Unit 6: KineticsIB Topics 6 & 16AP Chapters (Zumdahl): 12(all); 18.2 (nuclear decay) AP Chapters 1-5

NOTES - Unit 6: Kinetics

PART 1: Reaction Rates

Chemical Kinetics: The study of the factors that control the rate (______) of a chemical reaction

  • Kinetic measurements are often made under conditions where the reverse reaction is insignificant.
  • The kinetic and thermodynamic properties of a reaction are not fundamentally related.
  • ______ is defined in terms of the change in concentration of a given reaction component per unit time.

NOTE: whether you are measuring increase in product over time or decrease in reactant over time, by convention rate is expressed as a -______value.

Rate = change in amt., or concentration over time, so units are…

From a graph of [A] v. time, instantaneous rate can be determined by taking the slope of the tangent line at a given time.

Measuring rates of reaction: different techniques depending on reaction

  1. Change in ______
  • Convenient method if one of products is a gas
  • Ex: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)
  1. Change in ______
  • If rxn is giving off a gas, the corresponding decrease in mass can be measured by standing the rxn mixture directly on a balance.
  • Ex: CaCO3(s) + 2HCl(aq) → CaCO3(aq) + CO2(g) + H2O(l)
  1. Change in absorbance/transmission of ______: colorimetry/spectrophotometry
  • Useful if one of the reactants or products is colored (and thus will give characteristic absorption in the visible region)
  • Ex: 2HI(g) → 2H2(g) + 2I2(g)

colorless colorless colored

  1. Change in ______measured using titration
  • In some rxns it may be possible to measure the conc. of a reactant or product by titrating it against a solution of known conc..
  • However, since titrating changes the conc. of sol’n, this cannot be done continuously as rxn proceeds.
  • Instead, samples can be ______at given intervals in time & then titrated.
  • But since titration takes time, a technique known as ______must be used on sample removed (an introduced substance halts rxn)
  1. Change in concentration measured using ______
  • Useful when there is a change in ionic concentrations (total conductivity of sol’n depends on total conc. of ions and their charges).
  • Ex: BrO3-(aq) + 5Br-(aq) + 6H+(aq) → 3Br2(aq) + H2O(l)
  • Can be measured directly with conductivity meter, which involves immersing inert ______in the sol’n
  1. Non-continuous methods of detecting change during a reaction: “______”
  2. Sometimes it’s difficult to record continuous change in the rate of a reaction.
  3. In these cases, it may be more convenient to measure the time it takes for a rxn to reach a fixed observable point.
  4. Time taken to reach this pt. over varied conditions can be measured.
  5. Limitation: can only measure ______ over the time interval

Collision Theory

Kinetic energy and temperature

  • Particles in a substance move ______as a result of the kinetic energy they possess.
  • Due to random nature of movements and collisions, not all particles in a substance have the same values of kinetic energy, but instead a ______of values.
  • The average kinetic energy is directly proportional to ______(measured in Kelvin).
  • When a substance is ______, the absorbed energy leads to an increase in average kinetic energy (and therefore ______increases).

The Maxwell-Boltzman Distribution Curve

Shows # particles that have a particular KE (or probability of that value occurring) plotted against the values of KE:

AUC (area under the curve) = total # particles

AUCT1 = AUCT2(amt. or #particles is constant)

Note: Ea= activation energy (minimum energy particles must possess to react in a collision)

How reactions happen:
For a reaction to occur, three conditions must be met:

  1. Atoms, ions and/or molecules must collide.
  2. Must collide with the correct orientation.
  3. Must collide with sufficient energy to form the activated complex.

Factors affecting reaction rates:

1): Some elements/compounds are more reactive than others

2): As concentration ↑, frequency of collisions ↑, and therefore rxn rate ↑

3): For gases, ↑ pressure creates the same effect as ↑concentration

4): As surface area ↑, rxn rate ↑

5): Generally, ↑ temp = ↑ rate

Why? Higher temp = faster molecular motion = more collisions and more energy per collision = faster rxn

6): Adding a catalyst speeds up the rxn by lowering the activation energy

Catalyst: a substance that speeds up the rate of a reaction without being consumed in the reaction.

Provides an easier way to react

Lowers the activation energy

Enzyme = biological catalyst

PART 2: Reaction Order & Half Life

Expressing rxn rates in quantitative terms:

Example: Reaction data for the reaction between butyl chloride (C4H9Cl) and water is given below. Calculate the average reaction rate over this time period expressed as moles of C4H9Cl consumed per liter per second.

Table 17-1: Molar Concentration

[C4H9Cl] at t=0.00 s / [C4H9Cl] at t=4.00 s
0.220 M / 0.100 M

Rate Laws and Reaction Order

  • The equation that expresses the mathematical relationship between the ______of a chemical reaction and the ______of reactants is a rate law / rate expression.
  • Two forms of rate laws/expressions:
  • Differential rate laws: Show how rate depends on concentration. Sometimes called just the “rate law”.
  • Integrated rates laws: Shows how the concentration depends on time.
  • The choice of which rate law to use depends on the type of data that can be collected conveniently and accurately. Once you know one type, the other can be calculated .
  • IB focuses mostly on differential rate laws. AP students will come back to re-examine integrated rate laws in greater depth later in this course (when we get to IB options)
  • The reaction ______ for a reactant defines how the rate is affected by the concentration of that reactant.
  • The overall reaction order of a chemical reaction is the ______for the individual reactants in the rate law.
  • In general, the rate is proportional to the product of the concentrations of the reactants, each raised to a power. For the reaction aA + bB  products,
  • The exponents m and n are called .
  • The value of ______is the order of the rxn with respect to A.
  • The value of ______is the order of the rxn with respect to B.
  • The sum (m + n) is called the ______.
  • Only if the rxn between A and B happens in a single step (with a single activated complex… which is unlikely) does m=a and n=b.
  • Thus, the values of m and n must be determined !!!
  • Rate laws ______be predicted by looking at the overall balanced chemical equation.

Finding the rate law

  • The most common method for experimentally determining the differential rate law is the method of ______.
  • In this method several experiments are run at different initial concentrations and the instantaneous rates are determined for each at the same value of time (as near ______as possible)

Example: A + B  C

Exp # / Initial [A] / Initial [B] / Rate (M/s)
1 / 4x10-5
2 / 4x10-5
3 / 16x10-5

From this data, find the form of the rate law: Rate = k[A]m[B]n

1)Calculate m2) Calculate n3) Calculate k

(note: units of k depend on rate law)

Knowing rate laws and rate orders helps us predict how the reaction will proceed over time

Application: Radioactive decay is a first order reaction; Half life is constant over time; Allows us to date fossils, etc.

Deriving a rate expression by inspection of data

Example: Experimental data obtained from the reaction between hydrogen and nitrogen monoxide at 1073 K is listed below. Determine the rate expression and the value of the rate constant, k.

2H2(g) + 2NO(g) → 2H2O(g) + N2(g)

Experiment / Initial conc. of H2(g) (mol dm-3) / Initial conc. of NO(g) (mol dm-3) / Initial rate of formation of N2(g) (mol dm-3)
1 / 1 x 10-3 / 6 x 10-3 / 3.0 x 10-3
2 / 2 x 10-3 / 6 x 10-3 / 6.0 x 10-3
3 / 6 x 10-3 / 1 x 10-3 / 0.5 x 10-3
4 / 6 x 10-3 / 2 x 10-3 / 2.0 x 10-3

So this is obviously an initial rates problem like the one you just solved. While being so thorough is nice, you will have very limited time on your exams, so instead of showing all that work you may wish to solve by inspection and justify your answer in words…

Think about it…

•If a reaction is 1st order with respect to a reactant, then the effect of doubling that reactant conc. (while holding the other constant) is a doubling (21=2) of the rate. Tripling the reactant conc. will triple (31=3) the rate and so on.

•If a reaction is 2nd order with respect to a reactant, then the effect of doubling that reactant conc. is a quadrupling (22=4) of the rate. Tripling the reactant conc. will cause the rate to become 6 times faster (32=6) and so on.

•Note: If a reaction is zeroth order w/ respect to a reactant, then changing its concentration will have no effect on the rate of reaction. (20=1; 30=1, etc., so the rate will remain unchanged even if reactant concentration changes).

Thus,

Graphical representations of reaction kinetics

Zero-order reaction

rate = Concentration of reactant A does not affect the rate of rxn.

First-order reaction

rate = Rate is directly proportional to the concentration of reactant A.

Second-order reaction

rate = Rate is proportional to the square of the concentration of A.

Half-life, t½

  • First order reactions have a constant half-life.
  • ______half-life is a feature of only ______reaction kinetics, so it can be used to establish that a reaction is first order with respect to that reactant.
  • The shorter the value of the half-life, the ______the rxn.
  • Radioactive decay reactions follow first-order kinetics and are often described in terms of the half-life of the isotopes involved. For example, iodine-131, a radioisotope used in the diagnosis and treatment of thyroid cancer, has a constant half-life of ______.

PART 3: Reaction Mechanisms & Activation Energy

Reaction Mechanisms: most reactions that occur at a measurable rate occur as a ______, each involving a small number of particles. This sequence of steps is known as the reaction mechanism. Individual steps, called ______steps, usually cannot be observed directly, so the mechanism is in effect a theory about the sequence of events as the overall reaction proceeds from reactants to products.

  • Catalyst: speeds up a reaction ______(should not appear in overall reaction because it was present initially and then reforms as a product somewhere in the process.}
  • Intermediate / ______: product of one elementary step that is used up in a subsequent step.

Chemical reactions take place as a result of collisions between molecules. Each type of collision in a given reaction is called a single event or an elementary step.

Molecularity: the ______participating as reactants in a given step of a reaction.

  • Unimolecular: A ______reactant particle is involved in the elementary step
  • Bimolecular:______are involved as reactants
  • Termolecular: Three particles are involved. Termolecular steps are far less probable than unimolecular or bimolecular processes and are rarely encountered.
  • The chances that four or more molecules will collide simultaneously with any regularity is extremely remote, consequently, such collisions are never proposed as a part of a reaction mechanism.

Example:The reaction between NO2and CO has the overall reaction NO2 + CO  NO + CO2

A study of the kinetics of this reaction revealed the rate law for the reaction is rate = k[NO2]2

This rate expression requires that the slow step of the reaction involves a collision between two NO2 molecules. How can this be a step in the seemingly simple reaction above?

Further study of this reaction established that two NO2 molecules can react as follows:

NO3 is a highly reactive material which is capable of transferring an oxygen atom.

The rate law only provides information about the slowest reaction in the mechanism.

The rate law is based off of the first elementary step, so it must be the slow/rate-determining one.

Thus, the reaction mechanism can be expressed as follows:

Which molecule is an intermediate in the reaction mechanism above?

Determining the rate expression for an overall reaction from the reaction mechanism

  • The sum of the elementary steps must give the overall balanced equation for the reaction.
  • The rate-determining step, which is the slowest step in the sequence of steps leading to product formation, should predict the same rate law & order as is determined experimentally.
  • For elementary steps (since they are true single-step reactions), the exponents in the rate laws are the same as the coefficients of the reactants in the chemical equation.

Eq’n for rate-determining step / Molecularity / Rate law
  • The rate law for the rate-determining step, predictable from its equation, leads to the rate expression for the overall reaction. If the rate-determining step is the first step (or only step) in the mechanism, then its rate law is the rate expression for the overall reaction.

Example: The overall reaction 2NO2Cl(g)  2NO2(g) + Cl2(g) is believed to have the following mechanism

The rate expression for the overall reaction is that of the rate-determining step. rate=

This is a first-order reaction.

  • What if the rate-determining step is not the first step in the mechanism? It’s a little more complicated because the reactant concentrations depend on an earlier step, so this must be taken into account.

Example: For the reaction NO(g) + O2(g) 2NO2(g), the following reaction mechanism has been proposed

So the rate depends on step 2, for which the rate law is: rate=

But N2O2 is a product of step 1, so the concentration of this intermediate depends on [NO]2.

Therefore, we substitute this into the equation above and the rate expression for the overall reaction is

rate =(This is a third-order reaction)

Activation Energy

The rate constant, k, is temperature dependent

  • Rxn rate increases as temperature ______
  • Rule of thumb: a ______increase in temperature leads to a ______of the rate.
  • Note: this is only a rule of thumb, not a law of nature. Thus, it is not true for all reactions.
  • When activation energy is large, temperature has a greater effect on the number of particles with sufficient energy to react (and thus rate of reaction). This can be shown by studying Maxwell-Boltzman distributions.

Arrhenius Equation: mathematical relationship between temperature, the rate constant and the activation energy.

  • Svante Arrhenius showed that the fraction of molecules with energy greater than activation energy, Ea, at temperature T is proportional to the expression e-Ea/RT
  • k = rate constant (units vary depending on rate law)
  • A = Arrhenius constant (a.k.a. frequency factor, pre-exponential factor, and steric factor)
  • Takes into account the frequency with shich successful collisions occur based on collision geometry and energy requirements
  • Constant for a rxn & has units the same as k (and so varies with the order of the reaction)
  • Ea = activation energy (in Joules mol-1)
  • R = 8.31 J mol-1 K-1 (ideal gas constant)
  • T = absolute temperature (in Kelvin)
  • Taking the natural logarithm (ln base e) of both sides of the equation above:
  • Notice that this is a form of y = mx + b (straight line)

Arrhenius plot:

1