Chemical KineticsChemical Kinetics

Sorry not all reactions are instantaneous!

What is Chemical Kinetics?What is Chemical Kinetics?Kinetics examines the rates at which chemical reactions occur. Consider the decomposition of:

2NI3(s) N2(g) and 3I2(s)

This reaction is SOOO rapid that we say it occurs instantaneously.

NI3 is very unstable with respect to its elements, it is sensitive to light and vibration.

What about a non-instantaneous What about a non-instantaneous reaction?reaction?

Na2S2O3(aq) + 2HCl S(s) + H2SO3(aq) + 2NaCl(aq)

We saw that the rate which S(s) was formed, so the rate of the reaction could be altered by adjusting the concentration of S2O3

2- or by varying the temperature.

What do we mean by rate of What do we mean by rate of reaction?reaction?

In general terms rate means how many of something can be done per unit of time.(ie km/h, m/s etc)

In chemistry though we refer to rates of reaction based on how much reactant was consumed or how much product was produced per unit of time (usually seconds).Consider our experiment . . .

Na2S2O3(aq) + 2HCl S(s) + H2SO3(aq) + 2NaCl(aq)

We agreed that the reaction was complete when 0.25mmol of sulfur was present. (Amount of product formed)

Rate of reaction = ([A]final – [A]initial) / (tfinal – tinitial)

The 5 Factors That Can Affect the The 5 Factors That Can Affect the Rate of ReactionRate of Reaction

1) The rate of reaction can (generally) be increased by increasing the temperature.

2) Increasing reactant concentrations typically increases reaction rate.

3) An increase in surface are will increase the reaction rate.

4) The nature of the reactants (ie metal react quickly with strong acids)

5) The use of a catalyst will increase the rate of reaction (if the catalyst can interact with the reactants).

What causes molecules to What causes molecules to interact?interact?Kinetic Molecular Theory (KMT) or Collision Theory are often used to

describe this process.KMT maintains that: 1) all particles of matter are in constant motion (they possess kinetic

energy)2) there are spaces between the particles, how big the space and the

speed determine the state of matter (solid, liquid or gas)3) as we increase heat, the particles move faster increasing they’re

kinetic energy

Collision TheoryCollision TheoryThis theory is literally based around the notion that in order for two molecules, atoms or ions to react they must be able to successfully “bump into” each other.These collisions are increased at higher temperatures, with greater concentrations, if the reactants are ionic rather that molecular, with greater surface area.A catalysts helps bring together the two reacting pieces thereby facilitating a collision.

Read pages 469 – 473 for general information.481 – 482

Section Review Questions 1, 2, 7, 11 (484)

So what do we measure?So what do we measure?Consider the following reaction

2H2O2(aq) 2H2O + O2(g)

We can say the rate of this reaction is equal to the disappearance of H2O2 or the appearance of O2.Rate = -[H2O2] Rate = [O2] . t tBut for every H2O2 that decomposes only 0.5 O2 is formed, thereforeRate = -0.5[H2O2] = [O2] . t tUnits = mol/L/s or M/s or M s-1

We call this the average rate of reaction.

What about the What about the InstantaneousInstantaneous Rate?Rate?2H2O2(aq) 2H2O + O2(g)

Time (s)Accumulated Mass O2 (g)

[H2O2] (M)

0 0 0.882

60 2.960 0.697

120 5.056 0.566

180 6.784 0.458

240 8.160 0.372

300 9.344 0.298

360 10.336 0.236

420 11.104 0.188

480 11.680 0.152

540 12.192 0.120

600 12.608 0.094

Rate of Disappearance of H2O2

y = 0.8874e-0.0037x

R2 = 0.9996

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800

Time (s)

Con

cent

ratio

n of

H2O

2

In order to get the rate of reaction at any given instant we need to find the negative slope of the tangent line . . . Huh? The derivative for those of you in calculus.

Initial rate = 3.21 x 10-3 M s-1

Ok well what about a different Ok well what about a different set of conditions?set of conditions?

We know from our experiments with the 5 factors that affect the rate of reaction that generally if we increase the concentration of the reactants the reaction will occur faster.The problem with our experimental determination of rates on the previous slide is that it works only for an initial concentration of H2O2 = 0.882 M.Enter the Rate Law.

The rate law for a chemical reaction relates the rate of reaction to concentration of reactants so it can be used to describe any concentration.Consider: a A + b B c C + d DRate = -(1/a)([A]/t) = -(1/b)([B]/t) (Negative b/c disappearance of reactants)

Rate = k[A]m[B]n (Rate Law)(m and n are determined experimentally)

Rate Law eh . . . ?Rate Law eh . . . ?a A + b B c C + d D

Rate = k[A]m[B]n

k is a proportionality constant called the rate constant. The numerical values of k depends on the reaction, the temperature and the catalyst (if any). The units of k depend on m and n. The values of the exponents determine the order of the reaction. If m = 1, the reaction is first order in A. If n = 2 the reaction is second order in B and the reaction is third order overall.

In general, the higher the order the more complex the mathematical expression describing the reaction. Therefore if you have a choice to treat a reaction using either reactant, choose the one with the lower order.

Back to HBack to H22OO22

The reaction is 1st order in H2O2, therefore the rate law is as follows:Rate = k[H2O2]1 = k[H2O2]

Remember the exponents are determined experimentally NOT from the balanced chemical equation.If we have determined the rates experimentally we can determine k mathematically.k = Rate/[H2O2] = 3.21 x 10-3 M s-1 / 0.882M = 3.64 x 10-3 s-1

Once we have the value of k, we can use it to determine the initial rate for any initial concentration of H2O2 (at the given temperature).

2H2O2(aq) 2H2O + O2(g)

If I tell you that a reaction is zero order with respect to A, what is the rate law . . . ?

Determining the Rate LawDetermining the Rate LawThe Method of Initial Rates for Determining The Method of Initial Rates for Determining mm

and and nn2NO(g) + Cl2(g) 2NOCl(g)

Experiment Initial [NO]Initial [Cl2]

Initial Rate, M s-1

1 0.0125 0.0255 2.27E-05

2 0.0125 0.0510 4.55E-05

3 0.025 0.0255 9.08E-05

(Initial rate)3 = k[NO]m[Cl2]n = (2 x 0.0125)m = 2m x (0.0125)m = 2m

(Initial rate)1 k[NO]m[Cl2]n (0.0125)m (0.0125)m

(Initial rate)3 = 9.08 x 10-5 M s-1 = 4

(Initial rate)1 2.27 x 10-5 M s-1

4 = 2m = 22, therefore the reaction is second order in NO

If the reaction is first order, when you double the concentration of a reactant, the rate doubles.

Applications of the Rate Law Applications of the Rate Law Determining Concentrations at a Later TimeDetermining Concentrations at a Later Time

First Order Integrated Rate Law

ln [A]t

[A]0

= -kt or ln[A]t – ln[A]0 = -ktln[A]t = (-k)t + ln[A]0 y = m x + b

Time (s)[H2O2] (M) ln[H2O2]

0 0.882 -0.12556

60 0.697 -0.36097

120 0.566 -0.56916

180 0.458 -0.78089Test for a First Order Decomposition

y = -0.0037x - 0.1195R2 = 0.9996

-2.5

-2

-1.5

-1

-0.5

00 200 400 600 800

Time (s)

ln[H

2O2]

By plotting these points we get a straight line, this confirms that the reaction is first order. Given the table you could solve for k.

Applications of the Rate Law Applications of the Rate Law Half LifeHalf Life

What is half life? the amount of time it takes for the concentration of something

to decrease to ½ its initial amount

ln ½ [A]0

[A]0

= -kt = ln (½) = -kt½ t½ = 0.693 / k

If you have the need for any diagnostic imaging you may be required to ingest some radioactive dye. This dye traces your insides so the image can be enhanced by X-ray. Biological dyes usually have a very short half-life and are nearly completely excreted within a few days.