2018-G11-Chemistry-E

10 ELECTROCHEMISTRY eLearn.Punjab10.4.1 Applications of Electrochemical Series(i) Prediction of the feasibility of a Chemical Reaction When we look at the electrochemical series, it is easy to predict whether a particular reactionwill take place or not. For example, Cu2+ (aq) can oxidize solid zinc but Zn2+ (aq) cannot oxidize solidcopper. Standard reduction potential values of copper and zinc can explain thisCu2+(aq) + 2e- → Cu(s) Eo =+0.34volt Eo = -0.76 voltsZn 2+ + 2e- → Zn(s) (aq)Since zinc is being oxidized so the reverse reaction will be considered.Zn(s) → Zn 2+ + 2e- Eo = -0.76 volts (oxidation) (aq)The overall reaction will thus beCu 2+ + Zn(s) → Cu(s) + Zn2+(aq) Eo = 1.10 volts (aq) cell The overall positive value for the reaction potential suggests that the process is energeticallyfeasible. If the sum of E° values of the two half cell reactions is negative, then the reaction will notbe feasible.(ii) Calculation of the Voltage or Electromotive Force (emf) of Cells: In a galvanic cell, the electrode occupying a higher position in the electrochemical series, willact as anode and oxidation takes place on it. Similarly, the electrode occupying the lower positionin the series will act as a cathode and reduction will take place on it. Let us ind out a cell potentialor the emf of the cell already discussed as above. The half cell reactions are: 33

10 ELECTROCHEMISTRY eLearn.PunjabZn(s) → Zn 2+ + 2e- (oxidation half reaction) (aq) (reduction half reaction) (complete cell reaction)Cu2+(aq) + 2e- → Cu(s)Cu2+(aq) + Zn(s) → Cu(s) + Zn2+(aq)The oxidation potential of Zn is positive. The reduction potential of Cu2+ is also positive. The cellvoltage or emf of the cell is given by Eo = Eo + Eo cell oxi red Eo = 0.76 + 0.34 = 1.10 volts cell The cell voltage or emf measures the force with which electrons move in the external circuitand therefore measures the tendency of the cell reaction to takes place. Galvanic cells, thus, givequantitative measure of the relative tendency of the various reactions to occur.(iii) Comparison of Relative Tendency of Metals and Nonmetals to Get Oxidized orReduced The value of the reduction potential of a metal or a nonmetal tells us the tendency to loseelectrons and act as a reducing agent. It also gives the information about the tendency of a speciesto gain electrons and act as an oxidizing agent. Greater the value of standard reduction potential ofa given species, greater is its tendency to accept electrons to undergo reduction and hence to actas an oxidizing agent. For example, ions like Au3+, Pt2+, Hg2+, Ag+, Cu2+ and the nonmetals elementslike F2, Cl2, Br2 and I2 which lie below the SHE, have a strong tendency to gain electrons and undergoreduction. The series tell us that strong oxidizing agents like F2, Cl2, Br2, etc. have a large positive valueof standard reduction potentials, while strong reducing agents have large negative values like Li, K,Ca, Na,etc. which lie above SHE. 34

10 ELECTROCHEMISTRY eLearn.Punjab(iv) Relative Chemical Reactivity of Metals Greater the value of standard reduction potential of a metal, smaller is its tendency to loseelectrons to change into a positive ion and hence lower will be its reactivity. For example, metals likeLi, Na, K and Rb are highly reactive. Coinage metals, Cu, Ag, and Au are the least reactive becausethey have positive reduction potentials. Similarly, metals like Pb, Sn, Ni, Co and Cd which are very close to SHE react very slowly withsteam to liberate hydrogen gas, while the metals like Fe, Cr, Zn, Mn, Al and Mg which have morenegative reduction potentials react with steam to produce the metallic oxides and hydrogen gas.(v) Reaction of Matels with Dilute Acids Greater the value of standard reduction potential of a metal, lesser is its tendency to loseelectrons to form metal ions and so weaker is its tendency to displace H+ ions from acids as H2 gas.For example, metals like Au, Pt, Ag and Cu which have suiciently high positive values of reductionpotentials, do not liberate hydrogen gas from acids. While, metals like Zn, Mg and Ca which areclose to the top of the series and have very low reduction potentials, liberate hydrogen gas, whenthey react with acids.(vi) Displacement of One Metal by Another from its Solution One metal will displace another metal from the aqueous solution of its salt if it lies above inthe electrochemical series. For example, Fe can displace Cu from CuSO4, Zn does not displace Mgfrom solution of MgSO4. 35

10 ELECTROCHEMISTRY eLearn.Punjab10.5 MODERN BATTERIES AND FUEL CELLS Those cells which cannot be recharged are called primary cells. Examples are dry cell, alkalinebattery, mercury and silver battery. Those ones which can be recharged are called secondary cells.Examples are lead-acid battery, Ni-Cd-battery and fuel cells. A few examples of some modern bat-teries and fuel cell are described in this section. Anim ation 10 .13: MODERN BATTERIES Source & Credit : technology student10.5.1 Lead Accumulator or Lead-Acid Battery (Rechargeable)It is commonly used as a car battery. It is secondary or a storage cell. Passing a direct currentthrough it must charge it. The charged cell can then produce electric current when required. Thecathode of a fully charged lead accumulator is lead oxide, PbO2 and its anode is metallic lead. Theelectrolyte is 30% sulphuric acid solution (density 1.25 g cm-3). When the two electrodes are con-nected through an external circuit, it produces electricity by discharge Fig (10.7). A single cell pro-vides around 2 volts. For 12 volts, 6 cells are connected in series. 36

10 ELECTROCHEMISTRY eLearn.Punjab Fig (10.7) Lead accumulator Anim ation 10 .14: Hy draulic Accum ulators Source & Credit : hy draulic 37

10 ELECTROCHEMISTRY eLearn.PunjabDischarging At the anode the lead atoms release two electrons each to be oxidized to Pb2+ ions, whichcombine with SO42- ions present in the electrolyte and get deposited on the anode as PbSO4.At the cathodePbO2(s) + 4H + (aq) + SO4 2- + 2e → PbSO4(s) + 2H 2O( ) (reduction) (aq)At the anodePb(s) + SO4 2- → PbSO4(s) + 2e− (oxidation) (aq) The electrons released pass round an external circuit as an electric current to be used forstarting the engine of a vehicle, for lighting up of car lights and so on. At the cathode the electrons from the anode are accepted by PbO2 and hydrogen ions fromthe electrolyte then undergo a redox reaction to produce lead ions and water as follows: The Pb2 ions then combine with the SO42 ions and they both deposit at the cathode as PbSO4.When both electrodes are completely covered with PbSO4 deposits, the cell will cease to dischargeany more current until it is recharged. The overall reaction is Pb(s) + PbO2(s) + 4H + + 2SO42-(aq) → 2PbSO4(s) + 2H 2O( ) (aq)A typical 12-V car battery has six cells connected in series. Each delivers 2V Each cell contains twolead grids packed with the electrode materials. The anode is spongy lead , and cathode is poweredPbO4. The grid is immersed in an electrolytic solution of ≈ 3.2M H2SO4 (30%). Fibre glass sheetsbetween the grids prevent shorting by accidental physic al contact. When the cell is discharged, itgenerates electrical energy as a voltaic cell.Recharging During the process of recharging, the anode and the cathode of the external electrical sourceare connected to the anode and the cathode of the cell respectively. The redox reactions at therespective electrodes are then reversed. These reactions are summarized as follows: 38

10 ELECTROCHEMISTRY eLearn.PunjabAt anode PbSO4(s) + 2e → Pb(s) + SO42-(aq) (reduction) (oxidation)At cathode PbSO4(s) + 2H2O → PbO2(s) + 4H + + SO42-(aq) 2e- (aq)The overall reaction is 2PbSO4(s) + 2H2O → Pb(s) + PbO2(s) + 4H+(aq) + SO42-(aq)During the process of discharging, the concentration of the acid falls decreasing its density to 1.15gcm3. After recharging, the acid is concentrated again bringing its density to its initial value of 1.25gcm3. At the same time the voltage of the battery, which has dropped during discharging, return toaround 12 volts.10.5.2 Alkaline Battery (non-rechargeable) It is a dry alkaline cell, which uses zinc and manganese dioxide as reactants. Zinc rod servesas the anode and manganese dioxide functions as the cathode. The electrolyte, however, containspotassium hydroxide and is therefore basic (alkaline).The battery is enclosed in a steel container. The zinc anode is also slightly porous giving it a largerefective area. This allows the cell to deliver more current than the common dry cell. It has alsolonger life. The reactions in the alkaline battery.are shown as follows: Zn(s) + 2OH - → Zn(OH)2(s) + 2e- (anode) (aq) (cathode) 2MnO2(s) + H2O() + 2e- → Mn2O3(s) + 2OH - (aq)The overall reaction is Zn(s) + 2MnO2(s) + H O2 (l) → Zn(OH)(s) + Mn O2 3(s)The voltage of the cell is 1.5 V 39

10 ELECTROCHEMISTRY eLearn.Punjab Anim ation 10 .15: Alkaline Battery Source & Credit : adafruit10.5.3 Silver Oxide Battery These tiny and rather expensive batteries Fig. 10.8 have become popular as power sourcesin electronic watches, auto exposure cameras and electronic calculators. The cathode is of silveroxide, Ag,0, and the anode is of zinc metal. The following reactions occur in a basic electrolyte.At the anodeZn(s) + 2OH - → Zn(OH)2(s) + 2e- (oxidation) (aq)At the cathodeAg2O(s) + H O2 () + 2e- → 2Ag(s) + 2OH - (reduction). (aq) 40

10 ELECTROCHEMISTRY eLearn.PunjabThe overall reaction is Zn(s) + Ag O2 (s) + H O2 (l) → Zn(OH)2 + 2Ag(s)The voltage of silver oxide battery is about 1.5 V Fig (10.8) A silver oxide battery10.5.4 Nickel Cadmium Cell (Rechargeable) A strong cell that has acquired wide spread use in recent years is the NICAD or nickel cadmiumbattery. It is a rechargeable cell. The anode is composed of cadmium, which undergoes oxidation inan alkaline electrolyte.At the anodeCd(s) + 2OH - → Cd(OH)2(s) + 2e- (oxidation) (aq) 41

10 ELECTROCHEMISTRY eLearn.PunjabThe cathode is composed of NiO2 which undergoes reduction.At the cathodeNiO2 + 2H2O() + 2e- → Ni(OH)2(s) + 2OH - (reduction) (aq)The net cell reaction during the discharge is : Cd(s) + NiO2(s) + 2H O2 () → Cd(OH)2(s) + Ni(OH)2(s) Just like lead storage cell, the solid reaction products adhere to the electrodes. For this reason,the reaction is easily reversed during recharging. Because no gases are produced during eithercharging or discharging, the battery can be sealed. It is used in battery operated tools and portablecomputers. It also inds its application in cordless razors, photolash units. It is light weight. Voltageof the cell is 1.4 V.10.5.5 Fuel Cells (rechargeable) Fuel cells are other means by which chemical energy may be converted into electrical energy.When gaseous fuels, such as hydrogen and oxygen are allowed to undergo a reaction, electricalenergy can be obtained. This cell inds importance in space vehicles. The cell is illustrated in Fig. (10.10). The electrodesare hollow tubes made of porous compressed carbon impregnated with platinum, which acts asa catalyst. The electrolyte is KOH. At the electrodes, hydrogen is oxidized to water and oxygen isreduced to hydroxide ions.[H 2 (g) + 2OH - → 2H2O() + 2e- ] x 2 (anode) (aq) (cathode) (overall reaction)O2(g) + 2H 2O( ) + 4e- → 4OH - (aq)2H2(g) + O2(g) → 2H2O()Such a cell runs continuously as long as reactants are supplied. 42

10 ELECTROCHEMISTRY eLearn.Punjab Fig (10.10) Hydrogen - Oxygen Fuel cell Anim ation 10 .16: Fuel Cells Source & Credit : solaren 43

10 ELECTROCHEMISTRY eLearn.Punjab This fuel cell is operated at a high temperature so that the water formed as a product ofthe cell reaction evaporates and may be condensed and used as drinking water for an astronaut.A number of these cells are usually connected together so that several kilowatts of power can begenerated. The fuel cell produce electricity and pure water during space lights. Fuel cell are light, portableand sources of electricity. Many fuel cells do not produce pollutants. Some other cell reactions infuel cell are :(i) 2NH3 + 3/2 O2 → N2 + 3H2O()(ii) N4H4 + O2 → N2 + 2H2O()(iii) CH4 + 2O2 → CO2 + 2H2O() Fuel cells are very eicient. They convert about 75% of fuels bond energy into electricity. 44

10 ELECTROCHEMISTRY eLearn.Punjab KEY POINTS1. Electrochemistry is the branch of science which deals with the conversion of electrical energy to chemical energy and vice versa.2. Electrolytic conduction is carried out by the ions produced when an ionic compound is in fused state or dissolved in water. Electrolysis is the process in which a chemical reaction takes place at the expense of electrical energy. Electrolysis is used for the extraction of elements and for the commercial preparation of several compounds. It is also used for electroplating.3. A Galvanic or a voltaic cell produces electrical energy at the expense of chemical energy. Electrode potential is developed when a metal is dipped into a solution of its own ions.4. The potential of standard hydrogen electrode is arbitrarily ixed as 0.00 volts. Electrode potential of an element is measured when it is coupled with standard hydrogen electrode. When elements are arranged in order of their standard electrode potentials on the hydrogen scale, the resulting list is known as electrochemical series. Electrochemical series is used to predict the feasibility of a redox chemical reaction.5. Modern batteries and fuel cell include lead accumulator, alkaline battery, silver oxide battery, nickel cadmium cell and hydrogen oxygen fuel cell.6. The oxidation number is the apparent charge which an atom has in a molecule. Redox chemical equations can be balanced using oxidation number method and ion electron method. 45

10 ELECTROCHEMISTRY eLearn.Punjab EXERCISEQ.1 Multiple choice questions. For each question there are four possible answers a, b, c and d.Choose the one you consider correct.(i) The cathodic reaction in the electrolysis of dil. H2SO4 with Pt electrodes is:-(a) Reduction (b) Oxidation(c) Both oxidation and reduction (d) Neither oxidation or reduction(ii) Which of the following statements is not correct about galvanic cell?(a) Anode is negatively charged (b) Reduction occurs at anode(c) Cathode is positively charged (d) Reduction occurs at cathode(iii) Stronger the oxidizing agent, greater is the:(a) oxidation potential (b) reduction potential(c) redox potential (d) E.M.F of cell(iv) If the salt bridge is not used between two half cells, then the voltage.(a) Decrease rapidly (b) Decrease slowly(c) Does not change (d) Drops to zero(v) If a strip of Cu metal is placed in a solution of FeSO4:(a) Cu will be deposited (b) Fe is precipitated out(c) Cu and Fe both dissolve (d) No reaction take placeQ.2 Fill in the blank.(i) The oxidation number of O-atom is ___________ in OF2 and is ___________ in H2O2.(ii) Conductivity of metallic conductors is due to the low of ________while that of electrolytesis due to low of_________ .(iii) Reaction taking place at the ________is termed as oxidation and at the _________ is calledas reduction.(iv) _________ is set up when a metal is dipped in its own ions.(v) Cu metal__________ the Cu-cathode when electrolysis is performed for CuSO4 solutionwith Cu- cathodes.(vi) The reduction potential of Zn is __________ volts and its oxidation potential is __________volts.(vii) In a fuel cell,___________react together in the presence of______ . 46

10 ELECTROCHEMISTRY eLearn.PunjabQ.3 Mark the following statements true or false. (i) In electrolytic conduction, electrons low through the electrolyte. (ii) In the process of electrolysis, the electrons in the external circuit low from cathode to anode. (iii) Sugar is a non-electrolyte in solid form and when dissolved in water will allow the passage of an electric current. (iv) A metal will only allow the passage of an electric current when it is in cold state. (v) The electrolytic products of aqueous copper (II) chloride solution are copper and chlorine. (vi) Zinc can displace iron form its solution. (vii) S.H.E. acts as cathode when connected with Cu-electrode. (viii) A voltaic cell produces electrical energy at the expense of chemical energy. (ix) Lead storage battery is not a reversible cell. (x) Cr changes its oxidation number when K2Cr2O7 reacts with HCl.Q.4 (a) Explain the term oxidation number with examples. (b) Describe the rules used for the calculation of oxidation number of an element in molecules and (c) ions giving examples. Calculate the oxidation number of chromium in the following compounds. (i) CrCl3 (ii) Cr2 (SO4 )3 (iii) K2CrO4 (iv) K2Cr2O7 (v) CrO3 (vi) Cr2O3 (vii) Cr2O72- (Ans: (i)+3,(ii)+3,(iii)+6,(iv)+6,(v) + 6(vi)+3)(d) Calculate the oxidation numbers of the elements underlined in the following compounds. (i) Ca(Cl O3)2 (ii) Na2CO3 (iii) Na2PO4 (iv) HNO3 (v) Cr2 (SO4 )3 (vi) HPO3 (vii) K2 MnO4 (Ans : (i) +5, (ii) +4, (iii) +5, (iv) +5, (v) +6 , (vi)+5 (vii) + 6)Q.5 (a) Describe the general rules for balancing a redox equation by oxidation number method. (b) (i) Balance the following equations by oxidation number method (ii) (iii) Cu + HNO3 → Cu(NO3)2 + NO2 + H2O (iv) Zn + HNO3 → Zn(NO3)2 + NO + H2O Br2 + NaOH → NaBr + NaBrO3 + H2O MnO2 + HCl → MnCl2 + H2O + Cl2 47

10 ELECTROCHEMISTRY eLearn.Punjab(v) FeSO4 + K2Cr2O7 + H2SO4 → Fe2 (SO4 )3 + Cr2 (SO4 )3 + K2SO4 + H2O(vi)(vii) HNO3+ HI → NO + H2O + I2(viii)(ix) Cu + H2SO4 → CuSO4 + SO2 + H2O HI + H2SO4 → I2 + SO2 + H2O NaCl + H2SO4 + MnO2 → Na2SO4 + MnSO4 + H2O + Cl2Q.6 (a) Describe the general rules for balancing a redox equation by ion-electron method.(b) Balance the following ionic equations by ion-electron method.(i) Fe3+ + Sn2+ → Fe2+ + Sn4+(ii) MnO41-(aq) + C O 2- → Mn 2+ + CO2(g)(iii) 2 4 (aq) (aq)(iv)(v) Cr2O72- + Cl- → 2Cr3+ + 3Cl2(vi)(vii) Cu + NO31- → Cu2+ + 2NO2(viii)(ix) Cr2O72- + Fe2+ → Cr3+ + Fe3+ (acidic media) (acidic media) S2O32- + OCl1- → Cl- + S4O62- (acidic media) (acidic media) IO31- + AsO33- → I- + AsO43- (acidic media) Cr3+ + BiO31- → Cr2O72- + 3Bi3+ H3AsO3 + Cr2O72- → 3H3AsO4 + 2Cr3+(x) CN- + MnO41- → CNO- + MnO2(s) (basic media)Q.7 Describe the electrolysis of molten sodium chloride, and a concentrated solution of sodium chloride.Q.8 What is the diference between single electrode potential and standard electrode potential? How can it be measured? Give its importance.Q.9 Outline the important applications of electrolysis. Write the electrochemical reactions involved therein.Discuss the electrolysis of CuSO4 using Cu-electrodes and AgNO3 solution using Ag electrode.Q.10 Describe the construction and working of standard hydrogen electrode.Q.11 Is the reaction Fe3+ + Ag → Fe2+ + Ag+ spontaneous? If not, write spontaneous reaction involving these species. 48

10 ELECTROCHEMISTRY eLearn.PunjabQ.12 Explain the diference between (a) Ionization and electrolysis. (b) Electrolytic cell and voltaic cell (c) Conduction through metals and molten electrolytes.Q.13 Describe a galvanic cell explaining the functions of electrodes and the salt bridge.Q.14 Write comprehensive notes on: (a) Spontaneity of oxidation reduction reactions. (b) Electrolytic conduction. (c) Alkaline, silver oxide and nickel-cadmium batteries, fuel cell. (d) Lead accumulator, its desirable and undesirable features.Q.15 Will the reaction be spontaneous for the following set of half reactions. What will be the value of ?Ecell (i) Cr3+(aq) + 3e- → Cr(s) (ii) MnO2(s) + 4H+ + 2e- → Mn2+(aq) + 2H2O() (Standard reduction potential for reaction (i) = -0.74V and for the reaction (ii) = + 1.28V).Q16. Explain the following with reasons. (a) A porous plate or a salt bridge is not required in lead storage cell. (b) The standard oxidation potential of Zn is 0.76 V and its reduction potential is -0.76 V (c) Na and K can displace hydrogen from acids but Pt, Pd and Cu can not. (d) The equilibrium is set up between metal atoms of electrode and ions of metal in a cell. (e) A salt bridge maintains the electrical neutrality in the cell. (f) Lead accumulator is a chargeable battery. (g) Impure Cu can be puriied by electrolytic process. (h) SHE acts as anode when connected with Cu electrode but as cathode with Zn electrode. 49

CHAPTER11 REACTION KINETICS Animation 11.1: Spectrometer Source & Credit: eLearn

11 REACTION KINETICS eLearn.Punjab11.0.0 INTRODUCTION It is a common observation that rates of chemical reactions difer greatly. Many reactions,in aqueous solutions, are so rapid that they seem to occur instantaneously. For example, a whiteprecipitate of silver chloride is formed immediately on addition of silver nitrate solution to sodiumchloride solution. Some reactions proceed at a moderate rate e.g. hydrolysis of an ester. Still otherreactions take a much longer time, for example,the rusting of iron, the chemical weathering ofstone work of buildings by acidic gases in the atmosphere and the fermentation of sugars.The studies concerned with rates of chemical reactions and the factors that afect the rates ofchemical reactions constitute the subject matter of reaction kinetics. These studies also throw lighton the mechanisms of reactions. All reactions occur in single or a series of steps. If a reactionconsists of several steps, one of the steps will be the slowest than all other steps. The slowest stepis called the rate determining step. The other steps will not afect the rate. The rates of reactionsand their control are often important in industry. They might be the deciding factors that determinewhether a certain chemical reaction may be used economically or not. Many factors inluence therate of a chemical reaction. It is important to discover the conditions under which the reaction willproceed most economically. Anim ation 11.2: Kinetics Source & Credit : ceb.cam 2

11 REACTION KINETICS eLearn.Punjab11.1.0 RATE OF REACTION During a chemical reaction, reactants are converted into products. So the concentration ofthe productsincreases with the corresponding decrease in the concentration of the reactants as they are beingconsumed. Anim ation 11.3: RATE OF REACTION Source & Credit : blobsThe situation is explained graphically in Fig.(11.1) for the reactant A which is changing irreversiblyto the product B. The slope of the graph for the reactant or the product is the steepest at the beginning. Thisshows a rapid decrease in the concentration of the reactant and consequently, a rapid increase inthe concentration of the product. As the reaction proceeds, the slope becomes less steep indicatingthat the reaction is slowing down with time. It means that the rate of a reaction is changing everymoment. The following curve for reactants should touch the time axis in the long run. This is thestage of completion of reaction. The rate of a reaction is deined as the change in concentration ofa reactant or a product divided by the tim e taken for the change. 3

11 REACTION KINETICS eLearn.Punjab Fig. (11.1) Change in the concentration of reactants and products with time for the reaction A→B The rate of reaction has the units of concentration divided by time. Usually the concentrationis expressed in mol dm-3 and the time in second, thus the units for the reaction rate are mol dm-3s-1. Rate of reaction = change in concentration of the substance time taken for the change For a gas phase reaction, units of pressure are used in place of molar concentrations. It followsfrom the above graph that the change in concentration of the reactant A or the product B is muchmore at the start of reaction and then it decreases gradually.So the reaction rate decreases with time. It never remains uniform during diferent time periods. Itdecreases continuously till the reaction ceases. Rate of reaction = mol dm-3 = mol dm-3 s-1 seconds 4

11 REACTION KINETICS eLearn.Punjab11.1.1 Instantaneous and Average Rate The rate at any one instant during the interval is called the instantaneous rate. The rate ofreaction between two speciic time intervals is called the average rate of reaction.The average rate and instantaneous rate are equal for only one instant in any time interval. At irst,the instantaneous rate is higher than the average rate. At the end of the interval the instantaneousrate becomes lower than the average rate. As the time interval becomes smaller, the average ratebecomes closer to the instantaneous rate. The average rate will be equal to the instantaneous rate when the time interval approacheszero. Thus the rate of reaction is instantaneous change in the concentration of a reactant or aproduct at a given moment of time. Rate of reaction = dx dt Where dx is a very small change in the concentration of a product in a very small time intervaldt. Hence, dx/dt is also called rate of change of concentration with respect to time. The rate of a general reaction, A → B , can be expressed in terms of rate of disappearance ofthe reactant A or jthe rate of appearance of the product B. Mathematically, Rate of reaction = -d[A] = + d[B] dt dt Where d[A] and d[B] are the changes in the concentrations of A and B, respectively. Thenegative sign in the term indicates a decrease in the concentration of the reactant A. Since theconcentration of product increases with time, the sign in rate expression involving the change ofconcentration of product is positive. 5

11 REACTION KINETICS eLearn.Punjab Anim ation 11.4: Average and Instantaneous Rate of Change Source & Credit : brilliant11.1.2 Speciic Rate Constant or Velocity Constant The relationship between the rate of a chemical reaction and the active masses, expressed asconcentrations, of the reacting substances is summarized in the law of mass action. It states thatthe rate of reaction is proport ional to the active mass of the reactant or to the product of activemasses if more than one reactants are involved in a chemical reaction. 6

11 REACTION KINETICS eLearn.PunjabFor dilute solutions, active mass is considered as equal to concentration. By applying the law ofmass action to a general reaction. aA + bB → cC + dD Rate of reaction = k [A]a [B]b This expression is called rate equation. The brackets [ ] represent the concentrations and theproportionality constant k is called rate constant or velocity constant for the reaction. If [A] = 1 mol dm-3 and [B] = 1 mol dm-3 Rate of reaction = k × 1a × 1b = k Hence the speciic rate constant of a chemical reaction is the rate of reaction when theconcentrations of the reactants are unity. Under the given conditions, k remains constant, but itchanges with temperature. Anim ation 11.5: Velocity Constant Source & Credit : w ikia 7

11 REACTION KINETICS eLearn.Punjab11.1.3 Order of ReactionFor a general reaction between A and B where ‘a’ moles of A and ‘b’ moles of B react to form ’c’moles of C and ’d’ moles of D. aA + bB → cC + dDWe can write the rate equation as: R =k [A]a [B]b The exponent ’a’ or ‘b’ gives the order of reaction with respect to the individual reactant. Thusthe reaction is of order ‘a’ with respect to A and of order b with respect to B. The overall orderof reaction is (a+b). The order of reaction is given by the sum of all the exponents to which theconcentrations in the rate equation are raised. The order of reaction may also be deined as thenumber of reacting molecules, whose concentrations alter as a result of the chemical change. It is important to note that the order of a reaction is an experimentally determined quantityand can not be inferred simply by looking at the reaction equation. The sum of the exponents inthe rate equation may or may not be the same as in a balanced chemical equation. The chemicalreactions are classiied as zero, irst, second and third order reactions. The order of reaction providesvaluable information about the mechanism of a reaction. Anim ation 11.6: Rate and Order of Reac- tion Source & Credit : science.uw aterloo 8

11 REACTION KINETICS eLearn.PunjabExamples of Reactions Showing Different Orders1. Decomposition of nitrogen pentoxide involves the following equation. 2N2O5(g) → 2N2O4 (g) + O2 (g)The experimentally determined rate equation for this reaction is as follows: Rate = k[N2O5]This equation suggests that the reaction is irst order with respect to the concentration of N2O5.2. Hydrolysis of tertiary butyl bromideCH 3 CH 3 Br + H2O → CH 3 C CH3 C OH + HBr CH 3 CH 3The rate equation determined experimentally for this reaction is Rate = k[(CH3)3CBr] The rate of reaction remains efectively independent of the concentration of water because,being a solvent, it is present in very large excess. Such type of reactions have been named aspseudo irst order reactions.3. Oxidation of nitric oxide with ozone has been shown to be irst order with respect to NO andirst order with respect to O3. The sum of the individual orders gives the overall order of reaction astwo. NO(g)+O3(g) → NO2 (g)+O2 (g) Rate = k[NO][O3]4. Consider the following reaction 2FeCl3(aq) + 6KI(aq) → 2FeI2(aq) + 6KCI(aq) + I2 9

11 REACTION KINETICS eLearn.Punjab This reaction involves eight reactant molecules but experimentally it has been found to be athird order reaction. Rate = k[FeCl3][KI]2 This rate equation suggests that the reaction is, in fact, taking place in more than one steps.The possible steps of the reaction are shown below. FeCl3(aq) + 2KI(aq) slow→ FeI2 (aq) + 2KCI(aq) + Cl− (aq) 2KI(aq) + 2Cl-(aq) fast→ 2KCl(aq) + I2 (s)5. The order of a reaction is usually positive integer or a zero, but it can also be in fraction or canhave a negative value. Consider the formation of carbon tetrachloride from chloroform. CHCl3()+Cl2 (g) → CCl4 ()+HCl(g) Rate = k[CHCl3][Cl2 ]1/2The sum of exponents will be 1 + 1/2= 1.5, so the order of this reaction is 1.5. From the above examples, it is clear that order of reaction is not necessarily depending uponthe coeients of balanced equation. The rate equation is an experimental expression. A reactionis said to be zero order if it is entirely independent of the concentration of reactant molecules.Photochemical reactions are usually zero order.11.1.4 Half Life Period Half life period of a reaction is the time required to convert 50% of the reactants into products.For example, the half life period for the decomposition of N2O5 at 45°C is 24 minutes. It means that if we decompose 0.10 mole dm-3 of N2O5 at 45 °C, then after 24 minutes 0.05mole dm-3 of N2O5 will be left behind. Similarly after 48 minutes 0.025(25%) mole dm-3 of N2O5 willremain unreacted and after 72 minutes (3 half times) 0.0125 (12.5%) mole dm-3 of N2O5, will remainunreacted. 10

11 REACTION KINETICS eLearn.Punjab Decomposition of N2O5 is a irst order reaction and the above experiment proves that thehalf-life period of this reaction is independent of the initial concentration of N2O5. This is true for allirst order reactions. The disintegration of radioactive U235 has a half-life of 7.1x108 or 710 million 92years. If one kilogram sample disintegrates, then 0.5 kg of it is converted to daughter elements in710 million years. Out of 0.5 kg of ,U235 0.25kg disintegrates in the next 710 million years. So, the 92half-life period for the disintegration of a radioactive substance is independent of the amount ofthat substance. What is true for the half-life period of irst order reactions does not remain true for thereactions having higher orders. In the case of second order reaction, the half-life period is inverselyproportional to the initial concentration of the reactant. For a third order reaction, half life isinversely proportional to the square of initial concentration of reactants. Briely we can say that [t1/2 ]1 ∝ 1 , scince[t1/2 ]1= 0.693 ao k [t1/2 ]2 ∝ 1 , scince[t1/2 ]2 = 1 a1 ka [t1/2 ]3 ∝ 1 , scince[t1/2 ]3= 1.5 a2 ka 2Where [t1/2 ]1 , [t1/2 ]2 , and [t1/2 ]3 are the half-life periods for 1st,2nd and 3rd order reactions respectively and ‘a’ is the initialconcentration of reactants. In general for the reaction of nthorder: [t1/2 ]n ∝ 1 a n-1 The half-life period of any order reaction is, thus, inversely Anim ation 11.7: Half Lifeproportional to the initial concentration raised to the power Source & Credit : askiitiansone less than the order of that reaction. So, if one knows theinitial concentration and half-life period of a reaction, thenorder of that reaction can be determined. 11

11 REACTION KINETICS eLearn.PunjabExample 1: Calculate the half-life period of the following reaction when the initial concentration of HI is0.05 M. 2HI(g) ฀ H2 (g) + I2 (g)The value of rate constant k = 0.079 dm3 mol-1 s-1 at 508 °C and rate expression is Rate = k[HI]2Solution: According to the rate expression it is a second order reaction. The half life paired of a secondorder reaction is  t  = 1 = 1 ka 2-1 ka 1 2 2Putting the values of k and a.So, t  = 1 = 1 = 1 sec. kxa (0.079dm3mol-1s-1 )(0.050moldm-3 ) 0.079 x 0.05 1 2 2  t  = 253sec Answer 1 2 2So, in 253 seconds, the half of HI i.e., 0.05/2=0.025 moles is decomposed.11.1.5 Rate Determining Step Finding out the rate equation of a reaction experimentally is very useful. Actually it gives usan opportunity to look into the details of reaction. Rate equation of example (4) in article 11.1.3showed clearly that the reaction is taking place in more than one steps. There are many suchreactions in chemistry which occur in a series of steps. 12

11 REACTION KINETICS eLearn.Punjab If a reaction occurs in several steps, one of the steps is the slowest. The rate of this stepdetermines the overall rate of reaction. This slowest step is called the rate determining or ratelimiting step. The total number of molecules of reacting species taking part in the rate determiningstep appear in the rate equation of the reaction. Let us consider the following reaction NO2(g) + CO(g) → NO(g) + CO2 (g) The rate equation of the reaction is found to beRate = k[NO2 ]2 This equation shows that the rate of reaction is independent of the concentration of carbonmonoxide. In other words the equation tells us that reaction involves more than one steps andtwo molecules of NO2 are involved in the rate determining step. The proposed mechanism for thisreaction is as follows.NO2(g) + NO2(g) slow→ NO3(g) + NO(g) (rate determining step)NO3(g) + CO(g) fast→ NO2 (g) + CO2 (g)The irst step is the rate determining step and Anim ation 11.8: Rate Determ ining StepNO3 which does not appear in the inal balanced Source & Credit : 80 0 m ainstreetequation, is called the reaction intermediate.The reaction intermediate has a temporaryexistence and it is unstable relative to thereactants and the products. This is a specieswith normal bonds and may be stable enoughto be isolated under special conditions. Thisreaction is a clear example of the fact that abalanced chemical equation may not giveany information about the way the reactionactually takes place. 13

11 REACTION KINETICS eLearn.Punjab11.2.0 DETERMINATION OF THE RATE OF A CHEMICAL REACTION Determination of the rate of a chemical reaction involves the measurement of the concentrationof reactants or products at regular time intervals as the reaction progresses. When the reactiongoes on, the concentrations of reactants decrease and those of products increase. The rate of areaction, therefore, is expressed in terms of the rates at which the concentrations change.Rate of reaction = ∆C = mol dm-3 ∆t seconds=mol dm-3s-1Suppose, the concentration of a reactant of any chemical reaction changes by 0.01 mol dm-3in one second, then rate of reaction is, 0 .01 mole dm-3 s-1.Rate of a chemical reaction always decreases with the passage of time during the progress ofreaction. To determine the rate of reaction for agiven length of time, a graph is plotted betweentime on x-axis and concentration of reactant ony-axis whereby a curve is obtained.To illustrate it, let us investigate thedecomposition of HI to H2 and I2 at 508°C.Table(11.1) tells us that the change inconcentration of HI for irst 50 seconds is 0.0284mol dm-3 but between 300 to 350 sec, thedecrease is 0.0031 mol dm3. By using the data, agraph is plotted as shown in Fig (11.2). The graphis between time on x-axis and concentration ofHI in mol dm-3 on y-axis. Since HI is a reactant,so it is a falling curve. The steepness of theconcentration-time curve relects the progressof reaction. Greater the slope of curve near the Fig.(l1.2) T he change in the HI concentration with time for thestart of reaction, greater is the rate of reaction. reaction 2HI(g) ฀ H2 (g) + I2 (g) at 508°C. 14

11 REACTION KINETICS eLearn.Punjab Table (11.1) Change in concentration of HI with regular intervals 2HI(g) ฀ H2(g) + I2(g) Concentrationof Time (s) HI (mol dm-3) 0.100 0 0.0716 50 0.0558 100 0.0457 150 0.0387 200 0.0336 250 0.0296 300 0.0265 350In order to measure the rate of reaction, draw a tangent say, at 100 seconds, on the curve andmeasure the slope of that tangent. The slope of the tangent is the rate of reaction at that pointi.e., after 100 seconds. A right angled triangle ABC is completed with a tangent as hypotenuse. Fig.(11.2) shows that in 110 sec, the change in concentration is 0.027 mole dm-3, and hence the 0.027mol dm-3 Slope or rate = 110 sec =2.5x10-4 mol dm-3s-1 Anim ation 11.9: Chem ical Reaction Rates Source & Credit : crescentok 15

11 REACTION KINETICS eLearn.Punjab This value of rate means that in a period of one sec in 1 dm3 solution, the concentration of HIdisappears by 2.5 x 10-4 moles, changing into the products. The right angled triangle ABC can be of any size, but the results for the rate of reaction will bethe same. If we plot a graph between time on x-axis and concentration of any of the products i.e H2 or I2,then a rising curve is obtained. The value of the tangent at 100 seconds will give the same value ofrate of reaction as 2.5 x 10-4 mol dm-3S-1. The change in concentrations of reactants or products can be determined by both physicaland chemical methods depending upon the type of reactants or products involved.11.2.1 Physical Methods Some of the methods used for this purpose cure the following: In these methods, a curve hasto be plotted as mentioned in 11.2.0. The nature of the curve may be rising for products and fallingfor reactants. Anyhow, the results will be same for the same reaction under the similiar conditions. Anim ation 11.10 : Electrical Conductivity of m aterials focused on poly m er Source & Credit : w ikidot(i) Spectrometry This method is applicable if a reactant or a product absorbs ultraviolet, visible or infraredradiation. The rate of reaction can be measured by measuring the amount of radiation absorbed. 16

11 REACTION KINETICS eLearn.Punjab(ii) Electrical Conductivity Method The rate of a reaction involving ions can be studied by electrical conductivity method. Theconductivity of such a solution depends upon the rate of change of concentration of the reactingions or the ions formed during the reaction. The conductivity will be proportional to the rate ofchange in the concentration of such ions.(iii) Dilatometric Method This method is useful for those reactions, which involve small volume changes in solutions.The volume change is directly proportional to the extent of reaction.(iv) Refractrometric Method This method is applicable to reactions in solutions, where there are changes in refractiveindices of the substances taking part in the chemical reactions.(v) Optical Rotation Method In this method, the angle through which plane polarized light is rotated by the reacting mixtureis measured by a polarimeter. The extent of rotation determ ines the concentration of opticallyactive substance. If any of the species in the reaction mixture is optically active, then this methodcan be followed to ind out the rate of reaction.11.2.2 Chemical Method This is particularly suitable for reactions in solution. In this method, we do the chemicalanalysis of a reactant or a product. The acid hydrolysis of an ester (ethyl acetate) in the presence of a small amount of an acid isone of the best examples. CH3COOC2H5() + H2O() ฀฀ ฀฀H฀+฀(c฀a฀ta฀l฀yst฀฀)฀฀ CH3COOH() + C2H5OH() 17

11 REACTION KINETICS eLearn.Punjab In case of hydrolysis of an ester, the solution of ester in water and the acid acting as a catalystare allowed to react. After some time, a sample of reaction mixture is withdrawn by a pipetteand run into about four times its volume of ice cold water. The dilution and chilling stops thereaction. The acid formed is titrated against a standard alkali, say NaOH, using phenolphthalein asan indicator.The analysis is repeated at various time intervals after the start of reaction. This would providean information about the change in concentration of acetic acid formed during the reaction atdiferent time intervals. The diferent concentrations of acetic acid are plotted against the timewhereby a rising curve is obtained as shown in Fig (11.3). Fig. (11.3 ) Measurement of rate of ester hydrolysisThe slope of the curve at any point will give the rate of reaction. Initially, the rate of reaction is highbut it decreases with the passage of time. When the curve becomes horizontal, the rate becomeszero. If we plot the graph for decreasing concentrations of CH3COOC2H5, then falling curvesare obtained as shown in Fig.(11.2) If we have any laboratory technique to record the changingconcentration of ester or alcohol, we can measure the rate of the reaction. This is a pseudo irstorder reaction. Actually water being in large excess in comparison to ester does not afect the rateand we think that water is not taking part in the reaction. 18

11 REACTION KINETICS eLearn.Punjab Anim ation 11.11: Chem ical Method Source & Credit : fg-a11.3. ENERGY OF ACTIVATION For a chemical reaction to take place, the particles atoms, ions or molecules of reactants mustform a homogeneous mixture and collide with one another. These collisions may be efective orinefective depending upon the energy of the colliding particles. When these collisions are efectivethey give rise to the products otherwise the colliding particles just bounce back. The efectivecollisions can take place only when the colliding particles will possess certain amount of energyand they approach each other with the proper orientation. The idea of proper orientation meansthat at the time of collision, the atoms which are required to make new bonds should collide witheach other. The minimum amount of energy, required for an efective collision is called activationenergy. If all the collisions among the reacting species at a given temperature are efective in formingthe products, the reaction is completed in a very short time. Most of the reactions, are, however,slow showing that all the collisions are not equally efective. 19

11 REACTION KINETICS eLearn.Punjab Let us study a reaction between molecules A2 and B2 to form a new molecule AB. If thesemolecules will have energy equal to or more than the activation energy, then upon collisions theirbonds will break and new bonds will be formed. The phenomenon is shown in Fig. (11.4) Fig. (11.4) Collisions of molecules, formation of activated complex and formation of products Activated complex is an unstable combination of all the atoms involved in the reactionfor which the energy is maximum. It is a short lived species and decomposes into the productsimmediately. It has a transient existence, that is why it is also called a transition state. When the colliding molecules come close to each other at the time of collision, they slowdown, collide and then ly apart. If the collision is efective then the molecules lying apart arechemically diferent otherwise the same molecules just bounce back. When the molecules slow down just before the collision, their kinetic energy decreases andthis results in the corresponding increase in their potential energy. The process can be understoodwith the help of a graph between the path of reaction and the potential energy of the reactingmolecules. Fig. (11.5a,b) The reactants reach the peak of the curve to form the activated complex. Ea is the energy ofactivation and it appears as a potential energy hill between the reactants and the products. Only,the colliding molecules with proper activation energy, will be able to climb up the hill and give theproducts. If the combined initial kinetic energy of the reactants is less than Ea, they will be unableto reach the top of the hill and fall back chemically unchanged. This potential energy diagram can also be used to study the heat evolved or absorbed duringthe reaction. The heat of reaction is equal to the diference in potential energy of the reactants andthe products. For exothermic reactions, the products are at a lower energy level than the reactantsand the decrease in potential energy appears as increase in kinetic energy of the products Fig.(11.5a). For endothermic reactions, the products are at higher energy level than the reactants andfor such reactions a continuous source of energy is needed to complete the reaction Fig. (11.5b). 20

11 REACTION KINETICS eLearn.Punjab Fig. (11.5) A graph between path of reaction and the potential energy of the reaction The energy of activation of forward and backward reactions are diferent for all the reactions.For exothermic reactions the energy of activation of forward reaction is less than that of backwardreaction, while reverse is true for endothermic reactions. Energy of activation of a reaction providesa valuable information about the way a reaction takes place and thus helps to understand thereaction. 21

11 REACTION KINETICS eLearn.Punjab Anim ation 11.12: Activation Energy and Spontaneous reactions Source & Credit : thom psona11.4 FINDING THE ORDER OF REACTION The order of a reaction is the sum of exponents of the concentration terms in the rateexpression of that reaction. It can be determined by the following methods.(i) Method of hit and trial(ii) Graphical method(iii) Diferential method(iv) Half life method(v) Method of large excessHere we will only discuss half-life method and the method of large excess. 22

11 REACTION KINETICS eLearn.Punjab Anim ation 11.13: Determ ination of Order of a Reaction Source & Credit : askiitians11.4.1 Half Life Method As mentioned earlier, half life of a reaction is inversely proportional to the initial concentrationof reactants raised to the power one less than the order of reaction.Therefore, (t1/2 )n ∝ 1 a n-1 Let us perform a reaction twice by taking two diferent initial concentrations ‘a1’ and ‘a2’ andtheir half-life periods are found to be t1 and t2 respectively. t1 ∝ 1 and t2 ∝ 1 a n-1 a n-1 1 2Dividing the two relations: t1 =  a2  n-1Taking log on both sides: t2 a1  log t1 =(n-1)log  a2  t2 a1 23

11 REACTION KINETICS eLearn.Punjab Anim ation 11.14: Half Life Source & Credit : w ikipedia n − 1 log  t1  =  t2    log  a2  a1Rearranging n= 1 + log  t1  log  t2    a2 a1So, if we know the two initial concentrations and two half life values we can calculate the order ofreaction (n).Example 2: In the thermal decomposition of N2O at 760 °C, the time required to decompose half ofthe reactant was 255 seconds at the initial pressure of 290 mm Hg and 212 seconds at the initialpressure of 360 mmHg. Find the order of this reaction. 24

11 REACTION KINETICS eLearn.PunjabSolution:The initial pressures of N2O(g) are the initial concentrations.Data a1 = 290mm Hg t1 = 255 seconds a2 = 360mm Hg t2 = 212 secondsFormula used n= 1 + log  t1  log t2   a2 a1Putting the values in the above equation n= 1 + log  255  log  212  360 290 n = 1+ 0.0802 0.0940 n = 1 + 0.85 = 1.85 ≈ 21.85 is close to 2, hence the reaction is of second order.11.4.2 Method of Large Excess In this method, one of the reactants is taken in a very small amount as compared to the restof the reactants. The active masses of the substances in large excess remain constant throughout.That substance taken in small amount controls the rate and the order is noted with respect to that. The reason is that a small change in concentration of a substance taken in very small amountafects the value of rate more appreciably. The hydrolysis of ethyl acetate as mentioned earliershows that water being in large excess does not determine the order. 25

11 REACTION KINETICS eLearn.Punjab In this way, the reaction is repeated by taking rest of the substances in small amounts one byone and overall order is calculated. The method will be further elaborated in article 11.5.2.11.5. FACTORS AFFECTING RATES OF REACTIONS All those factors which change the number of efective collisions per second, afect the rateof a chemical reaction. Some of the important factors are as follows. Anim ation 11.15: FACTORS AFFECTIN G RATES OF REACTION S Source & Credit : askiitians11.5.1 Nature of Reactants The rate of reaction depends upon the nature of reacting substances. The chemical reactivityof the substances is controlled by the electronic arrangements in their outermost orbitals. Theelements of I-A group have one ejectron in their outermost s-orbital. They react with water moreswiftly than those of II-A group elements having two electrons in their outermost s-orbital. Similarly,the neutralization and double decomposition reactions are very fast as compared to those reactionsin which bonds are rearranged. Oxidation-reduction reactions involve the transfer of electrons andare slower than ionic reactions. 26

11 REACTION KINETICS eLearn.Punjab11.5.2 Concentration of Reactants The reactions are due to collisions of reactant molecules. The frequency with which themolecules collide depends upon their concentrations. The more crowded the molecules are, themore likely they are to collide and react with one another. Thus, an increase in the concentrationsof the reactants will result in the corresponding increase in the reaction rate, while a decrease inthe concentrations will have a reverse efect. For example, combustion that occurs slowly in air (21% oxygen) will occur more rapidly in pure oxygen. Similarly, limestone reacts with diferent concentrations of hydrochloric acid at diferent rates.In the case of a gaseous reactant, its concentration can be increased by increasing its pressure.Therefore, a mixture of H2 and Cl2 will react twice as fast if the partial pressure of H2 or Cl2 isincreased from 0.5 to 1.0 atmosphere in the presence of excess of the other component. The efect of change in concentration on the rate of a chemical reaction can be nicelyunderstood from the following gaseous reaction. 2NO(g) + 2H2 (g) → 2H2O(g) + N2 (g) Anim ation 11.16: Reactants Source & Credit : giphy In this reaction, four moles of the reactants form three moles of the products, so the pressuredrop takes place during the progress of reaction. The rates of reaction between NO and H2 at800°C are studied by noting the change in pressure. The following Table (11.2 ) has been obtainedexperimentally for the above reaction. 27

11 REACTION KINETICS eLearn.PunjabTable (11.2) Effect of change inconcentrations of reactants on the rate of reaction [NO] in [H2] in Initial rate(mol dm-3) (mol dm-3) (atm min-1) 0.006 0.001 0.025 0.006 0.002 0.050 0.006 0.003 0.075 0.001 0.009 0.0063 0.002 0.009 0.025 0.003 0.009 0.056Table (11.2)shows the results of six experiments. In the irst three experiments the concentrationof H2 is increased by keeping the concentration of NO constant. By doubling the concentration ofH2, the rate is doubled and by tripling the concentration of H2, the rate is tripled. So, the rate ofreaction is directly proportional to the irst power of concentration of H2. Rate ∝ [H2 ]In the next three experiments, the concentration of H2 is kept constant. By doubling the concentrationof NO, the rate increases four times and by tripling the concentration of NO the rate is increasednine times. So, the rate is proportional to the square of concentration of NO. Rate ∝ [NO]2The overall rate equation of reaction is, Rate ∝ [H2 ][NO]2 or Rate = k[H2 ]1[NO]2 Hence, the reaction is a third order one. This inal equation is the rate law for this reaction.It should be kept in mind that rate law cannot be predicted from the balanced chemical equation.This set of experiments helps us to determine the order of reaction as well. 28

11 REACTION KINETICS eLearn.Punjab The possible mechanism consisting of two steps for the reaction is as follows:(i) 2NO(g) + H2(g) slow→ N2(g) + H2O2(g) (rate determining)(ii) H2O2 (g) + H2 (g) fast→ 2H2O(g)The step (i) is slow and rate determining. Anim ation 11.17: Concentration of Reactants Source & Credit : socratic11.5.3 Surface Area The increased surface area of reactants, increases the possibilities of atoms and molecules ofreactants to come in contact with each other and the rates enhance. For example, AI foil reacts withNaOH moderately when warmed, but powdered AI reacts rapidly with cold NaOH and H2 is evolvedwith frothing. 2AI + 2NaOH + 6H2O → 2NaAI(OH)4 + 3H2 29

11 REACTION KINETICS eLearn.Punjab Similarly, CaCO3 in the powder form reacts with dilute H2SO4 more eiciently than its bigpieces. Anim ation 11.18: Surface Area Source & Credit : darelhardy11.5.4 Light Anim ation 11.19: Light Source & Credit : w ikipediaLight consists of photons having deiniteamount of energies depending upontheir frequencies. When the reactantsare irradiated, this energy becomesavailable to them and rates of reactionsare enhanced. The reaction of CH4 andCl2 requires light. The reaction betweenH2 and Cl2 at ordinary pressure isnegligible in darkness, slow in daylight,but explosive in sunlight. Similarly, lightis vital in photosynthesis, and the rate isinluenced by light. 30

11 REACTION KINETICS eLearn.Punjab11.5.5 Effect of Temperature on Rate of ReactionThe collision theory of reaction rates convinces us that the rate of a reaction is proportional tothe number of collisions among the reactant molecules. Anything, that can increase the frequencyof collisions should increase the rate. We also know, that every collision does not lead to a reaction.For a collision, to be efective the molecules must possess the activation energy and they must alsobe properly oriented. For nearly all chemical reactions, the activation energy is quite large and atordinary temperature very few molecules are moving fast enough to have this minimum energy.All the molecules of a reactant do not possess the same energy at a particular temperature.Most of the molecules will possess average energy. A fraction of total molecules will have energymore than the average energy. This fraction of molecules is indicated as shaded area in Fig.(11.6).As the temperature increases, the number of molecules in this fraction also increases. Therehappens a wider distribution of velocities. The curve at higher temperature T2 has lattened. It showsthat molecules having higherenergies have increased andthose with less energies havedeceased. So, the number ofefective collisions increasesand hence the rate increases.When the temperature of thereacting gases is raised by10K, the fraction of moleculewith energy more than Earoughly doubles and so thereaction rate also doubles.Arrheinus has studied thequantitative relationshipbetween temperature, energyof activation and rate constantof a reaction. Fig. (11.6) Kinetic energy distributions for a reaction mixture at two different temperatures. The size of the shaded areas under the curves are proportional to the total fraction of the molecules that possess the minimum activation energy. 31

11 REACTION KINETICS eLearn.PunjabAnim ation 11.20 : Effect of Tem perature on Rate of Reaction Source & Credit : dy nam icscience11.5.6 Arrhenius Equation Arrhenius equation explains the efect of temperature on the rate constant of a reaction. Therate constant ‘k’ for many simple reactions is found to vary with temperature.According to Arrhenius:k=Ae-Ea/RT ........ (1) So, ‘k’ is exponentially related to activation energy (Ea) and temperature (T). R is general gasconstant and e is the base of natural logarithm. The equation shows that the increase in temperature,increases the rate constant and the reactions of high activation energy have low ’k’ values. 32

11 REACTION KINETICS eLearn.PunjabThe factor ‘A’ is called Arrhenius constant and it depends upon the collision frequency of the reactingsubstances. This equation helps us to determine the energy of activation of the reaction as well.For this purpose, we take natural log of Arrhenius equation, which is expressed as n . The base ofnatural log is e and its value is 2.718281.Now, take natural log on both sides nk = n(Ae-Ea/RT )or nk = nA + ne-Ea/RTor nk = nA + -E ne RTSince ne = 1 (log of a quantity with same base is unity)Therefore nk = -Ea + nA ........... (2) RT The equation (1) is the equation of straight line, and from the slope of straight line Ea can becalculated. In order to convert this natural log into common log of base 10, we multiply the n termwith 2.303. 2.303 log k = -Ea + 2.303 log A (The base of common log is 10) RTDividing the whole equation by 2.303 log k = -Ea + log A ........... (3) 2.303RT This equation (3) is again the equation of straight line resembling. y = -mx + c Where ‘m’ is slope of straight line and ‘c’ is the intercept of straight line. Temperature is inde-pendent variable in this equation while rate constant k is dependent variable. The other factors likeEa, R and A are constants for a given reaction. 1 When a graph is plotted between T on x-axis and log k on y-axis, a straight line is obtainedwith a negative slope. Actually, Ea has negative sign so the straight line has two ends in second andfourth quadrants, Fig. (11.7). RT 33