kinetics of most aromatic nitration reactions. With relatively unreactive aromatic substrates, second-order kinetics, first order in nitrating reagent and first order in aromatic compound, are observed. This finding corresponds to the rate-limiting step being the attack of the electrophile on the aromatic substrate. With more reactive aromatics, this step becomes faster than formation of the nitronium ion, and the concentration of the aromatic no longer appears in the rate expression. Under these conditions, different aromatic substrates suffer nitration at the same rate, since the rate-determining step does not directly involve the aromatic substrate. (Review Chapter 4, Section 4.2, p. 169, where the kinetic expressions for nitration under these conditions were discussed.)... 

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