CHEM1612 - Pharmacy Week 11: Kinetics - Rate Law Dr. Siegbert Schmid School of Chemistry, Rm 223 Phone: 9351 4196 E-mail: siegbert.schmid@sydney.edu.au

Unless otherwise stated, all images in this file have been reproduced from: Blackman, Bottle, Schmid, Mocerino and Wille,      Chemistry, John Wiley & Sons Australia, Ltd. 2008      ISBN: 9 78047081 0866

Chemical Kinetics Blackman, Bottle, Schmid, Mocerino & Wille: Chapter 14 KINETICS: the study of REACTION RATES and their relation to the way the reaction proceeds, i.e., its MECHANISM. Thermodynamics tells whether a reaction favours products or reactants (i.e. relative stabilities), but gives us no information on HOW FAST the reaction goes from reactants to products, e.g. H2 should react with O2 (ΔH° = –286 kJ mol-1) At RT the reaction is spontaneous and K = 3.6 x 1041! But no reaction occurs!!!! 2 H2 + O2 2 H2O

Factors affecting reaction rate Rate is proportional to collision rate which is proportional to Figure from Silberberg, “Chemistry”, McGraw Hill, 2006. Concentration of some or all of the molecules present Physical state: reactants need to mix to collide Temperature: the higher T, the more energetic the collisions, the faster the reaction Pressure (similar to concentration) Presence of a catalyst

Rate of a Reaction -Δ[A] Δt Δ[B] Δt Rate = = Figure from Silberberg, “Chemistry”, McGraw Hill, 2006. -Δ[A] Δt Δ[B] Δt Rate = = The rate of a reaction is the change in concentration of one of the reactants that occurs during a given period of time.

Rate of a Reaction Average reaction rate = – Δ[A] Δ t Time (s) [A] (mol L-1) Ave. Rate (mol L-1 s-1) 0 0.0750 100 0.0529 200 0.0372 The reaction rate varies with time as the reaction proceeds. Average rate is not constant. Minus sign: this is simply added in order to make the reaction rate a positive quantity (by convention) Note that DBr2 = [Br2]final - [Br2]initial (change in concentration) and similar equation for Dt Work through calculation for second ave. rate: ave rate = - (0.00846 - 0.0101) / (100 - 50) = 3.28 x 10-5 M/s Note: ave. reaction rate decreases as the concentration of Br2.decreases. It eventually becomes zero when all the bromine has reacted The average rates were calcuated over 50 sec above. One could also have calculated them over shorter times if the concentrations at shorter time intervals had been measured. Analogy: note also that the spending rate would also not be constant since as the balance approaches zero the spending rate normally drops off. Might want to calculate an instantaneous spending rate (very important particularly when money decreases. D[$] cf. - a [$] Dt

Rate of a Reaction An infinitesimally small change in the concentration, d[A], that occurs over the infinitesimally short period of time, dt, gives the instantaneous rate of reaction. You can work out that rate for any moment in time by determining the slope of a tangent drawn to the concentration-time curve at that exact moment. - d [A] Rate50s = d t Slope = rise over run

Expressing Reaction Rates For a generic chemical reaction the reaction rate is defined as: A + C → 2 B (1) (2) Expression 2 is just a rearrangement of 1, but its numerical value for the rate is double that of (1). The expression and its numerical value depend on the reactant taken as reference.

Expressing Reaction Rates Express the rate in terms of the change in concentration with time of each substance for the reaction: 2 N2O5 → 4 NO2 + O2 Rate of production of O2 = 2.6·10-6 M s-1. Rate of production of NO2 = 4 × 2.6·10-6 = 1.0·10-5 M s-1 Rate of consumption of N2O5 = - 2 × 2.6 · 10-6 = - 5.2·10-6 M s-1

Expressing Reaction Rates a A +b B → c D + d D In practice, you will commonly choose as a reference the species that appears with stoichiometric coefficient of 1.

Expressing Reaction Rates Express the rate of reaction in terms of concentration of reactants and products for the reaction: 4 NH3 (g) + 5 O2 (g)  4 NO (g) + 6 H2O (g) Solution: Rate of reaction

Example 1 The concentrations of N2O5 are 1.24 ·10-2 and 0.93 · 10-2 M at 600 s and 1200 s after the reactants are mixed at the appropriate temperature. Calculate the reaction rates for 2 N2O5 → 4 NO2 + O2 Solution: Rate of decomposition of N2O5 = What is the rate of formation of the products? rate of formation of NO2 = (2 × rate N2O5) =1.0 · 10-5 M s-1. rate of formation of O2 = (0.5 × rate N2O5) = 2.6 x 10-6 M s-1.

Example 2 Express the rate in terms of the change in concentration with time of each substance for the reaction: 2 O3 → 3 O2 Answer: If the rate at which O2 appears is 6·10-5 Ms-1, at what rate is O3 disappearing at the same time?

The Iodine Clock Mix different amounts of HIO3 + NaHSO3 + starch. Concentration of reactants is: [beaker I] > [beaker II] >[beaker III]. The following reactions take place consecutively in each beaker:   Starch forms a blackish blue complex with iodine. As the final reaction is the fastest, the colour of the elemental iodine only becomes apparent once the sulphite is fully consumed. The reaction is slowest in the solution with the lowest concentration, as the reaction time is dependent on the concentration.

Rate Law Expresses the rate as a function of reactant concentrations and T. For a generic reaction: aA + bB + …→ cC + dD + …. The rate law has the form: rate = k [A]m[B]n ….. k = rate constant, is independent of conc. but increases with T m,n,… reaction orders; if the rate doubles for doubling of [A], m = 1 In general m, n,… ≠ a, b, c, …

Rate Law Hydrolysis of cisplatin [Pt(NH3)2Cl2](aq) +H2O(l)  [Pt(NH3)2(H2O)Cl](aq) + Cl-(aq) Rate of hydrolysis of cis-platin is proportional to [Pt(NH3)2Cl2] We express this as a RATE LAW Rate laws can be determined ONLY experimentally, they cannot be deduced by reaction stoichiometry. Rate of reaction = k [Pt(NH3)2Cl2]

Experimental Tools Many methods are available to monitor reaction rates, e.g.: Spectrometric Methods (measure light adsorbed by a reactant or product) Conductometric Methods (measure change in conductivity during reaction) Manometric Methods (Monitor the change in pressure over time, at constant V, T) Direct Chemical Methods (a small aliquot of reaction mixture is sampled, cooled down, and titrated)

Reaction Orders For the general reaction: a A + b B + c C …  d D + e E …. rate = k [A]m [B]n [C]o … m is the order of the reaction with respect to A (or “in” A), n is the order of the reaction with respect to B… Overall order of the reaction is = m + n + o +…. e.g. if rate = k [A]2 [B] , then the reaction is second order with respect to A, first order with respect to B, and overall third order. Reaction orders cannot be deduced from the balanced reaction.

Reaction Orders For most reactions the order is a small positive integer or zero, but also: Fractional number: CHCl3 (g) + Cl2 (g) → CCl4 (g) + HCl (g) Rate = k [CHCl3] [Cl2] ½ Negative number: 2 O3 (g) → 3 O2 (g) Rate = k [O3]2 [O2]-1 = k [O3]2 / [O2]

NO (g) + O3 (g)  NO2 (g) + O2 (g) Reaction Orders What is the order of reaction with respect to NO, O3, and the overall order of reaction for the reaction: NO (g) + O3 (g)  NO2 (g) + O2 (g) Rate = k [NO] [O3] Answer: First order with respect to NO and O3, overall second order (1+1).

Reaction Orders What order is the following reaction? H2 (g) + 2 ICl (g)  2 HCl (g) + I2 (s) The reaction order can be determined ONLY by experiment. Rate = -d[H2] / dt = k [H2][ICl] = k [H2]1[ICl]1 This reaction is first order with respect to H2, first order with respect to ICl and second order overall.

2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g) Reaction Orders Express the rate in terms of the change in concentration with time of each substance for the reaction: 2 NO (g) + 2 H2 (g)  N2 (g) + 2 H2O (g) What is the order of reaction with respect to NO, H2 and the overall order of reaction for the reaction: Rate = k [NO]2 [H2] The reaction is second order with respect to NO, first order with respect of H2, overall third order (2+1).