 # Kinetics Chapter 6. 6.1 Rates of Reactions Define the term rate of reaction. Define the term rate of reaction. Describe suitable experimental procedures.

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Kinetics Chapter 6

6.1 Rates of Reactions Define the term rate of reaction. Define the term rate of reaction. Describe suitable experimental procedures for measuring rates of reactions. Describe suitable experimental procedures for measuring rates of reactions. Analyse data from rate experiments. Analyse data from rate experiments.

Rate of reaction is defined as the rate change in concentration Rate – per unit of time Rate – per unit of time 1/time 1/time Per second Per second 1 / s 1 / s s -1 s -1 Rate of reaction – how quickly a rxn happens Rate of reaction – how quickly a rxn happens How fast reactants are converted to products How fast reactants are converted to products Visa versa Visa versa

Concentration of product against time Concentration of product against time Concentration of reactant against time Concentration of reactant against time

Negative sign shows the concentration is decreasing, but rate is expressed as a positive value

Rate units – mol dm -3 s -1 Rate units – mol dm -3 s -1 Change in concentration per time Change in concentration per time Graphs Graphs Gradient of line is a measure of the change in concentration per time Gradient of line is a measure of the change in concentration per time On a curve gradient is not constant – draw a tangent line to the curve & calculate gradient of that line On a curve gradient is not constant – draw a tangent line to the curve & calculate gradient of that line

Rate of rxn is not constant Rate of rxn is not constant Faster at beginning – steep line Faster at beginning – steep line Slows as it continues – less steep line Slows as it continues – less steep line Rxns are compared at initial rates at time zero Rxns are compared at initial rates at time zero

Measuring rates of reaction uses different techniques depending on the reaction 1. Change in volume of gas produced 2. Change in mass 3. Change in transmission of light: colorimetry / spectrophotometry 4. Change in concentration measured using titration 5. Change in concentration measured using conductivity 6. Non-continuous methods of detecting change during a reaction: ‘clock reactions’

1. Change in volume of gas produced Graphing change in volume VS change in time Graphing change in volume VS change in time Gas syringe – tool to collect gas Gas syringe – tool to collect gas Inverted burette Inverted burette Most gases are less soluble in warm water – using warm water lowers error Most gases are less soluble in warm water – using warm water lowers error

2. Change in mass If the rxn gives off a gas If the rxn gives off a gas Works well for light gases Works well for light gases Graph – decreasing mass VS increasing time Graph – decreasing mass VS increasing time

3. Change in transmission of light: colorimetry/spectrophotometry Used if reactant or product is coloured Used if reactant or product is coloured Different absorption in the visible region of spectrum Different absorption in the visible region of spectrum Indicator can be used to make coloured compound Indicator can be used to make coloured compound

Colorimeter or spectrophotometer passes light of a selected wavelength through the solution measuring the intensity of the transmitted light Colorimeter or spectrophotometer passes light of a selected wavelength through the solution measuring the intensity of the transmitted light 2HI(g)  H 2 (g) + I 2 (g) colourless colourless coloured

Allows for continuous readings Allows for continuous readings Graph of absorbance VS time Graph of absorbance VS time Convert absorbance to concentration by using a standard curve based on readings of known concentrations Convert absorbance to concentration by using a standard curve based on readings of known concentrations

4. Change in concentration measured using titration Titrating against a ‘standard’ Titrating against a ‘standard’ Cannot be done continuously Cannot be done continuously Samples must be taken and tested at regular time intervals Samples must be taken and tested at regular time intervals Quenching – a substance is introduced stopping the rxn when the sample is taken Quenching – a substance is introduced stopping the rxn when the sample is taken

5. Change in concentration measured using conductivity Total electrical conductivity of a solution depends on the total concentration of its ions Total electrical conductivity of a solution depends on the total concentration of its ions change in conductivity indicates a change in the concentration of ions change in conductivity indicates a change in the concentration of ions Inert electrodes are immersed in solution – calibrated using known solutions Inert electrodes are immersed in solution – calibrated using known solutions

BrO 3 - (aq) + 5Br - (aq) + 6H + (aq)  3Br 2 (aq) + 3H 2 O(l) Sharp decrease in electrical conductivity due to decrease in ions Sharp decrease in electrical conductivity due to decrease in ions 12 mols of ions on the reactants side & 0 moles on products side 12 mols of ions on the reactants side & 0 moles on products side

6. Non-continuous methods of detecting change during a reaction: ‘clock reactions’ measure of the time taken to reach a certain chosen fixed point measure of the time taken to reach a certain chosen fixed point Time taken for a certain mass of Mg ribbon to react completely in dilute acid Time taken for a certain mass of Mg ribbon to react completely in dilute acid Color change Color change Limitation – only gives average rate over a time interval Limitation – only gives average rate over a time interval

6.2 Collision Theory Describe the kinetic theory in terms of the movement of particles whose average energy is proportional to temperature in kelvins. Describe the kinetic theory in terms of the movement of particles whose average energy is proportional to temperature in kelvins. Define the term activation energy, Ea. Define the term activation energy, Ea. Describe the collision theory. Describe the collision theory. Predict and explain, using the collision theory, the qualitative effects of particle size, temperature, concentration, pressure on the rate of reaction. Predict and explain, using the collision theory, the qualitative effects of particle size, temperature, concentration, pressure on the rate of reaction. Describe the effect of a catalyst on a chemical reaction. Describe the effect of a catalyst on a chemical reaction. Sketch and explain Maxwell-Boltzmann curves for reactions with and without catalysts. Sketch and explain Maxwell-Boltzmann curves for reactions with and without catalysts.

Kinetic energy & temperature Kinetic-molecular theory of matter Kinetic-molecular theory of matter All particles move randomly due to possessing kinetic energy All particles move randomly due to possessing kinetic energy Not all particles have the same values of kinetic energy Not all particles have the same values of kinetic energy

Absolute temperature – measure of the average kinetic energy of the particles – Kelvin scale Absolute temperature – measure of the average kinetic energy of the particles – Kelvin scale Increase in temperature = increase in average kinetic energy of the particles Increase in temperature = increase in average kinetic energy of the particles Differences in the 3 phases of matter is average kinetic energy of the particles Differences in the 3 phases of matter is average kinetic energy of the particles

The Maxwell- Boltzman distribution curve Shows the range of values of kinetic energy of particles in a gas Shows the range of values of kinetic energy of particles in a gas Shows the numbers of particles that have a particular value of kinetic energy Shows the numbers of particles that have a particular value of kinetic energy Area under the curve represents the total number of sample particles Area under the curve represents the total number of sample particles

How reactions happen Reactant particles collide with each other due to their kinetic energy Reactant particles collide with each other due to their kinetic energy Energy from collisions may result in bonds between reactants Energy from collisions may result in bonds between reactants being broken being broken being formed being formed Rate of rxn depends on the number of “successful” collisions – not all collisions will be successful Rate of rxn depends on the number of “successful” collisions – not all collisions will be successful

Two factors influence successful collisions Two factors influence successful collisions 1. Energy of the collision 1. Energy of the collision 2. Geometry of the collision 2. Geometry of the collision

1. Energy of collision 1. Energy of collision Activation energy (E a )- the particles must have a minimum value of kinetic energy – a threshold of energy Activation energy (E a )- the particles must have a minimum value of kinetic energy – a threshold of energy Necessary to overcome repulsion between molecules / to break bonds in reactants Necessary to overcome repulsion between molecules / to break bonds in reactants An energy barrier for the reaction An energy barrier for the reaction Only particles with the minimum kinetic energy will react Only particles with the minimum kinetic energy will react

Transition state – reactants after activation energy is supplied – products can form Transition state – reactants after activation energy is supplied – products can form Rate of rxn depends on the proportion of particles with kinetic energy values higher than E a Rate of rxn depends on the proportion of particles with kinetic energy values higher than E a

2. Geometry of collision 2. Geometry of collision Collisions occur with different orientations Collisions occur with different orientations For a rxn to occur both particles must have the correct orientation during the collision For a rxn to occur both particles must have the correct orientation during the collision

Factors affecting rate of reaction 1. Temperature 2. Concentration 3. Particle size 4. Pressure 5. Catalyst

1. Temperature Increase in temperature = increase in average kinetic energy of the particles = increase in collision frequency = increase in collisions with enough E a and correct orientation = increase in rate of rxn Increase in temperature = increase in average kinetic energy of the particles = increase in collision frequency = increase in collisions with enough E a and correct orientation = increase in rate of rxn

2. Concentration Increase in concentration = increase in frequency of collisions = increase in rate of rxn Increase in concentration = increase in frequency of collisions = increase in rate of rxn As rxn progresses reactants are used up (conc. Decreases) and rxn rate decreaces As rxn progresses reactants are used up (conc. Decreases) and rxn rate decreaces

3. Particle size Decreasing particle size = increases particle surface area = increase in rxn rate Decreasing particle size = increases particle surface area = increase in rxn rate Important in heterogenous rxns – reactants in different phases Important in heterogenous rxns – reactants in different phases 4. Pressure With gases, increase in pressure = increase in rxn rate With gases, increase in pressure = increase in rxn rate Same as increasing concentration Same as increasing concentration

5. Catalyst Increases rxn rate without undergoing a chemical change Increases rxn rate without undergoing a chemical change Lowers E a – provides a different route for the rxn Lowers E a – provides a different route for the rxn Increases the number of particles with enough E a to react without raising the temperature Increases the number of particles with enough E a to react without raising the temperature Equal reduction in E a for forward and reverse rxns Equal reduction in E a for forward and reverse rxns

Important to many industrial processes Important to many industrial processes Enzyme – every biological rxn is controlled by a catalyst Enzyme – every biological rxn is controlled by a catalyst

16.1 Rate Expression ≈ Distinguish between the terms rate constant, overall order of reaction and order of reaction with respect to a particular ≈ Deduce the rate expression for a reaction from experimental data. ≈ Solve problems involving the rate expression. ≈ Sketch, identify and analyse graphical representations for zero-, first- and second-order reactions

The rate law for a reaction is derived from experimental data See page 216 See page 216 Chart for data collected in lab Chart for data collected in lab Graph made from data on chart. Graph made from data on chart.

“Rate Law” = a math formula “Rate Law” = a math formula AKA – “rate expression” AKA – “rate expression” Reaction rate = k[conc.] Reaction rate = k[conc.] k = rate constant – fixed for a particular rxn at a specific temp. k = rate constant – fixed for a particular rxn at a specific temp.

Rate is dependent on one of the reactants’ conc. Rate is dependent on one of the reactants’ conc. A + B  products A + B  products Rate = k[A] m [B] n Rate = k[A] m [B] n Proportional to the concentrations of the reactants Proportional to the concentrations of the reactants

”Order with respect to…” ”Order with respect to…” A + B  products A + B  products Rate = k[A] 2 [B] 1 Rate = k[A] 2 [B] 1 Rxn is 2 nd order with respect to hydrogen Rxn is 2 nd order with respect to hydrogen Rxn is 1 st order with respect to oxygen Rxn is 1 st order with respect to oxygen Overall order of the rxn is 3 rd order  2 + 1 = 3 Overall order of the rxn is 3 rd order  2 + 1 = 3

2H 2 (g) + 2NO(g)  2H 2 O(g) + N 2 (g) is show to be 2 nd order with respect to NO and 1 st order with respect to H 2. Write the rate expression for the above rxn. Overall order?

Units of k vary depending on the overall order of the reaction Rxn Order with respect to reactant 1 Order with respect to reactant 2 Overall order of rxn H 2 (g)+I 2 (g)  2HI(g) 2H 2 O 2 (aq)  2H 2 O(l)+O 2 (g) S 2 O 8 -2 (aq)+2I - (aq)  2SO 4 -2 (aq)+I 2 (aq ) 2N 2 O 5 (g)  4NO 2 (g)+O 2 (g) The orders of reaction do NOT necessarily correspond to their coefficients.

Units of k vary depending on the overall order of the rxn Zero Order First Order Second Order Third Order Rate = k Rate = k[A] Rate = k[A] 2 Rate = k[A] 3 mol dm -3 s -1 s -1 mol -1 dm 3 s -1 mol -2 dm 6 s -1 Points are given for the correct units of the rate constant. You must memorize the units… they are different for each over-all order.

A rxn has the rate expression: rate = k[A] 2 [B] Calculate the value of k, including units, for the reaction when the conc. of A & B are 2.50 X 10 -2 mol dm -3, and the reaction rate is 7.75 x 10 -5 mol dm -3 min -1.

Graphical representations of rxn kinetics Zero-order rxn Zero-order rxn Rate = k[A] 0 or rate = k Rate = k[A] 0 or rate = k Conc. Vs. time graph Conc. Vs. time graph Gradient = k Gradient = k Rate Vs. conc. Graph Rate Vs. conc. Graph Horizontal line Horizontal line You will have to identify reaction orders by reading a graph…

1 st order rxn 1 st order rxn Rate = k[A] Rate = k[A] Conc. Vs. Time graph Conc. Vs. Time graph Curve showing rate decreasing with conc. Curve showing rate decreasing with conc. Rate Vs. Conc. Graph Rate Vs. Conc. Graph Straight line passing through the orgin Straight line passing through the orgin Gradient = k Gradient = k

2 nd order rxn 2 nd order rxn Rate = k[A] 2 Rate = k[A] 2 Conc. VS. Time graph Conc. VS. Time graph Curve; steeper at start Curve; steeper at start Rate Vs. Conc. Graph Rate Vs. Conc. Graph Parabola Parabola Gradient Gradient proportional to the conc. proportional to the conc. Initially zero Initially zero

Only 1 st order rxns have a constant half-life Only 1 st order rxns have a constant half-life Conc. Vs. Time graph Conc. Vs. Time graph Half-life – t 1/2 Half-life – t 1/2 Time for conc. to decrease to half of original value Time for conc. to decrease to half of original value Constant half-life Constant half-life

Determination of the order of a reaction Initial rates method Initial rates method Several separate experiments with different starting conc. of reactant A & measuring the initial rate of each rxn Several separate experiments with different starting conc. of reactant A & measuring the initial rate of each rxn Process repeated for reactant B Process repeated for reactant B

If changing conc. of A has no effect on rate  order of zero with respect to A If changing conc. of A has no effect on rate  order of zero with respect to A If changes in conc. A produce directly proportional changes in the rate  1 st order with respect to A If changes in conc. A produce directly proportional changes in the rate  1 st order with respect to A If a change in conc. A leads to an increase in the rate of rxn equal to the square of the change  2 nd order with respect to A If a change in conc. A leads to an increase in the rate of rxn equal to the square of the change  2 nd order with respect to A

Use the following data to work out the order of the rxn with respect to reactants A & B. Write the rate expression for the reaction. Experiment Number Initial concentration (mol dm -3 ) Initial rate of reaction (mol dm- -3 s -1 ) [A][B] 10.10 2.0 x 10 -4 20.200.104.0 x 10 -4 30.300.106.0 x 10 -4 40.300.202.4 x 10 -4 50.30 5.2 x 10 -4

Summary of dedcutions Change in [A] Change in rate of zero- order rxn Change in rate of 1 st - order rxn Change in rate of 2 nd order rxn [A] doublesNo change Rate doubles (x 2) Rate x 4 [A] triplesNo change Rate triples (x 3) Rate x 9 [A] increases four-fold No change Rate increases four-fold (x 4) Rate x 16

16.2 Reaction Mechanism ≈ Explain that reactions can occur by more than one step and that the slowest step determines the rate of reaction (rate determining step). ≈ Describe the relationship between reaction mechanism, order of reaction and rate-determining step.

Most reactions involve a series of small steps Reaction mechanism Reaction mechanism The theory of what’s happening in a rxn The theory of what’s happening in a rxn Series of simple steps making a rxn Series of simple steps making a rxn Elementary steps – individual steps – cannot be observed directly Elementary steps – individual steps – cannot be observed directly Intermediates – products of one elementary step that are used as reactants in the next elementary step Intermediates – products of one elementary step that are used as reactants in the next elementary step The sum of the elementary steps must equal the overall rxn The sum of the elementary steps must equal the overall rxn

NO 2 (g) + CO(g)  NO(g) + CO 2 (g) Step 1: NO 2 (g) + NO 2 (g)  NO(g) + NO 3 (g) Step 2: NO 3 (g) + CO(g)  NO 2 (g) + CO 2 (g) NO 3 – is an intermediate – produced and then consumed

Molecularity - references an elementary step indicate the number of reactant species involved Molecularity - references an elementary step indicate the number of reactant species involved Unimolecular rxn – elementary rxn involves a single reactant particle Unimolecular rxn – elementary rxn involves a single reactant particle Bimolecular rxn – involves two reactant particles Bimolecular rxn – involves two reactant particles NO 2 (g) + CO(g)  NO(g) + CO 2 (g) Termolecular - very rare due to 3+ particles colliding at same time with energy and orientation to react Termolecular - very rare due to 3+ particles colliding at same time with energy and orientation to react

The rate-determining step is the slowest step in the reaction mechanism Rate-determining step – slowest step Rate-determining step – slowest step

The rate expression for an overall reaction is determined by the reaction mechanism

Equation for rate- determining step MolecularityRate Law A  productsUnimolecularRate = k[A] 2A  productsBimolecularRate = k[A] 2 A + B  products BimolecularRate = k[A][B]

2NO 2 Cl(g)  2NO(g) + Cl 2 (g) Step 1: NO 2 Cl(g)  NO 2 (g) + Cl(g)slow Step 2: NO 2 Cl(g) + Cl  NO 2 (g) + Cl 2 (g)fast Overall: 2NO 2 Cl(g)  2NO(g) + Cl 2 (g) Rate = ? Order of rxn = ?

2NO(g) + O 2 (g)  NO 2 (g) Step 1: NO(g) + NO(g)  N 2 O 2 (g)fast Step 2: N 2 O 2 (g) + O 2 (g)  2NO 2 (g)slow Overall: 2NO(g) + O 2 (g)  NO 2 (g) Rate = ? Overall order of rxn = ?

Zero order reactant – does not take part in the rate of the rxn

16.3 Activation Energy ≈ Describe qualitatively the relationship between the rate constant (k) and temperature (T). ≈ Determine activation energy (Ea) values from the Arrhenius equation by a graphical method.

The rate constant k is temperature dependent Rule of Thumb: 10°C increase = doubling of the rate Rule of Thumb: 10°C increase = doubling of the rate Rate of Rxn depends on two things: Rate of Rxn depends on two things: Rate constant, k Rate constant, k Conc. of reactants raised to a power Conc. of reactants raised to a power Increasing the temp has no effect on the conc; changes the value of the rate constant k Increasing the temp has no effect on the conc; changes the value of the rate constant k k is temperature specific k is temperature specific

Collision Theory Collision Theory Increasing temp.  increases collisions  increases rxn rate Increasing temp.  increases collisions  increases rxn rate

The temperature dependence of the rate constant is expressed in the Arrhenius equation Arrhenius Equaiton – shows that the fraction of molecules with energy > Ea at T is proporitonal to e -Ea/RT Arrhenius Equaiton – shows that the fraction of molecules with energy > Ea at T is proporitonal to e -Ea/RT k = Ae -Ea/RT k = Ae -Ea/RT R = gas law constant; 8.31 J/K mol R = gas law constant; 8.31 J/K mol T = absolute temp; K T = absolute temp; K A = Arrhenius constant; frequency factor; pre- exponential factor A = Arrhenius constant; frequency factor; pre- exponential factor E a = activation energy E a = activation energy

Arrhenius constant Arrhenius constant Frequency w/which successful collisions occur Frequency w/which successful collisions occur Collision geometry Collision geometry Energy requirements Energy requirements Constant for the rxn Constant for the rxn Same units as k – varies with order of rxn Same units as k – varies with order of rxn

Taking the natural log of both sides of the equation Taking the natural log of both sides of the equation ln k = -E a /RT + ln A ln k = -E a /RT + ln A Form of equation for straight line Form of equation for straight line y = mx + c y = mx + c Arrhenius plot – graphing ln k VS. 1/T gives a straight line with a gradient of -E a /R Arrhenius plot – graphing ln k VS. 1/T gives a straight line with a gradient of -E a /R

Determine the activation energy in kJ mol -1 by graphical method. Rate constant (s -1 )Temperature (°C) 2.88 x 10 -4 320 4.87 x 10 -4 340 7.96 x 10 -4 360 1.26 x 10 -3 380 1.94 x 10 -3 400

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