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Quantitative Aspects of Kinetics

Key Points
Rate Laws and Order of Reactions
Rate law is a mathematical expression that relates the rate of reaction to the concentrations of reactants and temperature and other factors like the presence of the catalyst or enzyme as well as the inert species present in moderation as solvent molecules and some other molecules of indifferent nature and shows the kinetics of any reaction through a constant of proportionality (an experimentally determined constant).
The "Rate Law or Rate Equation or Rate Expression."
Rate = k [Reactants]^Order
Types of Order of Reaction
Zero order reaction
First order reaction
Pseudo first order reaction
Second order reaction
Third order reaction
Fractional order reaction
Rate Law Determination
Rate of reaction is the measure of the change in concentration of reactants and or products in a particular time interval calculated by its difference in their initial and final concentrations divided by the time interval in which that change in concentration has taken place and the average rate is a smooth measure of rates of reactions taking place over a measurable time interval while the instantaneous rate refers to that precise moment of time and technique used involves titrimetric method of determination by detecting the linear change in the concentration of the substance over time in proportion to other substances involved as well as the spectroscopic method of determining the rates of reactions using absorbance and transmittance techniques over a measurable time interval and while the final technique involves using a stopped flow technique in which reactants are mixed thoroughly and allowed to react for a short period of time after which the reaction is stopped and analyzed to get the change in concentrations of the reactants involved over a very small time interval accurately and precisely and initial rate is extensively used for determining the rate laws of the reactions involving gaseous reactants and products as well as in cases where fast reactions pose problems in using other techniques and widely used in enzyme kinetics and heterogeneous catalysis and in reactions involving free radicals and the order of a reaction is determined by carrying out experiments in a system where all the variables that affect the rate of reaction are controlled except the concentration of the reactants and finding the partial order of reaction for each reactant by systematically varying the other variables such as temperature and the presence of the catalyst and is represented by the constant term of proportionality in the rate law expression of the equation through experiments and finally by adding all the partial orders together to get the overall order of the reaction involved in a particular chemical reaction taking place in the reaction vessel and it provides information about the mechanism of a particular reaction taking place in the reaction vessel by examining the values of the order of the reaction with respect to the reactants involved and needs only one experiment for the determination of zero order reaction while multiple experiments are necessary for the determination of the orders of other types of reactions and a further technique for determining the mechanism of a reaction is the method of initial rates in which concentrations of all the reactants are known at the beginning of each experiment and many experimental techniques used for determining the rate of reaction include continuous flow method and relaxation method and stop flow method and flash photolysis and temperature jump methods and ultrasonic absorption method and NMR and ESR spectroscopy methods and these techniques are useful in determining the rates of reactions with half life periods ranging from a few seconds to several milliseconds to several years and are useful in determining the rates of reactions that occur in various chemical systems of homogeneous and heterogeneous nature in gas and liquid and solid states and also biochemical reactions involving enzymes and determination of rates of reactions of industrial importance are useful in optimizing the industrial production of various substances in chemical industries and some of the reactions are acid base reactions and precipitation and condensation reactions and redox reactions and biochemical reactions and gas phase reactions and heterogeneous catalysis and enzyme kinetics and metal complex reactions and free radical reactions and determination of reaction rates is essential in carrying out research in the areas of reaction mechanisms and catalysis and are a useful tool in solving various problems in the fields of analytical chemistry and chemical engineering and solid state chemistry and surface chemistry and electrochemistry by efficiently designing various reactors which are used in industries for the production of various substances and in designing the quality of products in pharmaceutical industries and food industries and polymer industries and paints and coatings industries research and also find applications in all other manufacturing industries and effective in understanding various biological processes of life as well as in efficient drug interactions with enzymes and receptors of the body which are useful in drug designing and effective in imaging various biochemical processes in living bodies through medical imaging techniques which play a vital role in the synthesis of new drugs and discovery of new catalytic systems of industrial and economical importance as well as in carrying out research in many unexplored areas of science for the betterment of society and mankind and a few applications of kinetics in various fields are briefly discussed below and rate constants are evaluated at different temperatures to find the activation energy of a particular reaction and the Arrhenius equation is used for finding the values of activation energy from the experimentally determined values of rate constants and the collision theory is the theory for calculating the rate constants theoretically without determining them experimentally and the Lindemann mechanism is the theory for calculating the rate constants of a specific reaction used in gas phase reactions involving gaseous reactants and the rate determining step of that reaction involved in a particular chemical reaction is the slowest step of the reaction involved in the reaction mechanism and thus it is the rate limiting step of the reaction mechanism taking place in the reaction vessel and responsible for determining the overall rate of that particular reaction of interest under investigation and the catalyst provides an alternate pathway for the reaction to take place by lowering the activation energy of the reaction and hence enhancing the reaction rate and rate of a reaction can be increased by increasing the concentration of reactants and increasing the temperature of the reaction and adding a catalyst and changing the solvent system in which the reaction is taking place and addition of inert species to the reaction mixture may or may not affect the rate of the reaction depending on the nature and the composition of the reaction mixture and the homogeneous reactions involve the reactants and products of the reaction which are uniformly distributed throughout the reaction mixture may be it gaseous or liquid state while heterogeneous reactions occur at the phase boundary of the reaction mixture such as between a solid and a liquid and between a solid and a gas and the complex reactions involve a number of elementary steps taking place in a sequential manner which makes it a complex process and elementary reactions consist of only one step thus making them simple processes and first order reactions can be either elementary reactions or complex reactions while elementary reactions are always first order reactions and the methods of determining the molecularity of the reactions are by using the stoichiometry method and the experimental rate law method and the equilibrium method and the method based on the effect of temperature on the reaction rates while the order of a reaction and the molecularity of a reaction are the same for elementary reactions while they are different for complex reactions as the order of a reaction is always an experimentally determined quantity while the molecularity of a reaction is the theoretical expression for the number of molecules that take part in an elementary reaction and the kinetic salt effect is the effect of neutral salts in modifying the rate of ionic reactions taking place in a solution where the neutral salts are present in small amounts and play a significant role during the studies of reaction mechanisms in solutions and also play an important role in biological processes living in the ocean as sea water contains various types of salts in relatively large amounts and the cage effect is the effect of surrounding solvent molecules in a solution on the rate of a reaction in which the solvent molecules keep the reactants in close proximity until they react to form the products of the reaction taking place and is important in homogeneous gas phase and liquid phase reactions and the orientation effect is a special type of cage effect observed in reactions involving dipolar molecules as a result of the alignment of the reactant molecules with respect to each other by the orientation effect caused by the surrounding solvent molecules or by the electric field and is important in the study of reactions taking place in non aqueous solvents and the Bronsted catalysis law states that a reaction is efficiently and effectively catalysed by acids which are good proton donors as they increase the concentration of electrophiles while bases which are good proton acceptors catalyse reactions by increasing the concentrations of nucleophiles and Bronsted acids can effectively donate protons and bronsted bases can efficiently accept protons and according to the Bronsted theory of acids and bases the substance which donates a proton is the acid and the substance which accepts a proton is the base and Bronsted bases have the ability to donate electrons as they are good nucleophiles and Bronsted acids are good electrophiles as they have the ability to accept electrons and thus play a significant role in acid base catalysed reactions and the specific acid catalysis is a mechanism of acid catalysis which occurs only in the presence of strong acids while general acid catalysis can efficiently occur in the presence of weak acids as well as strong acids and the nucleophilic catalysis is a basic catalysis that takes place in the presence of nucleophiles and the specific base catalysis takes place only in the presence of strong bases while the general base catalysis occurs in the presence of both strong bases and weak bases and a specific acid catalyst provides a proton to the reactant which is a weak nucleophile and converts it to a strong nucleophile thus increasing the rate of the reaction efficiently while general acid catalysts donate protons to weak nucleophiles as well as strong nucleophiles to enhance the rate of the reaction under investigation and in cases where the reactant is a weak acid the specific base catalyst accepts a proton from it converting it to a weaker acid enhancing the rate of the reaction efficiently while in general base catalysis bases accept protons from weak acids as well as strong acids to drive the reaction in the forward direction and in the absence of acid base catalysts such reactions occur to a very small extent and acidic catalysts are known to enhance electrophilic reactions as acids donate protons to electron rich centres thus increasing the electron density at those centres and basic catalysts are known to enhance nucleophilic reactions as bases donate electrons to electron poor centres thus enhancing the electron density at those centres and in electrophilic catalysis an electrophile is donated by the catalyst while nucleophilic catalysis is the process of donating nucleophiles by the catalyst and a nucleophile is an electron rich species having a great tendency to donate electrons to a vacant orbital of an electrophile and electrophile is an electron poor species with an empty