Chemical Kinetics PDF

CHEMICAL KINETICS RATE OF A CHEMICAL REACTION: is defined as change in concentration of any of the reactant or product per unit time. Rate = Unit = moles L-1s-1 The rate of reaction are of two types: 1) Average rate of reaction 2) Insta...

CHEMICAL KINETICS RATE OF A CHEMICAL REACTION: is defined as change in concentration of any of the reactant or product per unit time. Rate = Unit = moles L-1s-1 The rate of reaction are of two types: 1) Average rate of reaction 2) Instantaneous rate of reaction AVERAGE RATE OF REACTION: It depends on the change in concentration of reactants or products and the time taken for that change to occur. For reaction, R → P, if [R1], [P1] are the concentrations at time t1 and [R2], [P2] are the concentrations at time t2, then, ∆ [R] = R2-R1 ∆ [P] = P2-P1 ∆ 𝑡 = t2-t1 Then average rate = Rate of disappearance of R = rate of appearance of P 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑐𝑜𝑛𝑐 𝑜𝑓 𝑅 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑐𝑜𝑛𝑐 𝑜𝑓 𝑃 = = 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 ∆ [R] ∆ [P] =- = ∆𝑡 ∆𝑡 INSTANTANEOUS RATE OF REACTION: The rate of change of concentration of reactants or products at a particular instant of time is called instantaneous rate of reaction. For the given reaction, A + B C Instantaneous rate = NOTE: negative sign for reactants indicates that concentration of reactants decreases with time while positive sign for products indicates that concentration of products increases with time. For reactions involving stoichiometric coefficients: aA + bB cC + dD Instantaneous Rate = Note: Symbol ′∆′ is used for larger change i.e average rate and symbol ‘d’ is used for small change i.e for instantaneous rate. Units of rate of reaction: Generally concentration is expressed in moles/litre and the time is min or seconds so unit of rate is mol L-1 s-1 For Gaseous reactions, Pressures ( in atm) are used in place of molar concentration so rate is expressed as atm s-1. The relationship between partial pressure of gas and its molar concentration (c) follows the relationship: 𝑛 𝑝 𝑝 pV = nRT ; or = ; or c = 𝑉 𝑅𝑇 𝑅𝑇 𝑁𝑜.𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑎𝑠 where partial pressure, p = × Total pressure 𝑇𝑜𝑡𝑎𝑙 𝑚𝑜𝑙𝑒𝑠 FACTORS AFFECTING RATE OF REACTION 1) Nature of reactants: Reactions involving polar and ionic substances are fast whereas the reactions involving covalent bonds are slow. 2) Concentrations of reactants: Rate of reaction increases with increases in concentration because then the rate of molecular collisions increases. 3) Temperature: The rate of molecular collisions, hence rate of reaction increases with temperature. 4) Presence of catalyst: Rate of reaction increases with the use of catalyst. 5) Surface area: Rate increases with increase in surface area of reactants. COLLISION THEORY OF REACTION RATE 1) Reaction occurs only when reactant molecules undergo collision. 2) Only the effective collisions leads to product formation. 3) Collisions are effective only when the reactant molecules acquire definite amount of energy called Threshold energy ( It is the minimum amount of energy required to make effective collisions). Effective collisions are governed by following factors: a) Energy Barrier: Threshold energy is the minimum energy which when acquired by the reactants leads to product formation. Energy less than this will not lead to product formation. b) Orientation barrier: Reactant molecules with proper orientation only, will lead to the breaking of old bonds and formation of new bonds. ACTIVATION ENERGY: The excess energy that the reactant molecules must acquire in order to cross the energy barrier and to change into the products is called activation energy (Ea). ILLUSTRATION OF ACTIVATION ENERGY IN REACTIONS EXOTHERMIC REACTIONS: Heat is given out in these reactions. Energy of reactants (ER) is more than energy of products (EP) for exothermic reactions so extra energy is released out & representated as E. E = E p – ER ( so E is negative for exothermic) where Ea = activation energy ET = Threshold energy ER = Energy of reactants Ep = Energy of products. With the help of activation energy (Ea) , reactant molecules acquire threshold energy (ET), makes an activated complex over there which breaks up finally forming the products with lower energy. Thus giving out excess of heat Endothermic reaction: Heat is absorbed in these reactions. Energy of reactants is less than energy of products for endothermic reactions. ER < EP E = EP - ER Ea = ET - ER NOTE: Activation energy is low for fast reactions while it is high for slow reactions. DEPENDENCE OF REACTION RATE ON TEMPERATURE It has been seen that for every 10oC rise in temperature, the reaction rate increases two to three fold. Explanation for increase in reaction rate with temperature The temperature T1 , T2, T3 follows the increasing order: T1 < T2 < T3 1). At low temperature, T1, the molecules acquire less kinetic energy and hence less effective collisions occur. Thus the shaded area abcd represents the number of molecules undergoing effective collisions ( i.e; the molecules whose energy is greater than or equal to threshold energy.)  2). At higher temperature ,T2, more kinetic energy is acquired and hence number of molecules reaching the threshold level and thus leading to effective collisions increases ( area abef). 3). At highest temperature ,T3, the effective collisions are maximum as more fraction of molecules acquire high kinetic energy and thus the speed of the reaction increases. DEPENDENCE OF REACTION RATE ON CONCENTRATION OF REACTANTS Law of mass action: Rate of reaction is directly proportional to the concentration of reactants raised to the power equal to stoichiometric coefficients. For the reaction aA + bB cC + dD Rate of reaction [A]a [B]b Or r = k [A]a [B]b where k = rate constant or velocity constant. CHARACTERISTICS OF RATE CONSTANT 1. It is the measure of rate of reaction. 2. Higher is the rate constant , higher is the rate of reaction. 3. A particular reaction has definite value of rate constant (k) at particular temperature. 4. “k” increases with increase of temperature. 5. “ k “ does not depend upon initial concentration of reactants. 6. Its unit depends upon order of reaction. Molecularity of a reaction: The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a raction. If one reactant is involved, the reaction is unimolecular. Eg : NH4NO2 N2 + 2H2O If two reactants are involved, it is bimolecular reaction and so on. 2HI H2 + I2 (bimolecular) The molecularity of a reaction cannot be zero, fractional or more than three Eleementary reaction: The reactions taking place in one step is called elementary reaction. Eg : NH4NO2 N2 + 2H2O Complex ractions: Chemical reactions which proceed through more than one steps are termed as complex reactions and detailed description of various steps of complex chemical reaction is called mechanism of the reaction. Eg: 4HBr + O2 2H2O + 2Br2 Step 1: HBr + O HOOBr Step 2: HOOBr + HBr 2HOBr Step 3: HOBr + HBr O + Br2 ] × 2 4HBr + O2 2H2O + 2Br2 The different steps of the given reaction are based upon the experimental evidencs like detection of the presence of some short lived intermediates. All the above steps proceed at different rates and slowest step of mechanism is known as the rate determining step and rate law is written for slowest step. Rate = k[ HBr] [ O2] The reaction is first order w.r.t both HBr and O2. ORDER OF REACTION The power to which the concentration term of a particular reactant in the rate law is raised is called the order of reaction of reaction with respect to the reactant. Overall order of reaction is the sum of all powers to which the concentration terms in the rate law are raised to express the observed rate of reaction. Difference between law of mass action and rate law The powers in the expression of rate of reaction in law of mass action are just the stoichiometric coefficients which just tell the number of moles of reactants taking part in reaction. This expression can be written just by looking at the reaction.  While the powers in rate law expression indicate how the rate of reaction varies with concentration. This rate expression can be written only after experimental verification. The expressions of rate in law of mass action and rate law can be or can not be same. Eg: 3A + 2B 2C Law of mass action : r = [A]3 [B]2 The powers here are just the stoichiometric coefficients Rate law: r = [A]2 [B]1 : The powers here indicates that order of reaction with respect to A is 2, while with respect to B is 1. Overall order of reaction is 2+1=3. Difference between order and molecularity Molecularity Order of reaction 1. It is equal to the total number of It is equal to the sum of the powers of molecules present in one step of the concentration terms present in the reaction. rate law. 2. It cannot be zero or fractional. It can be zero or fractional. 3. Molecularity is for each step of It is for the overall reaction and is the reaction and is explained by determined experimentally. mechanism of the reaction. 4. It is a theoretical concept. It is an experimental fact. TYPES OF REACTIONS DEPENDING ON ORDER OF REACTION 1. Zero order reactions For the reaction A P r = k [A]0 order of reaction = 0, i.e; rate of reaction is independent of concentration of its reactants.  Unit of k for zero order reaction : k= = mol L-1 s-1 2. First order reactions: For the reaction A P r = k [A]1 order of reaction = 1, i.e; rate is directly proportional to concentration of A. On doubling the concentration of A, rate gets doubled For the reaction A + B P r = k [A]1 [B]0 Here overall order of reaction is 1 and rate is directly proportional to A but independent of concentration of B. Unit of rate constant : r = k [A]1 k= 3. Second order reactions: For reaction A P r = k [A]2 i.e; as concentration of A is doubled, rate increases four times. Unit of k: r = k [A]2 k= = mol-1 L s-1 4. Third order reactions: For reaction A P r = k [A]3 k= = mol-2 L2 s-1 NOTE: In general unit of rate constant = mol 1-n L n-1 s -1 Pseudo first order reactions: For an elementary reaction, the order is same as molecularity. In several reactions, the order is different from molecularity. This is particularly the case when one of the reactants is present in large excess. Eg: C12H22O12 + H2 O C6H12O6 + C6H12O6 The molecularity in above reaction is 2 whereas its order is 1. Such reactions in which molecularity is 2 but they confirm to the first order are known as pseudo first order reactions. Value of rate of pseudo first order reactions depends upon the concentration of the reactant present in small amount. MATHEMATICAL DERIVATION OF ZERO ORDER REACTIONS If A P Suppose initial concentration of A is [A]0 After time t, concentration is [A] So for zero order reaction, rate is proportional to zero power of concentration of A at that time Thus rate [A]0 = -d[A]/dt [A]0 = -d[A]/dt = k × 1 Or, -d[A] = kdt = d[A] = -kdt On integration we have, ∫ d[A] = - k ∫ dt [A] = - kt + I, ---------- 1. where I is the constant of integration If t = 0, at the start of the reaction then [A] = [A]0 Then substituting these in eq 1. [A]0 = -k x 0 + I, So, I = [A]0 , substituting this value of I in eq 1, we get  [A] = - kt + [A]0 ----------------------- Comparing above eq. with straight line equation, y = mx + c, if we plot [A] against ‘t’, we get a staright line with slope = -k and intercept equal to [A]0 On simplifying above eq. [𝑨]𝟎−[𝑨] k= 𝒕 Examples of zero order equation: 1. Enzyme catalyzed reactions 2. Decomposition of gaseous ammonia 𝟏𝟏𝟑𝟎𝑲 Eg. 2NH3 (g) N2(g) + 3H2(g) 𝑷𝒕 MATHEMATICAL DERIVATION OF FIRST ORDER REACTION A P Suppose initial concentration of A is [A]0 After time t, concentration is [A] So for first order reaction, rate is proportional to concentration of A at that time Thus rate [A] -d[A]/dt [A] -d[A]/dt = k[A] Or, -d[A]/[A] = kdt  On integration we have, ∫ -d[A]/[A] = k ∫ dt -loge [A] = kt + I, ---------- 1. where I is the constant of integration If t = 0, at the start of the reaction then [A] = [A]0 Then substituting these in eq 1. -loge [A]0 = k x 0 + I, So, I = -loge [A]0 , substituting this value of I in eq 1, we get -loge [A] = kt + [-loge [A]0 ] loge [A] - loge [A]0 = -kt loge[A] /[A]0 = -kt -----------2. [A] /[A]0 = e-kt [A] = [A]0 e-kt Thus a first order reaction is an exponential process and the concentration of A decreases exponentially with time. Equation 2 can be written as follows: 1 [𝐴] 1 [𝐴]0 K = - 𝑡 loge [𝐴] or k= loge 0 𝑡 [𝐴] K= If initial concentration of A is ‘a’ mol/lt and ‘ x’ mol of it changes into products during time interval t, then above eq. becomes k= This is the integrated rate law for first order reaction.  GRAPHICAL REPRESENTATION OF FIRST ORDER REACTIONS 1. Reaction rate vs concentration plot: If a graph is plotted between rate of reaction and concentration of reactant in the equation, r = k [A]1 , a straight line is obtained whose slope is equal to k. 2. Concentration vs time plot For first order reaction, k = The above equation can be written as : [A] = [A]0 e-kt From above equation it is understood that concentration of reactant decreases with time. Therefore , on plotting a graph between concentrations of reactants at different instant of time, an exponential decay curve is obtained.  𝑨𝒐 3. Log10 [ ] vs time plot 𝑨 For first order reaction, k = [𝑨]𝟎 𝒌𝒕 Or, log10 = [𝑨] 𝟐.𝟑𝟎𝟑 A graph drawn between log10 [A]0/[A] vs ‘t’ gives slope = k/2.303 4. Log10 [A] vs time plot For first order reaction, k = 𝒌𝒕 log10 [A] = - + log10 [A]0 𝟐.𝟑𝟎𝟑 The above equation corresponds to straight line equation. If a graph is plotted between log10 A vs t , a straight line is obtained whose slope = -k/ 2.303 and Intercept on the log10 [A] axis = log 10 [A]0 HALF LIFE OF A ZERO ORDER REACTION (t1/2) Time taken for half of the reaction to be completed is called half life of a reaction (t1/2). [𝑨]𝟎−[𝑨] For a Zero order reaction, k = 𝒕 For half reaction,t = t1/2 [A]0 = [A]0 [A] = ½[A]0 𝟏 [𝑨]𝟎− [𝑨]𝟎 [𝑨]𝟎 𝟐 K= or t1/2 = 𝒕𝟏/𝟐 𝟐𝒌 Thus half life for a zero order reaction is directly proportional to initial concentration of reactants. HALF LIFE OF A FIRST ORDER REACTION (t1/2) Time taken for half of the reaction to be completed is called half life of a reaction (t1/2). For a first order reaction, k = For half reaction,t = t1/2 [A]0 = [A]0 [A] = ½[A]0 Then the above reaction becomes , k= or, Hence it is clear that half life period for first order reaction does not depend upon initial concentration of reactants. a) Time required to complete one third of the reaction [A] 0 = a, [A] = a-a/3 = 2/3a t b) Time required to complete three fourth of the reaction [A] 0 = a, [A] = a-3 /4a = 1/4a t AMOUNT OF REACTANTS LEFT AFTER n HALF LIVES : If [A]0 is the initial concentration of reactants then amount of reactants left after ‘n’ half lives is given by = CHARACTERISTICS OF FIRST ORDER REACTIONS 1. Rate is directly proportional to concentration of reactants. 2. Half life is independent of initial concentration of reactants. EXAMPLES OF FIRST ORDER REACTIONS 1. Decomposition of nitrogen pentoxide 𝟐.𝟑𝟎𝟑 𝑽∞ K= log 𝒕 𝑽∞− 𝑽𝒕  𝟐.𝟑𝟎𝟑 𝒂 K= log 𝒂−𝒙 𝒕 EXPERRIMENTAL DETERMINATION OF RATE LAW, RATE CONSTANT AND ORDER OF REACTION 1. GRAPHICAL METHOD For first order reaction r = k [A]1 Or, k = r / [A]1 If a graph is drawn between r and [A] and a straight line is obtained then it is a first order reaction. For a second order reaction, r = k [A]2 Or, k = r/ [A]2 If a graph is drawn between r and [A]2 and a straight line is obtained then it is a second order reaction., and so is the case for third order reaction. 2. HALF LIFE METHOD 𝟏 For any reaction ,t1/2 , where n is the order of reaction. [𝑨]𝒏−𝟏 𝟎 𝟏 For another reaction, t1/2’ [𝑨]′𝟎 𝒏−𝟏 So, 𝑡1/2 [𝐴]′0 Taking log on both sides, log = n-1 log ( 𝑡 ′ 1/2 [𝐴]0 𝑡1/2 𝑙𝑜𝑔 ′ 𝑡1/2 n=1+ [𝐴]′ 𝑙𝑜𝑔 0 [𝐴]0  ARRHENIUS EQUATION Arrhenius gave an equation to relate rate constant with temperature which is as follows: Where A = Frequency factor Ea = Activation energy The above equation gives the number of binary collisions of reactant molecules per unit time. Taking log on both sides in above equation, 𝐸𝑎 𝐸𝑎 loge k = logeA - or ln k = ln A - --------------1 𝑅𝑇 𝑅𝑇 𝐸𝑎 Or , 2.303 log10k = 2.303 log10 A – 𝑅𝑇 𝐸𝑎 2.303 log10k = – + 2.303 log10 A 𝑅𝑇 𝐸𝑎 log10k = – 2.303𝑅𝑇 + log10 A -----------------2 where R = gas constant ( 8.314 J/K/mol) GRAPHICAL REPRESENTATION OF ARRHENIUS EQUATION AND CALCULATION OF ACTIVATION ENERGY (Ea) 𝐸𝑎 ln k = ln A - -----------1 𝑅𝑇 Comparing eq. 1 with straight line eq. y = mx + c, graph plotted between ln k vs 1/T, gives straight line whose slope = - Ea/R 𝐸𝑎 Considering eq. 2 , log10k = – 2.303𝑅𝑇 + log10 A -----------------2 Graph plotted between log10k and 1/T gives a straight line whose slope = – Ea/2.303R  RELATION BETWEEN RATE CONSTANT AND TEMPERATURE Suppose for one reaction rate constant is k1 and temperature is T1 then, A --------- 1 and at temperature T2, subtracting 1 from 2 Effect of catalyst on rate of reaction: A catalyst provides a new path of lower activation energy to the reaction. Now, more reactant molecules can cross this low energy barrier to form the products. This increases the rate of reaction. Therefore , lower is the activation energy , faster is the reaction. CATALYSIS Positive catalyst: speeds up the chemical reaction. Eg; 2KClO3 2KCl + 3O2 Here MnO2 acts as positive catalyst. Negative catalyst: slows down the sped of reaction eg; oxidation of sodium sulphite by air is retarded by alcohol. Homogeneous catalyst: when the reactants and catalyst are in same phase and the reaction system is homogeneous throughout, the catalyst is called homogeneous. The physical state of reactants and catalyst are same Eg; 2SO2 (g) + O2 (g) 2SO3 (g) Heterogeneous catalyst: Here catalyst and reactants are in different phase. Eg; N2 (g) + 3H2 (g) 2NH3 (g) Auto catalyst: the phenomenon in which one of the products formed itself acts as catalyst is called autocatalysis and the catalyst is autocatalyst. Such a reaction is slow In the beginning but speed up once the product is formed. Eg; 1. CH3COOC2H5 + H2O CH3COOH + C2H5OH Here CH3COOH acts as catalyst. 2. oxidation of oxalic acid by acidified potassium permanganate 5 (COOH)2 + 2KMnO4 + 3H2SO4 2MnSO4 + K2SO4 +10CO2 + 8H2O Here Mn+2 ion acts as autocatalyst Induced catalyst:When chemical reaction influences the rate of some other reaction which does not occur in ordinary conditions, the phenomenon is called induced catalysis and catalyst is termed induced catalyst. Eg; The reduction of mercuric chloride with oxalic acid is very slow but KMnO4 is reduced easily with oxalic acid. But when both mercuric chloride and KMnO4 are reacted together with oxalic acid , both gets reduced. So, here KMnO4 acts as induced catalyst.  CHARACTERISTICS OF CATALYST 1. Catalyst remains unchanged in mass and chemical composition at the end of the reaction. 2. Only small quantity of catalyst is sufficient. 3. Catalyst are specific in action: A catalyst may act as positive catalyst for one reaction but might act as negative catalyst for another reaction. Eg; MnO2 acts as positive catalyst for decomposition of KClO3 but acts as negative catalyst for decomposition of potassium perchlorate. 4. Does not initiate the reaction. 5. Does not alter the position of equilibrium. 6. A catalyst catalyses both forward and backward reactions to the same extent. Thus equilibrium constant remains unchanged but may be attained faster. 7. Effect of temperature on catalytic activity: Catalytic activity is maximum at a particular temperature, i.e optimum temperature. 8. Use of promoter: promoter or activator increases the efficiency of the catalyst. Eg; In Habers process, Fe is a catalyst while Mo acts as promoter. 9. Cataytic poisoning: Heterogeneous catalyst is often rendered ineffective in presence of a poison ( catalytic poisoning). A foreign substance which renders heterogeneous catalyst ineffective is called a poison. Eg; The Fe catalyst in Habers process is poisoned by H2S. MECHANISM OF CATALYSIS The main role of catalyst is to lower the activation energy of the reaction providing another path with lower energy barrier. Thus , because of lower activation anergy, reaction proceeds faster. Theories of catalysis 1. Intermediate compound formation theory: According to this theory , an intermediate compound is formed with one of the reactants and the catalyst having lower activation energy. This intermediate compound is unstable and highly reactive ad involves a lower energy barrier.  Consider a reaction: A + B AB (high activation energy). In this reaction , a product with high activation energy (AB) is formed but with the use of a catalyst according to the intermediate theory, an intermediate compound of low activation energy is formed with the catalyst first which then dissociates to form the product. First step: A + X AX (intermediate compound of low Ea) Second step: AX + B AB + X Merits of intermediate compound theory:. It explains why catalyst remains unchanged in mass and composition at the end of the reaction. Applicable to only homogeneous reactions Demerits : It fails to explain action of catalytic poison and activators. 2. Adsorption Theory: The above theory is applicable to heterogeneous reactions. According to this theory, the reactants are adsorbed on surface of catalyst and due to increased concentration on the surface, rate of reaction is increased according to law of mass action. The catalytic power of catalyst depends on the number of free valencies due to which chemisorption takes place thereby breaking the bonds of reactant moleculs. This provides the new pathway to the reaction with lower activation energy. Free valencies and active centres: In the bulk of metals , atoms satisfies their valencies but at the surface, atoms possess unbalanced chemical bonds called free valencies. The edges, cracks, peaks, corners on rough surfaces have greater number of free valencies called active centres. The efficiency of catalyst is mainly due to these active centres. Free valencies can be increased by : 1. Sub division of catalyst. 2 Making surface of catalyst rough.