First order reaction, rate expression, characteristics, examples

Problem 4 What is a first order reaction Derive the rate expression for it and discuss its characteristics. Give some examples of first order reaction. 

A reaction in which the reaction rate depends only on one concentration term is said to be a first order reaction. 

Consider the following simplest first order reaction. 

Let a mole/litre be the initial concentration of the reactant A. Suppose x mole/litre of A decomposes in time t, leaving behind (a - x) mole/litre of it. For a first order reaction, the reaction rate at any time t is given by  

If time is expressed in second or minute, k is expressed in second 1 or minuterespectively. 

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Analyses of rate measurements for the decomposition of a large number of basic halides of Cd, Cu and Zn did not always identify obedience to a single kinetic expression [623—625], though in many instances a satisfactory fit to the first-order equation was found. Observations for the pyrolysis of lead salts were interpreted as indications of diffusion control. More recent work [625] has been concerned with the double salts jcM(OH)2 yMeCl2 where M is Cd or Cu and Me is Ca, Cd, Co, Cu, Mg, Mn, Ni or Zn. In the M = Cd series, with the single exception of the zinc salt, reaction was dehydroxylation with concomitant metathesis and the first-order equation was obeyed. Copper (=M) salts underwent a similar change but kinetic characteristics were more diverse and examples of obedience to the first order, the phase boundary and the Avrami—Erofe ev equations [eqns. (7) and (6)] were found for salts containing the various cations (=Me). 

While it may not be intuitively obvious, if the displacement from equilibrium is small, the rate of return to equilibrium can always be expressed as a first-order process (e.g., see Eq. 9-13). In the event that there is more than one chemical reaction required to reequilibrate the system, each reaction has its own characteristic relaxation time. If these relaxation times are close together, it is difficult to distinguish them however, they often differ by an order of magnitude or more. Therefore, two or more relaxation times can often be evaluated for a given solution. In favorable circumstances these relaxation times can be related directly to rate constants for particular steps. For example, Eigen measured the conductivity of water following a temperature jump18 and observed the rate of combination of H+ and OH for which x at 23°C equals 37 x 10 6 s. From this, the rate constant for combination of OH and H+ (Eq. 9-52) was calculated as follows (Eq. 9-53) ... 

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... 

Rate equations based on concentration dependence (reaction order) Under some conditions, the rate characteristics of solid-state processes can be expressed through a concentration-type dependence. For example, if the decomposition of a large number of small crystallites is controlled by an equally probable nucleation step at each particle, then this is a first-order process (Al, FI). These rate equations are also used in nonisothermal kinetic analyses of rate data in the form g(a) = kt and are therefore included in Table 5.1. 

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