How rapidly reactions proceed - rate of reaction Details of process from reactants to products - mechanism Thermodynamics determines the direction in which reactions proceed spontaneously and the conditions at equilibrium, but not the rate at which equilibrium is reached. For a complete picture of a chemical reaction need both the thermodynamics and kinetics of a reaction. Chemical Kinetics

N 2 (g) + 3H 2 (g)  2NH 3 (g) At 298 K  G o = kJ  H o = -92 kJ; exothermic reaction K = 6.0 x 10 5 ; thermodynamically favored at 298 K, Rate is slow at 298K Commercial production of NH 3 is carried out at temperatures of 800 to 900 K, because the rate is faster even though K is smaller.

Thermodynamic functions are state functions (  G,  H,  E) Thermodynamic functions do not depend on the mechanism of the reaction. The rate of the reaction is very dependent on the path of the process or path between reactants and products. Kinetics reveals information on the rate of the reaction and the mechanism (path) of the reaction.

Thermodynamics vs Kinetics A + B  C + DK 1 A + B  E + FK 2 If K 1 > K 2 - products C & D are thermodynamically favored over E & F. If products observed are C & D: reaction is thermodynamically controlled If products observed are E & F: reaction is kinetically controlled

Zn 2+ (aq) + S 2- (aq)  ZnS(s)K = 1/K sp = 2.2 x Fe 2+ (aq) + S 2- (aq)  FeS(s)K = 1/K sp = 2.7 x On addition of S 2- to an aqueous solution containing both Zn 2+ and Fe 2+, ZnS precipitates first - reaction is thermodynamically controlled.

(1) 2NO(g) + O 2 (g)  2NO 2 (g) (2) 2CO(g) + O 2 (g)  2CO 2 (g) Both have large values of K; both are thermodynamically favored in the forward direction Reaction (1) is very fast; reaction (2) slow Reactions are kinetically controlled Result is brown color of air due NO 2 and buildup of CO in the air

Rates of Reactions Rate of a reaction: change in concentration per unit time Zn(s) + 2 H + (aq)  Zn 2+ (aq) + H 2 (g)

average reaction rate = change in concentration change in time Units of rate: concentration / time NO 2 (g) + CO(g)  NO(g) + CO 2 (g) average reaction rate = [NO] final - [NO] initial t final - t initial

NO 2 (g) + CO(g)  NO(g) + CO 2 (g) Time (s)[NO] mol L Average rate 1st 50 seconds = 3.2 x mol L -1 Average rate 2nd 50 seconds = 1.6 x mol L -1 Average rate 3rd 50 seconds = 9.6 x mol L -1

Instantaneous Rate - rate at a particular moment in time

NO 2 (g) + CO(g)  NO(g) + CO 2 (g)  [NO] tt  [CO] tt  [NO 2 ] tt  [CO 2 ] tt rate ==== - - For a general reaction: aA + bB  xC + yD d[C] dtdt d[B] dtdt rate = == = - 1 x 1 b d[A] dtdt - 1 a d[D] dtdt 1 y For an infinitesimally small changes, the instantaneous rate d[NO] d t d[CO] d t d[NO 2 ] d t d[CO 2 ] d t rate ==== - -

initial rate (t = 0)

Rate (at 5 weeks) = -6.3 x Rate (at 10 weeks) = -2.6 x 10 -3

Factors affecting rates of reactions a) Nature of reactants 2NO(g) + O 2 (g)  2NO 2 (g)fast 2CO(g) + O 2 (g)  2CO 2 (g)slow b) Concentration of reactants: reactions proceed by collisions between reactants c) Temperature: In general, as T increases, rate increases d) Catalyst: increases rate of reaction e) Surface: larger surface area increases rate of reaction f) Nature of solvent

Effect of concentration Effect of surface area Effect of temperature

Initial reaction rate: instantaneous rate of change in concentration of a species at the instant the reaction begins. (products present later in the reaction may affect the rate) 2 N 2 O 5 (g)  4 NO 2 (g) + O 2 (g) Perform a series of experiments with different initial concentrations of N 2 O 5 (g). For each, monitor the concentration of N 2 O 5 (g) versus time Determine the initial rate of reaction at t = 0 Rate Laws and Rate Constant

2 N 2 O 5 (g)  4 NO 2 (g) + O 2 (g) For this reaction, experiments indicate: rate  initial concentration of N 2 O 5 (g) rate = k x initial concentration of N 2 O 5 (g)

Rate = - d[N 2 O 5 ] / dt = k [N 2 O 5 ] Rate law k = 5.2 x s -1 k is the specific rate constant Units of k depends on the rate law Rate laws are determined experimentally = k [NO 2 ] 2 Rate Law 2 NO 2 (g)  2 NO(g) + O 2 (g) d[NO 2 ] dtdt rate = k = 0.54 (mol NO 2 ) -1 s -1 -

2 NO 2 (g)  2 NO(g) + O 2 (g) Rate = k [NO 2 ] 2

For a general reaction: aA + bB  cC + dD d[C] dt d[B] dt rate = == = - 1 c 1 b d[A] dt - 1 a d[D] dt 1 d rate = k [A] m [B] n For a reaction k has a specific value; k for the reaction changes with temperature Note: m need not equal a; n need not equal b Rate Law

Order of a Reaction rate = k [A] m [B] n Reaction is m th order in A and n th order in B Overall reaction order = m + n The reaction order is determined by the experimentally determined rate law N 2 O 5 (g)  N 2 O 4 (g) + 1/2 O 2 (g) Rate = k [N 2 O 5 ]First order reaction For a 1st order reaction, units of k: time -1

C 2 H 6 (g)  2 CH 3 (g) rate = k [C 2 H 6 ] 2 second order reaction 2NO 2 (g)  2NO(g) + O 2 (g) Rate = k [NO 2 ] 2 second order reaction For 2nd order reactions, units of k: concentration -1 time -1

S 2 O 8 2- (aq) + 3 I - (aq)  2 SO 4 2- (aq) + I 3 - (aq) (S 2 O 8 2- persulfate) Rate of disappearance of S 2 O 8 2- = k [S 2 O 8 2- (aq)] [I - (aq)] Overall reaction order = = 2 1st order in S 2 O 8 2- (aq) and 1st order in I - (aq) If the above reaction was carried out at a high concentration S 2 O 8 2- (aq), and experimentally: Rate of disappearance of S 2 O 8 2- = k’ [I - (aq)] pseudo first-order reaction

2 NH 3 (g)  N 2 (g) + 3 H 2 (g) Rate of disappearance of NH 3 = kzero order reaction