# Kinetics.

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Kinetics

Reaction rates Concerned with why some reactions are fast and others are slow. A reaction rate is quantitatively written as either: Change in concentration of a reactant/time Change in concentration of a product/time Units may vary. Some examples are: Molarity/hour, nmol/sec.

Reaction rate graph showing two curves: reactant and a product
Reaction: NO2 + CO  NO + CO2 concentration reactants equilibrium equilibrium products

Factors which influence a reaction rate.
Internal factors More bond breaking and bond making, slower the reaction. Each bond broken or made adds a step to the overall reaction. The physical state ( s,l,aq,or g) in the reactants: solids can slow down a reaction. Gases are faster. (Slow: s,l, aq,g: fast) Example: CH4(g) + 2O2(g)  2H2O(g) + CO2(g) C8H18(l) + 25/2 O2(g)  8CO2(g) + 9H2O(g)

Factors which influence a reaction rate continued
External Factors Temperature: Increasing a temp. will increase a rate because: K.E. increases so the velocity of the molecules increases. Therefore, the molecules collide with more force and more often, so there are more successful collisions. A change in temp. has more impact on the rate of a reaction, more than any other factor.

External factors continued
Concentration- increasing the concentration of a reactant will increase the rate of a reaction because there will be more collisions/time. Applies to gases and aq solutions. Pressure-increasing the pressure will increase the rate of a reaction if there are any gaseous reactants only. The increased pressure increases the collisions/time. Applies to gases. Surface area- increasing the surface area will increase the rate of a reaction only if there are any liquid or solid reactants. The increase in surface area increases the collisions/time. Applies to solids and liquids.

The effects of concentration and a solid

Reaction rate graph showing the effects of surface area

A quantitative look at a reaction rate.
A rate is the Δ concentration/time The change in concentration can be for any reactant or product. Just pick the easiest species to measure. Example: determining the rate of H2 gas produced by Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g) Measure the volume of the H2 at regular time intervals .(use a gas law to turn the vol. into a conc. ) Plot the volumes or concentrations on a graph with time as x axis, and volume and concentration as y.

Take the slope of the line early in the reaction: the Δy/ Δx
Take the slope of the line early in the reaction: the Δy/ Δx. This equals the change in volume or concentration over time which is a rate. This rate changes at any point on the graph since the slope is not constant. The rate obtained through this method is an instantaneous rate-accurate at that point in time. Since rates change during a reaction the rate law of the reaction is more useful.

Making a rate graph Ml of H2 Volume of H2 collected time

Reaction mechanisms A reaction mechanism is the series of steps that occur in order for a reaction to reach completion. The mechanism must be determined experimentally. Restrictions to a reaction mechanism are: Each step in the mechanism usually involves a collision between 2 molecules or the splitting of one molecule The individual steps must add up to the overall final reaction. The mechanism must support the rate law.

The individual steps must add up to equal the overall reaction.
The reaction: AB + CD AC + BD AB  A + B B + CD  C +BD A + C  AC

Each step usually involves the collision between 2 molecules only
example reaction is: HBr + CH3CH2OH  CH3CH2Br + H2O

Reaction mechanisms: the slow step (rate determining step)
The slow step or rate determining step is the step in the reaction mechanism which is the slowest. It is the slowest for these possible reasons: It has the highest energy requirement for a successful collision. (The bond being broken has a high bond enthalpy). This energy requirement is called the Activation energy. The molecule formed during this step is called the activated complex. There may be a special angle of orientation for a successful collision.

There may be a special angle of orientation.

Catalysts A catalyst is a substance which can speed up an existing reaction. A catalyst works by: Speeding up the slow step in the reaction mechanism through: Lowering the activation energy required for a successful collision. Widening the angle of orientation required for a successful collision.

Catalysts continued. Catalysts do not:
Cause a reaction. They only speed up existing ones. Change either the reactants or products, or the enthalpy for a reaction. Get used up. They are recycled and used over again.

Catalysts continued Some examples of catalysts are: Enzymes
Vitamins (actually they are coenzymes) Catalytic converters in cars Transition metals such as Platinum, Osmium, Manganese.

Diagrams to know: Maxwell Boltzman diagram: temperature effects and activation energy (Ea) T1 Moles Of Mole- cules 1 T2 is a higher temp. Ea energy

Diagrams to know continued
Potential energy diagrams: shows the energy changes that occur during the progress of a reaction. RDS/activated complex Potential Energy kJ/mole This reaction is Endothermic. The Products have more Energy than the Reactants. Enthalpy is Positive. Ea H (reactants) (products) Progress of the reaction

Potential energy diagram of an exothermic reaction with a catalyst

Potential energy diagrams continued
On PE diagrams, you must know how to: determine if the reaction is endothermic or exothermic. determine the enthalpy for the reaction determine the Ea determine the location of the R.D.S. and the activated complex. Determine the line for a catalyst. Estimate whether a reaction will be slow or fast.

Rate Laws IB optional material
General information: A rate law is constant for a reaction unless the temperature is changed. A rate law uses only reactants. A rate law is determined using the initial concentrations of reactants. A rate law helps explain a reaction mechanism. If we know the rate law we have a better understanding on how to control the reaction.

Rate laws continued. The general form of a rate law is:
Given the reaction: 2A + B  A2B The rate law expression will look like: rate = k[A]n[B]m k is a rate constant n and m are rate orders Both of the above are determined experimentally. Coefficients are not used in the expression

Rate Laws and graphs 2nd order Intial rate 1st order Zero order
Initial concentration

Summary of rate orders Zero order [x]0 altering the concentration of the reactant has no effect on the rate. First order [x]1 doubling the concentration of the reactant will double the rate, cutting the concentration in half will cut the rate in half etc. Second order [x]2 doubling the concentration will quadruple the rate. Cutting in1/2 the concentration will cut the rate to ¼ etc. Overall rate order: add the rate orders together.

Half-life of first-order reactants
A half-life is the time it takes for the concentration of a reactant (1st order) to decrease to half of its original concentration. In the 2nd half-life interval, the concentration will be cut in half again to 1/4th its original concentration. So the change in concentration is continually being cut in half with each successive half-life.

Determining the half-life.
First method: make a rate graph using concentration over time. From the graph determine where the concentration is cut in half.This time interval is the half-life. This half-life is constant. t1/2= 2t1/2=3t1/2=4t1/2 For a zero order: each half-life is half the time of the preceding half-life. ex. T1/2=1min. 2t1/2 = 0.5min., 3t1/2= 0.25min. For 2nd order: each half-life is double the preceding half-life. ex. T1/2= 1min. 2t1/2= 2min., 3t1/2= 4min., Second method: use t1/2 = ln2 / k ln 2 = 0.693, k= the rate constant for the reaction.

Graph showing the half-life of a 1st order reactant.
Conc. Of a reactant Time

Reaction mechanisms: Molecularity optional IB material
There are two basic types of steps or processes in a mechanism: 1. unimolecular: A reactant breaks up into two products. If the species is in the r.d.s. then the reacting species is first order. 2.bimolecular: two species collide to form the product(s). It they are in the slow step then each reacting species is first order, and 2nd order over all. There is initially a product made which quickly breaks down into either reactants or products. This temporary product is called the activated complex and has the maximum energy requirement, ie, activation energy, for a successful collision. Whether a reaction step is unimolecular or bimolecular is called the step’s molecularity.

Molecularity continued
These molecularity concepts along with the rate law are used to determine the rate determining step for a reaction. Any reactant in the rate determining step or in the step preceding the r.d.s. determines the overall rate of the reaction. So it is in the rate law Knowing the rate law expression for the reaction can help to predict the process or molecularity in the r.d.s.

Determining a rate expression based upon the mechanism IB text pg 234, 235 The chart refers to the reaction: 2A + B C + D Possible mechanisms Rate expression A+B  X+C Slow RDS A+X  D Fast A+B  X Fast A+X  C+D Slow RDS A+A  A2 Fast A2+B  C+D Slow RDS A+A  A2 Slow RDS A2+B  C+D Fast BX Slow RDS X+A  Y+C Fast Y+A  D Fast Rate k [A] [B] Rate k [A]2[B] Rate k [A]2[B] Rate k [A]2 Rate k [B]