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

N2(g) + 3H2(g) 2NH3(g)

At 298 K

Go = -33.0 kJ

Ho = -92 kJ; exothermic reaction

K = 6.0 x 105 ; thermodynamically favored at 298 K,

Rate is slow at 298K

Commercial production of NH3 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 + D K1

A + B E + F K2

If K1 > K2 - 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

Zn2+(aq) + S2-(aq) ZnS(s) K = 1/Ksp = 2.2 x 1023

Fe2+(aq) + S2-(aq) FeS(s) K = 1/Ksp = 2.7 x 1018

On addition of S2- to an aqueous solution containing both Zn2+ and Fe2+, ZnS precipitates first - reaction is thermodynamically controlled.

(1) 2NO(g) + O2(g) 2NO2(g)

(2) 2CO(g) + O2(g) 2CO2(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 NO2 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) Zn2+(aq) + H2(g)

average reaction rate =change in concentration

change in time

Units of rate: concentration / time

NO2(g) + CO(g) NO(g) + CO2 (g)

average reaction rate =[NO]final - [NO]initial

tfinal - tinitial

NO2(g) + CO(g) NO(g) + CO2 (g)

Time (s) [NO] mol L-1

0 0

50 0.0160

100 0.0240

150 0.0288

200 0.0320

Average rate 1st 50 seconds = 3.2 x 10-4 mol L-1

Average rate 2nd 50 seconds = 1.6 x 10-4 mol L-1

Average rate 3rd 50 seconds = 9.6 x 10-5 mol L-1

Instantaneous Rate - rate at a particular moment in time

NO2(g) + CO(g) NO(g) + CO2 (g)

[NO]t

[CO]t

[NO2]t

[CO2]trate = === - -

For a general reaction:

aA + bB xC + yD

d[C]dt

d[B]dtrate = === -1

x1b

d[A]dt

- 1a

d[D]dt

1y

For an infinitesimally small changes, the instantaneous rate

d[NO]d t

d[CO]d t

d[NO2]d t

d[CO2]d trate = === - -

initial rate (t = 0)

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

Factors affecting rates of reactions

a) Nature of reactants

2NO(g) + O2(g) 2NO2(g) fast

2CO(g) + O2(g) 2CO2(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 N2O5 (g) 4 NO2 (g) + O2 (g)

Perform a series of experiments with different initial concentrations of N2O5 (g).

For each, monitor the concentration of N2O5 (g) versus time

Determine the initial rate of reaction at t = 0

Rate Laws and Rate Constant

2 N2O5 (g) 4 NO2 (g) + O2 (g)

For this reaction, experiments indicate:

rate initial concentration of N2O5 (g)

rate = k x initial concentration of N2O5 (g)

Rate = - d[N2O5] / dt = k [N2O5] Rate law

k = 5.2 x 10-3 s-1

k is the specific rate constant

Units of k depends on the rate law

Rate laws are determined experimentally

= k [NO2]2 Rate Law

2 NO2(g) 2 NO(g) + O2 (g)

d[NO2]dt

rate =

k = 0.54 (mol NO2)-1 s-1

-

2 NO2(g) 2 NO(g) + O2 (g)

Rate = k [NO2]2

For a general reaction:

aA + bB cC + dD

d[C]dt

d[B]dtrate = === -1

c1b

d[A]dt

- 1a

d[D]dt

1d

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 mth order in A and nth order in B

Overall reaction order = m + n

The reaction order is determined by the experimentally determined rate law

N2O5(g) N2O4(g) + 1/2 O2(g)

Rate = k [N2O5] First order reaction

For a 1st order reaction, units of k: time-1

C2H6(g) 2 CH3(g)

rate = k [C2H6]2 second order reaction

2NO2(g) 2NO(g) + O2 (g)

Rate = k [NO2]2 second order reaction

For 2nd order reactions, units of k: concentration-1 time-1

S2O82-(aq) + 3 I-(aq) 2 SO4

2-(aq) + I3-(aq) (S2O8

2- persulfate)

Rate of disappearance of S2O82- = k [S2O8

2-(aq)] [I-(aq)]

Overall reaction order = 1 + 1 = 2

1st order in S2O82-(aq) and 1st order in I-(aq)

If the above reaction was carried out at a high concentration S2O8

2-(aq), and experimentally:

Rate of disappearance of S2O82- = k’ [I-(aq)]

pseudo first-order reaction

2 NH3(g) N2 (g) + 3 H2(g)

Rate of disappearance of NH3 = k zero order reaction