Chemical Kinetics Petrucci, Harwood and Herring (8th edition) Problem Set: Chapter 5 questions 29, 33, 35, 43a, 44, 53, 63, 8 CHEM 3. Chemical Kinetics Kinetics versus Thermodynamics - thermodynamics tells us which direction a reaction will go (e.g. at room temperature and standard pressure, carbon is stable as graphite) - kinetics can tell us how quickly it will get there (e.g. a diamond will not convert to graphite during your lifetime) (Thermodynamics will be considered later in this course.) CHEM 3. Chemical Kinetics 2
Aims of Chemical Kinetics ) at the macroscopic level - to define rate of reaction, order of reaction and rate law - to examine how rates and orders are determined 2) at the molecular level - to predict plausible reaction mechanisms from experimental rate laws CHEM 3. Chemical Kinetics 3 Knowing Balanced Chemical Reaction is Essential (i.e. the stoichiometry must be known for determining reaction rates) Warm up example: 2 Fe 3+ + Sn 2+ 2 Fe 2+ + Sn 4+ rate of Fe 3+ consumption is twice as high as that of Sn 2+ rate of Fe 3+ consumption has same absolute value as rate of Fe 2+ production, but it is negative CHEM 3. Chemical Kinetics 4
General Reaction aa + bb gg + hh The rates of loss of A and B and production of G and H can be expressed through the rates of change in their concentrations (if the volume is constant): [B] [G] [H],,, t t t t Units: M/s or mol L - s - CHEM 3. Chemical Kinetics 5 Relation Between the rates of Loss and Production as reactants are consumed, their concentrations drop while those for products increase the rates of production are positive and those of consumption are negative rates of production and loss are related by the stoichiometry of the balanced reaction: [B] [G] [H] - = - = = a t b t g t h t As usually: = -, t = t - t t t 2 2 CHEM 3. Chemical Kinetics 6
Definition of the Rate of Reaction [B] rateof reaction = - = - a t b t [G] [H] = = g t h t The rate of reaction may be expressed in terms of either the consumption of reactants, or the production of products. CHEM 3. Chemical Kinetics 7 Example (similar to the warm-up one) H 2 (g) + 2 ICl(g) I 2 (g) + 2 HCl(g) [H ] [ICl] t 2 t [I ] [HCl] t 2 t 2 rateof reaction = - = - 2 = = CHEM 3. Chemical Kinetics 8
Real Kinetics! (for the same example) H 2 (g) + 2 ICl(g) I 2 (g) + 2 HCl(g) - rate slows as reaction approaches equilibrium CHEM 3. Chemical Kinetics 9 Measuring Reaction Rates is Generally Not Trivial determining reaction rates requires measuring changes in concentration over time (e.g. / t) measuring time is simple; determining concentrations of products or reactants can be more difficult could measure partial pressures of gases, ph of a solution, colour changes (spectroscopy), etc., to monitor the progress of the reaction (i.e. the change in concentration) the method for monitoring the reaction is dependent upon the properties of the substances in the reaction CHEM 3. Chemical Kinetics
Example (Experiment) H 2 O 2 (aq) H 2 O(l) + O 2 (g) could follow this reaction by measuring volume of O 2 (g) produced at different times, or could titrate small samples of the solution with permanganate from time to time to follow the progress of the reaction by measuring the loss of H + (change of ph) electrochemically: 2 MnO 4- + 5 H 2 O 2 + 6 H + 2 Mn 2+ + 8 H 2 O + O 2 (g) - let s follow the reaction by the latter method every 4 s CHEM 3. Chemical Kinetics Experimental Data (Tabulated) CHEM 3. Chemical Kinetics 2
Same Experimental Data (Plotted) - rate of reaction decreases as H 2 O 2 is consumed CHEM 3. Chemical Kinetics 3 Average and Instantaneous Rates calculating - [H 2 O 2 ]/ t gives average rate of reaction over the time interval (e.g. between 2 and 6 s average rate of 6.3 X -4 M s - approximates the rate at the middle of the interval at about t = 4 s) instantaneous rate of reaction is best determined by tangent to the curve (blue line on previous diagram gives rate = 6. x -4 M s - at t = 4 s) using t to calculate rates give accurate values as t becomes very small (i.e. as it approaches zero) and / t becomes d/dt a tangent to the concentration-time curve at t = will provide the initial rate of reaction (black line in the previous plot) which is very important in determining reaction orders CHEM 3. Chemical Kinetics 4
The Rate Law one objective of chemical kinetics is to establish a relationship between the rate of reaction and the concentration of the reagents - this relationship is called the rate law, or rate equation for the general reaction, aa + bb gg + hh, we can write rate of reaction = k m [B] n in which and [B] represent reactant molarities and the exponents m and n are generally small, positive integers, but may be zero, fractional and/or negative CHEM 3. Chemical Kinetics 5 The Meaning of m, n and k Reaction: aa + bb gg + hh rate of reaction = k m [B] n the exponents are generally not related to the stoichiometric coefficients in the balanced reaction (i.e. usually m a, n b). the reaction is of order m for reactant A, order n for reactant B, and the overall order of reaction is m + n k is a proportionality constant known as the rate constant - the faster the reaction, the larger the value for k (k is also temperature dependent) the units for k depend upon the order of reaction The meaning of m, n and k can be fully understood only on the microscopic level CHEM 3. Chemical Kinetics 6
Establishing the Rate Law i.e. Determining m, n, and k The rate law can only be established by analysing experimental data - two methods will be considered ) Method of Initial Rates at the start of an experiment (t = ), the initial concentration of the reagents can be known a tangent to the concentration-time curve at t = will provide the initial rate of reaction Based on this we will: measure initial rates for two different concentrations of every reactant keeping concentrations of other reactants constant compare relative rates and initial concentrations to find m, n and k CHEM 3. Chemical Kinetics 7 Example: Method of Initial Rates rate of reaction = k[hgcl 2 ] m [C 2 O 4 2- ] n - consider experiments 2 & 3 [HgCl 2 ] approximately doubles, [C 2 O 2-4 ] remains constant, and the initial rate doubles (approximately) CHEM 3. Chemical Kinetics 8
Determination of m Relative Rates and Relative Initial Concentration From the rate law: m n m R2 k(.5) (.3).5 = = 2. m n = R3 k(.52) (.3).52 From the initial rates: -5 R 2 7. X = = 2. -5 R 3.5X 3 2 = 2 m, therefore m = m CHEM 3. Chemical Kinetics 9 Determination of n still need to determine n, order of reaction for [C 2 O 2-4 ] consider experiments & 2 [HgCl 2 ] remains constant, [C 2 O 2-4 ] doubles From the rate law n -5 R 2 k(.5)(.3) n 7. X = = 2. = =3.94 n -5 R k(.5)(.5).8 X 2 n 4, n = 2 (by inspection) or, take logs of both sides of the equation n log(2.) = log(3.94) n (.3) =.595, n =.99 2 CHEM 3. Chemical Kinetics 2
Determination of k The rate law thus far is rate of reaction = k[hgcl 2 ][C 2 O 2-4 ] 2 still need to determine the rate constant, k use data from any one of the experiments k = initial rate/{[hgcl 2 ][C 2 O 2-4 ] 2 } in which concentrations are initial values, and solve for k: k = 7.5 x -3 M -2 min - (from exp. 2) therefore rate law is rate of reaction = 7.5 x -3 [HgCl 2 ][C 2 O 2-4 ] 2 (rate of reaction will be expressed in M min - ) CHEM 3. Chemical Kinetics 2 Units of the Rate Constant Depend on the Order of Reaction Order of Reaction Units of Rate Constant [ ] time - time - 2 [ ] - time - 3 [ ] -2 time - [ ] represents concentration, usually M, or mol L - time represents s, min, h, etc. CHEM 3. Chemical Kinetics 22
2) Method of Integrated Rate Laws the Method of Initial Rate uses data from the initial portion of multiple experiments the Method of Integrated Rate Laws uses the full concentration-time curve from one experiment the integrated rate equation relates concentration and time for a given order of reaction =F(t) it can also be used to calculate the half-life, t, of a reactant which is the time it takes for half of that reactant to be converted into product CHEM 3. Chemical Kinetics 23 Method of Integrated Rate Laws - continued For the general reaction aa products we can write d n rate of reaction = - = k a dt in which n is the order of the reaction for the reactant A - the integration of this expression for different values of n gives the integrated rate laws Note: Petrucci, Harwood & Herring do not include the a term but this approach is more general CHEM 3. Chemical Kinetics 24
Zero-Order Reactions: n= rate of reaction = k = k = constant d = k a dt d = akdt Expression = = akt akt is called the integrated rate law for zero-order reactions concentration-time graph is a straight line with a negative slope CHEM 3. Chemical Kinetics 25 Half-Life for Zero-Order Reactions integrated rate law for zero-order reactions: = -akt half-life, t, is time required for the concentration of the reactant A to decrease to half its initial value t = /2 by definition t = akt from the integrated rate law /2 = akt t = /2ak CHEM 3. Chemical Kinetics 26
First-Order Reactions: n = d rate of reaction = - = k a dt integrated rate law: = e -akt (exponential decay) often represented as ln = akt to get a straight line Concentration 5 4.5.75 4 3.5 3.5 2.5 2.25.5.5 ak = slope 2 3 4 5 2 3 4 5 Time CHEM 3. Chemical Time Kinetics 27 ln(/) Half-Life for First-Order Reactions Integrated rate law in this form ln can be used for easy calculation of half-life ln = ln = ln2 from definition of / 2 ln t = akt from the integrated rate law akt = ln2 t = ln2/ak =.693/ak Therefore t is independent of (i.e. it is constant for a first-order reaction) = akt t t CHEM 3. Chemical Kinetics 28
Examples of First-Order Reactions CHEM 3. Chemical Kinetics 29 Second-Order Reactions: n = 2 d 2 rate of reaction = - = k a dt Integrated rate law : = akt + Integrated rate law in linearized form : - = akt.75.5.25 2 3 4 5 Time /-/ 5 4.5 4 3.5 3 2.5 2.5.5 2 3 4 5 Time CHEM 3. Chemical Kinetics 3
Half-Life for Second-Order Reactions From the integrated rate law : From the definition of akt = t : t t t = ak CHEM 3. Chemical Kinetics 3 = akt t is not constant for second-order reactions = Method of Integrated Rate Laws - continued How can we use these integrated rate law equations to solve for reaction order? make the appropriate plot! Plot Order Zero First Second vs. t ln vs. t / vs. t Slope -ak -ak ak Intercept ln / - or test for the consistency of the half-life (Note: only a first-order reaction has a constant t ) CHEM 3. Chemical Kinetics 32
Integrated Rate Laws - more than one reactant thus far only considered integrated rate laws for simple reactions with only one reactant - how can we analyse reactions with more than one reactant? Consider the following rate law rate of reaction = k m [B] n - control the experiment so that» [B] - very little A will be consumed so and rate law becomes rate of reaction = k m [B] n = k [B] n - allows dependence on B to be isolated from dependence on A CHEM 3. Chemical Kinetics 33 Ex: More Than One Reactant BrO 3- (aq) + 5Br - (aq) + 6H + (aq) 3Br 2 (l) + 3H 2 O(l) has the rate law Rate = k[bro 3- ][Br - ][H + ] 2 if [Br - ] =. M, [H + ] =. M, & [BrO 3- ] =. X -3 M, then both [Br - ] and [H + ]» [BrO 3- ] and relatively little of them will be consumed; rate law can be written as Rate = k[br - ] [H + ] 2 [BrO 3- ] = k [BrO 3- ] where k = k[br - ] [H + ] 2 - a plot of ln[bro 3- ] versus t would be a straight line with slope of k (pseudo-first-order reaction) CHEM 3. Chemical Kinetics 34