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Absorption of radiant energy by reactant molecules brings in photophysical as well as photochemical changes. According to Einstein's law of photochemical equivalence, the basic principle of photo processes, each reactant molecule is capable of absorbing only one photon of radiant energy. The absorption of photon by a reactant molecule may lead to any of the photo process.                                                                                                                                                                                                                                                                 The chemical reactions, which are initiated as a result of absorption of light, are known as photochemical reactions. In such cases, the absorbed energy is sufficient to activate the reactant molecules to cross the energy barrier existing between the reactants and products or in other words, energy associated with each photon supplies activation energy to reactant molecule required for the change. (1) Characteristics of photochemical reactions (i) Each molecule taking part in a photo process absorbs only one photon of radiant energy thereby increasing its energy level by \[hv\,\,or\,\frac{hc}{\lambda }\] (ii) Photochemical reactions do not occur in dark. (iii) Each photochemical reaction requires a definite amount of energy which is characteristic of a particular wavelength of photon. For example, reactions needing more energy are carried out in presence of UV light (lower \[\lambda \], more E/Photon). A reaction-taking place in UV light may not occur on exposure to yellow light (lower \[\lambda \]and  lesser E/Photon) (iv) The rate of photochemical reactions depend upon the intensity of radiation’s absorbed. (v) The \[\Delta G\] values for light initiated reactions may or may not be negative. (vi) The temperature does not have marked effect on the rate of light initiated reactions. (2) Mechanism of some photochemical reactions (i) Photochemical combination of H2 and Cl2 : A mixture of \[{{H}_{2}}\] and \[C{{l}_{2}}\] on exposure to light give rise to the formation of HCl, showing a chain reaction and thereby producing \[{{10}^{6}}\,\text{to}\,{{10}^{8}}\]molecules of \[HCl\] per photon absorbed.      \[{{H}_{2}}+C{{l}_{2}}\xrightarrow{sunlight}\,2HCl\] The mechanism leading to very high yield of HCl as a result of chemical change can be as follows. Chlorine molecules absorb radiant energy to form an excited molecule which decomposes to chlorine free radicals (Cl) to give chain initiation step. Light absorption step : \[C{{l}_{2}}\xrightarrow{hv}\,C{{l}_{2}}^{*}\]                       ........(i) Chain initiation step : \[C{{l}_{2}}^{*}\to \,C{{l}^{\bullet }}\,+\,C{{l}^{\bullet }}\]                   ........(ii) The chlorine free radical more...

(1) Reaction involving first order consecutive reactions (i) In such reactions, the reactions form a stable intermediate compound before they are finally converted into the products. (ii) For example, reactants (R) are first converted to intermediate (I) which is then converted to product (P) as \[R\xrightarrow{{{k}_{1}}}I\xrightarrow{{{k}_{2}}}P\]  Therefore, the reaction takes place in two steps, both of which are first order i.e., Step I :   \[R\xrightarrow{{{k}_{1}}}I\] ;  Step II :        \[I\xrightarrow{{{k}_{2}}}P\] This means that I is produced by step I and consumed by step II. In these reactions, each stage will have its own rate and rate constant the reactant concentration will always decrease and product concentration will always increase as shown in fig. (2) Reaction involving slow step : When a  reaction occurs by a sequence of steps and one of the step is slow, then the rate determining step is the slow step. For example in the reaction \[R\xrightarrow{{{k}_{1}}}I\]; \[I\xrightarrow{{{k}_{2}}}P\],  if \[{{k}_{1}}<<{{k}_{2}}\] then I is converted into products as soon as it is formed, we can say that \[\frac{-d[R]}{dt}=\frac{d[P]}{dt}={{k}_{1}}[R]\] (3) Parallel reactions : In such type of reactions the reactants are more reactive, which may have different orders of the reactions taking place simultaneously. For example, in a system containing \[N{{O}_{2}}\] and \[S{{O}_{2}},\ N{{O}_{2}}\] is consumed in the following two reactions,\[2N{{O}_{2}}\xrightarrow{{{k}_{1}}}{{N}_{2}}{{O}_{4}}\]; \[N{{O}_{2}}+S{{O}_{2}}\xrightarrow{{{k}_{2}}}NO+S{{O}_{3}}\] The rate of disappearance of \[N{{O}_{2}}\] will be sum of the rates of the two reactions i.e., \[-\frac{d[N{{O}_{2}}]}{dt}=2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}+{{k}_{2}}[N{{O}_{2}}][S{{O}_{2}}]\].

Arrhenius proposed a quantitative relationship between rate constant and temperature as, \[k=A\,{{e}^{-{{E}_{a}}/RT}}\]                                                …..(i) The equation is called Arrhenius equation. In which constant  A is known as frequency factor. This factor is related to number of binary molecular collision per second per litre. \[{{E}_{a}}\] is the activation energy. T is the absolute temperature and R is the gas constant Both A and \[{{E}_{a}}\] are collectively known as Arrhenius parameters. Taking logarithm equation (i) may be written as, \[\log k=\log A-\frac{{{E}_{a}}}{2.303\,RT}\]                                             …..(ii) The value of activation energy \[({{E}_{a}})\] increases, the value of k decreases and therefore, the reaction rate decreases. When log k plotted against \[1/T\],  we get a straight line. The intercept of this line is equal to log A and slope equal to \[\frac{-{{E}_{a}}}{2.303\,R}\]. Therefore \[{{E}_{a}}=-2.303\,R\times \text{slope}\]. Rate constants for the reaction at two different temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\], \[\log \frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\]                                    …..(iii) where \[{{k}_{1}}\]and \[{{k}_{2}}\]are rate constant at temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] respectively \[({{T}_{2}}>{{T}_{1}})\].

(1) Collision theory (i) The basic requirement for a reaction to occur is that the reacting species must collide with one another. This is the basis of collision theory for reactions. (ii) The number of collisions that takes place per second per unit volume of the reaction mixture is known as collision frequency (Z). The value of collision frequency is very high of the order of \[{{10}^{25}}\,\text{to }{{10}^{28}}\] in case of binary collisions. (iii) Every collision does not bring a chemical change. The collisions that actually produce the product are effective collisions. The effective collisions, which bring chemical change, are few in comparison to the total number of collisions. The collisions that do not form a product are ineffective elastic collisions, i.e., molecules just collide and disperse in different directions with different velocities. (iv) For a collision to be effective, the following two barriers are to be cleared, (a) Energy barrier : “The minimum amount of energy which the colliding molecules must possess as to make the chemical reaction to occur, is known as threshold energy”.

• In the graph 'E' corresponds to minimum or threshold energy for effective collision.
• There is an energy barrier for each reaction. The reacting species must be provided with sufficient energy to cross the energy barrier.

(b) Orientation barrier : The colliding molecules should also have proper orientation so that the old bonds may break and new bonds are formed. For example, \[N{{O}_{2}}(g)+N{{O}_{2}}(g)\to {{N}_{2}}{{O}_{4}}(g).\] During this reaction, the products are formed only when the colliding molecules have proper orientation at the time of collisions. These are called effective collisions. (v) Thus, the main points of collision theory are as follows, (a) For a reaction to occur, there must be collisions between the reacting species. (b) Only a certain fraction of the total number of collisions is effective in forming the products. (c) For effective collisions, the molecules should possess sufficient energy as well as orientation. (vi) The fraction of effective collisions, under ordinary conditions may vary from nearly zero to about one for ordinary reactions. Thus, the rate of reaction is proportional to : (a) The number of collisions per unit volume per second (Collision frequency, Z) between the reacting species (b) The fraction of effective collisions (Properly oriented and possessing sufficient energy), f i.e.,   \[\text{Rate}=\frac{-dx}{dt}=f\times Z\] Where f is fraction of effective collision and Z is the collision frequency. (vii) The physical meaning of the activation energy is that it is the minimum relative kinetic energy which the reactant molecules must possess for changing into the products molecules during their collision. This means that  the fraction of successful collision is equal to \[{{e}^{-{{E}_{a}}/RT}}\] called Boltzmann factor. (viii) It may be noted that besides the requirement of sufficient energy, the molecules must be properly oriented in space also for a collision to be successful. Thus, if \[{{Z}_{AB}}\] is more...

(1) Integration method (Hit and Trial method) (i) The method can be used with various sets of \[a,\ x\] and \[t\] with integrated rate equations. (ii) The value of \[k\] is determined and checked for all sets of \[a,\ x\] and \[t\]. (iii) If the value of \[k\] is constant, the used equation gives the order of reaction. (iv) If all the reactants are at the same molar concentration, the kinetic equations are : \[k=\frac{2.303}{t}\ {{\log }_{10}}\frac{a}{(a-x)}\]                                     (For first order reactions) \[k=\frac{1}{t}\left[ \frac{1}{a}-\frac{1}{a-x} \right]\]                              (For second order reactions) \[k=\frac{1}{2t}\left[ \frac{1}{{{(a-x)}^{2}}}-\frac{1}{{{a}^{2}}} \right]\] (For third order reactions) (2) Half-life method :  This method is employed only when the rate law involved only one concentration term. \[{{t}_{1/2}}\propto {{a}^{1-n}}\]; \[{{t}_{1/2}}=k{{a}^{1-n}}\]; \[\log {{t}_{1/2}}=\log k+(1-n)\ \log a\] A plotted graph of \[\log {{t}_{1/2}}\]vs log a  gives a straight line with slope \[(1-n)\], determining the slope we can find the order n. If   half-life at different concentration is given then, \[{{({{t}_{1/2}})}_{1}}\propto \frac{1}{a_{1}^{n-1}};\] \[{{({{t}_{1/2}})}_{2}}\propto \frac{1}{a_{2}^{n-1}};\] \[\frac{{{({{t}_{1/2}})}_{1}}}{{{({{t}_{1/2}})}_{2}}}={{\left( \frac{{{a}_{2}}}{{{a}_{1}}} \right)}^{n-1}}\] \[{{\log }_{10}}{{({{t}_{1/2}})}_{1}}-{{\log }_{10}}{{({{t}_{1/2}})}_{2}}=(n-1)\ [{{\log }_{10}}{{a}_{2}}-{{\log }_{10}}{{a}_{1}}]\] \[n=1+\frac{{{\log }_{10}}{{({{t}_{1/2}})}_{1}}-{{\log }_{10}}{{({{t}_{1/2}})}_{2}}}{({{\log }_{10}}{{a}_{2}}-{{\log }_{10}}{{a}_{1}})}\] This relation can be used to determine order of reaction ‘n’ Plots of half-lives Vs concentrations (t1/2 µ a1–n) (3) Graphical method :  A graphical method based on the respective rate laws, can also be used. (i) If the plot of \[\log (a-x)\] Vs \[t\] is a straight line, the reaction follows first order. (ii) If the plot of \[\frac{1}{(a-x)}\] Vs \[t\] is a straight line, the reaction follows second order. (iii) If the plot of \[\frac{1}{{{(a-x)}^{2}}}\] Vs \[t\] is a straight line, the reaction follows third order. (iv) In general, for a reaction of nth order, a graph of \[\frac{1}{{{(a-x)}^{n-1}}}\] Vs \[t\] must be a straight line.   Plots from integrated rate equations    Plots of rate Vs concentrations [Rate = k(conc.)n ]    (4) Van't Haff differential method :  The rate of reaction varies as the nth power of the concentration Where \['n'\] is the order of the reaction. Thus for two different initial concentrations \[{{C}_{1}}\] and \[{{C}_{2}}\] equation, can be written in the form, \[\frac{-d{{C}_{1}}}{dt}=kC_{1}^{n}\] and \[\frac{-d{{C}_{2}}}{dt}=kC_{2}^{n}\] Taking logarithms,  \[{{\log }_{10}}\left( \frac{-d{{C}_{1}}}{dt} \right)={{\log }_{10}}k+n{{\log }_{10}}{{C}_{1}}\]                                                                                                 …..(i) and \[{{\log }_{10}}\left( \frac{-d{{C}_{2}}}{dt} \right)={{\log }_{10}}k+n{{\log }_{10}}{{C}_{2}}\]                                                                                                          …..(ii) Subtracting equation (ii) from (i), \[n=\frac{{{\log }_{10}}\left( \frac{-d{{C}_{1}}}{dt} \right)-{{\log }_{10}}\left( \frac{-d{{C}_{2}}}{dt} \right)}{{{\log }_{10}}{{C}_{1}}-{{\log }_{10}}{{C}_{2}}}\]                                                                                                                  …..(iii) \[\frac{-d{{C}_{1}}}{dt}\] and \[\frac{-d{{C}_{2}}}{dt}\] are determined from concentration Vs time graphs and the value of \['n'\] can be determined. (5) Ostwald's isolation method (Initial rate method) This method can be used irrespective of the number of reactants involved e.g., consider the reaction, \[{{n}_{1}}A+{{n}_{2}}B+{{n}_{3}}C\to \text{Products}\]. This method consists in finding the initial rate of the reaction taking known concentrations of the different reactants (A, B, C). Suppose it is observed as follows, more...

The rate at which a substance reacts is directly proportional to its active mass and the rate at which a reaction proceeds is proportional to the product of the active masses of the reacting substances.

• For a reaction, \[aA+bB\to \] product

Rate \[=\left( \frac{dx}{dt} \right)\propto {{[A]}^{a}}{{[B]}^{b}}\]; \[\left( \frac{dx}{dt} \right)=k{{[A]}^{a}}{{[B]}^{b}}\] Where k is called rate constant or velocity constant. When \[[A]=[B]=1\ mol/litre\], then \[\frac{dx}{dt}=k\] Thus, rate constant k is also called specific reaction rate.

• The value of rate constant depends on, nature of reactant, temperature and catalyst. It is independent of concentration of the reactants.
• Unit of rate constant \[={{\left[ \frac{\text{litre}}{\text{mol}} \right]}^{n-1}}\times {{\sec }^{-1}}\]\[\ ={{\left[ \frac{\text{mol}}{\text{litre}} \right]}^{1-n}}\times {{\sec }^{-1}}\]

  Where \[n=\] order of reaction.

The rate of a chemical reaction depends on the following things (1) Nature of reactants (i) Physical state of reactants : This has considerable effect over rate of reaction. \[\underset{\text{Decreasing rate of reaction}}{\mathop{\xrightarrow{\text{Gaseous satae }>\text{Liquid state}>\text{Solid state}}}}\,\] (ii) Physical size of the reactants : Among the solids, rate increases with decrease in particle size of the solid. (iii) Chemical nature of the reactants (a) Reactions involving polar and ionic substances including the proton transfer reactions are usually very fast. On the other hand, the reaction in which bonds is rearranged, or electrons transferred are slow. (b) Oxidation-reduction reactions, which involve transfer of electrons, are also slow as compared to the ionic substance. (c) Substitution reactions are relatively much slower. (2) Effect of temperature : The rate of chemical reaction generally increases on increasing the temperature. The rate of a reaction becomes almost double or tripled for every \[{{10}^{o}}C\] rise in temperature. Temperature coefficient of a reaction is defined as the ratio of rate constants at two temperatures differing by (generally 25°C and 35°C) 10°C. \[\mu =\]\[\text{Temperature coefficient}=\frac{k\,\text{at (t}+\text{1}{{\text{0}}^{\text{o}}}C)}{k\,\text{at }{{t}^{o}}C}=\frac{{{k}_{{{35}^{o}}C}}}{{{k}_{{{25}^{o}}C}}}\]  (3) Concentration of reactants : The rate of a chemical reaction is directly proportional to the concentration of the reactants means rate of reaction decreases with decrease in concentration. (4) Presence of catalyst : The function of a catalyst is to lower down the activation energy. The greater the decrease in the activation energy caused by the catalyst, higher will be the reaction rate.             (5) Effect of sunlight :  There are many chemical reactions whose rate are influenced by radiations particularly by ultraviolet and visible light. Such reactions are called photochemical reactions. For example, Photosynthesis, Photography, Blue printing, Photochemical synthesis of compounds etc. The radiant energy initiates the chemical reaction by supplying the necessary activation energy required for the reaction.