Rates Description of time dependence requires a statement of the time derivatives of the concentrations of reactants and products Physical Chemistry Lecture 5 Introduction to chemical kinetics H2 gas 1 O gas 2 2 H2 O liquid Rates Rate of change of H2O Rate of change of H2 Rate of change of O2 d H2O dt d H2 dt d O2 dt Rates are not independent because of mass conservation Thermodynamics and kinetics Thermodynamics Relative stability of states Characterized by free energy differences Static comparisons of states Kinetics Changes of state over time Several different topics Empirical description of the rates of reaction Determination of experimental parameters Microscopic theories of reaction 1 oxygen molecule disappears for every 2 hydrogen molecules in forming 1 water molecule Reaction velocity The rates of appearance of products and disappearance of reactants are related by stoichiometry of the reaction Reaction velocity v normalizes rates of appearance of products and disappearance of reactants Stoichiometric coefficient i Found from balanced equation Positive for products Negative for reactants v 1 d i i dt H 1 O 1 2 H O 1 2 2 2 1 H 2 gas O2 gas H 2O liq 2 Descriptions of reactions Chemical reaction often given by an equation of the type H2 gas 1 O gas H2 O liquid 2 2 Rate law Description of how the reaction velocity depends on parameters such as concentrations temperature pressure etc v This description is incomplete Only gives beginning and ending states Sometimes does not even describe the final state correctly Gives stoichiometry of change Must describe time dependences of amounts of materials to describe the reaction more completely f Areact B prod T P Function may be complex Gives insight into the reaction s progress Reactions do not necessarily occur as implied by the overall equation Attempts to describe the features of the underlying physical chemistry of reaction in detail 1 Determining reaction rate Initial order determination Must determine how the reaction velocity depends on concentration temperature etc Major method for finding reaction velocity under limiting conditions Follows the concentration only at early times initial rate May not completely describe the reaction Often done as a convenience Determine time dependence of concentration At any point rate of loss of reactant is slope of tangent to a plot of reactant concentration versus time Changes from time to time Depends on the instantaneous concentration Not always easy to monitor concentration Care must be exercised in making general conclusions based on initial rate studies Must find measurable parameter proportional to reactant concentration Sometimes monitor appearance of product rather than reactant Order Isolation method In many situations one may formally write the reaction velocity approximately as a function of the form v k A a B b C c a b c are the orders of reaction under the conditions k is the rate constant Many rate laws are more complex functions of concentration than the simple product given above Example Production of HBr from H2 and Br2 v HBr k Orders are usually determined over a limited range of conditions Orders are not necessarily the same as the stoichiometric coefficients for the reaction Differential method of determining order ln v k nln C Example Decomposition of di tert butyl peroxide Line slope 1 04 Order with respect to DTBP is close to 1 under these conditions and probably is 1 When there are multiple reactants it helps to create a situation in which one reactant dominates the measurement H2 Br2 1 2 HBr 1 k Br2 Calculate approximate derivatives as ratios of differences for specific concentrations Plot approximate derivatives versus concentration Follow reaction for a limited time Can optimize sensitivity Ri Ci 1 Ci ti 1 ti Ci Ci 1 Ci 2 R1 R2 Create isolation by making one material the limiting reagent Generally requires one to have other reagents in significant excess A 1 A 2 a Can be used with an initialrate measurement Ratios of reaction rates allow one to determine initial order Determining initial order Measure initial velocity as a function of the initial amounts of reactants in the mixture Example OCl I OI Cl OCl I OH 0 0017 0 0017 1 00 0 0034 0 0017 1 00 0 0017 0 0034 1 00 0 0017 0 0017 0 50 Concentrations are in mol dm 3 Rate is mol dm 3 sec 1 Initial rate 1 75 10 4 3 50 10 4 3 50 10 4 3 50 10 4 By comparison one finds the initial rate equation vinitial k OCl I OH 1 k 60 55 s 1 2 Measurement methods Concentration as a function of time Example decomposition of ditert butyl peroxide slope k1 Rate constant for this reaction under these conditions is k1 0 0193 min 1 from the slope of the line Chemical wet methods such as titration Take aliquots as a function of time Analyze separately Limited time scales 1 10 s Physical methods Spectrometry electrical conductivity pressure etc Usually measured in situ Requires one to find a physical property proportional to the concentration of a reactant or perhaps a product Can often measure faster than chemical methods Faster reactions are observed down to 10 15 s Stopped flow reactions Flash photolysis Relaxation methods Integrated rate law second order in one reactant Integrated rate laws Gives an expression for the time dependence of the concentration rather than derivative of the concentration with time Can be used under a variety of conditions First order rate law Second order rate law can also be integrated Linear plot of 1 A t versus t Often see reported rate constant for disappearance of A Limiting reagent Single molecule Fast reactions Concentration is an exponential function of time Logarithm of the concentration is linear in time Usually plot linear form Slope gives k1 keff 2 k2 Exercise caution in assessing reported rate constants Is it the inherent rate constant Is it the rate constant for the disappearance of the reactant Integrated first order rate law Rate linear in reatant concentration Integration to find Reactant concentration as a function of time v d A dt A v 1 d A 2 dt k 2 A 2 1 d A 2k 2 dt A 2 A t 1 d A 2k 2 dt A 2 A 0 0 1 A t 1 A 0 2k 2 t Second order rate law Example k1 A 1 d A k1dt A A 0 2 A Products t 1 d A k1dt A 0 A t A 0 exp k1t ln A t ln A 0 k1t Collision induced decomposition of diacetylene DA Hou and Palmer 1965 Linear plot of DA 1 versus t keff 6 79 x107 cm3 mol sec Note units of the rate constant 3 Second order rate law first order in two different reactants A Integration relies on the stoichiometry