CHEM1612 - PharmacyWeek 11: Kinetics - Rate Law

Dr. Siegbert SchmidSchool of Chemistry, Rm 223Phone: 9351 4196E-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

Lecture 30- 3

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.

Chemical Kinetics

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

Lecture 30- 4

Factors affecting reaction rate Rate is proportional to collision rate which is proportional to

Figure from S

ilberberg, “Chem

istry”,

McG

raw H

ill, 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

Lecture 30- 5

Rate of a Reaction

The rate of a reaction is the change in concentration of one of the reactants that occurs during a given period of time.

-Δ[A]

ΔtRate = =

Figure from S

ilberberg, “Chem

istry”,

McG

raw H

ill, 2006.

Δ[B]

Δt

Lecture 30- 6

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.

Rate of a Reaction

Lecture 30- 7

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.

Rate of a Reaction

- d [A]

d tRate50s =

Lecture 30- 8

Expressing Reaction Rates For a generic chemical reaction the reaction

rate is defined as:

A + C → 2 B

(1)

(2)

ΔtΔ[A]rate

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.

ΔtΔ[B]

21

ΔtΔ[C]

Lecture 30- 9

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

tO

tON

][2][ 252

tON

tOrate

][21][ 522

tO

tNO

][4][ 22

tNO

tOrate

][41][ 22

Lecture 30- 10

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.

tD

dtC

ctB

btA

arate

][1][1][1][1

Lecture 30- 11

Expressing Reaction RatesExpress 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

dtO]d[H

61

dt

d[NO] 41

dt

]d[O 51-

dt]d[NH

41-

2

2

3

Lecture 30- 12

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

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.

1622

Ms105.2600s

M100.31600)s(1200

M101.24)(0.93

Solution:

Rate of decomposition of N2O5 =

Example 1

Lecture 30- 13

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?

tO

tOrate

][31][

21 23

5523 104)106(32][

32][

t

Ot

O

Lecture 30- 14

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.

Lecture 30- 15

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, …

Lecture 30- 16

Rate Law

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]

dt O)Cl](H)d[Pt(NH

dt] Cl)d[Pt(NH - Rate 223223

Hydrolysis of cisplatin

[Pt(NH3)2Cl2](aq) +H2O(l) [Pt(NH3)2(H2O)Cl](aq) + Cl-(aq)

Lecture 30- 17

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)

Lecture 30- 18

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

Lecture 30- 19

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]

Lecture 30- 20

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

Lecture 30- 21

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.

Reaction Orders

Lecture 30- 22

Reaction OrdersExpress 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).

Δt]Δ[N2

ΔtΔ[NO]

Δt]Δ[Nrate

2

2

ΔtO]Δ[H

21

Δt]Δ[H

21

ΔtΔ[NO]

21

Δt]Δ[Nrate 222