Chapter 14: Rates of Reaction

Chemistry 1062: Principles of Chemistry II

Andy Aspaas, Instructor

Chemical kinetics

• Study of the rate or speed of reactions

• Rate may be affected by any of the following:

– Concentration of reactants– Presence or concentration of a catalyst– Temperature at which reaction occurs– Surface area of solid reactant or catalyst

Reaction rate

• Reaction rate can be defined in terms of appearance of product or disappearance of reactant

• Rates are given as a change in molar concentration in a certain time interval, unit mol/(L·s)

• For the reaction A + 2B C, the rate of the reaction may be expressed 3 ways

Rate [C]

t

[A]

t 1

2

[B]

t

Dependence of rate on concentration

• Reaction rate usually depends on the concentrations of reactants and catalysts

• Rate law shows this dependence

• For the reaction a A + b B d D + e E

(reactants A and B form D and E with catalyst C)

Rate = k [A]m[B]n[C]p

where m, n, and p are exponents, usually integers

• m, n, and p must be detemined experimentally!

C

Reaction order

• The reaction order can be given with respect to a certain reactant, or overall– For a certain reactant, it’s the exponent in the

rate law– Overall, it’s the sum of the exponents

• Ex. 2NO(g) + 2H2(g) N2(g) + 2H2O(g)

Rate = k [NO]2[H2]• The reaction is second order in NO, first order in H2,

and third order overall.

Determining the rate law

• The method of initial rates is often used to determine the rate law and order of a reaction– Several experiments are run, varying the

concentration of individual reactants and catalysts

– The exponents in the rate law can be determined algebraically

– The rate constant is determined by substituting the concentrations of any experiment into the rate law

Method of initial rates

I–(aq) + ClO–(aq) IO–(aq) + Cl–(aq)

What is the rate law, and what is the rate constant, k?

Concentrations are in mol/L, rates are in mol/(L·s)

[I–] [ClO–] OH– Rate

Exp. 1 0.010 0.020 0.010 12.2 x 10-2

Exp. 2 0.020 0.010 0.010 12.2 x 10-2

Exp. 3 0.010 0.010 0.010 6.1 x 10-2

Exp. 4 0.010 0.010 0.020 3.0 x 10-2

OH–

Change of concentration writh time

• First order rate law for aA products:

• Second-order rate law for aA products:

Rate A

tk[A]

ln[A]t[A]0

kt (first - order integrated rate law)

or [A]t [A]0e-kt

Rate [A]

tk[A]2

1[A]t

kt 1[A]0

(second - order integrated rate law)

Change of concentration with time

• Zero-order rate law for aA products:

• Half life (t1/2): time at which [A]t = -(1/2)[A]0

(Reactant concentration is at 1/2 its initial value

Radioactive decay, etc.

Rate k[A]0 k[A]t kt [A]0 (zero - order integrated rate law)

order) (zero 2

][

order) (second ][

1

order)(first ln

02/1

02/1

21

2/1

k

At

Akt

kt

Graphing kinetic data

• While the method of initial rates is a quick way of determining reaction order, graphing the data is more effective

• Concentration of a reactant is measured in several time intervals throughout the reaction

• Integrated rate laws can be rearranged if necessary to y = mx + b format for graphing, where m is the slope and b is the y-intercept

ln[A]t[A]0

kt (first order)

ln[A]t ln[A]0 ktln[A]t kt ln[A]0

slope kt, y - intercept ln[A]0

Determination of reactant order by graphing

• Graph 3 times for the 3 rate laws, and determine which has a straight line

• Zero order: [A] vs. t is linear, slope = -k

• 1st order: ln[A] vs. t is linear, slope = -k

• 2nd order: 1/[A] vs. t is linear, slope = k

Rate dependence on temperature

• Collision theory: rate constant of a reaction is a factor of molecular collision frequency, activation energy, and the fraction of collisions which occur with a constructive orientation

• Activation energy: minimum molecular energy required in order for a collision to produce a reaction

• Transition-state theory: reactions must pass through an activated complex, an unstable grouping of atoms that has an equal chance of breaking into reactants or products

Potential energy diagrams

• Plot of potential energy (kJ/mol) vs. the course of a reaction (reactants becoming products by passing through an activated complex)

• NO + Cl2 NOCl2‡ NOCl + Cl

+

=

=+

∆ =

Arrhenius equation

• Rate constant of a chemical reaction is related to the activation energy and temperature

• A is a constant, based on collision frequency, and proper orientation, etc.

k Ae Ea /RT

lnk lnA EaRT

lnk2

k1

EaR

1

T1

1

T2

Elementary reactions

• A chemical reaction may consist of several steps in order to get from reactants to products

• Elementary reaction: a single molecular event, ex. the collision of molecules, or the separation of a molecule

• Reaction intermediate: species produced during a reaction that does not appear in the net equation (cancels out when elementary reactions are added)

• The order of a rate law for an elementary reaction can be predicted, but without knowledge of the mechanism, the rate law for an overall reaction cannot be predicted

Catalysis

• A catalyst increases the rate of a reaction but is not consumed

• Must be re-generated stiochiometrically in an elementary reaction

• Catalysts do not appear as a reactant or product in the overall reaction (shown above arrow)

• Work by reducing activation energy