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Rate of Reaction
University of Lincoln presentation
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Why the difference?
Is it the enthalpy change (Heat of combustion) ?
Paraffin wax 42 MJ kg-1
Petrol 45 MJ kg-1
Is it the temperature?Yellow/white – 1300oCPale orange/yellow – 1100oC
What is it then?
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Approximately how long will a 2 litre pool of petrol burn for?Important values: Petrol density = 0.8 kg litre-
1
Heat of combustion is 45 MJ kg-1
2 litres of petrol has a mass of 1.6 kg (from the density)Total energy available from 1.6 kg petrol= 1.6 kg x 45 MJ kg-1 = 72 MJ
2 litre petrol pool is a 1 MW fire (this is a measured value)1 MW = 1 MJ s-1 so at this rate it would take 72 s
ΔHmq
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How do ignitable liquids burn?
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2 litre petrol bomb takes about 10s to burn. What is the rate of heat release? 72 MJ in 10 s = 7.2 MW2 litre petrol fully evaporated takes about 1 s to burn. What is the rate of heat release?72 MJ in 1s = 72 MW
Conclusion: Same total energy available but released at a faster rate
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How long to burn a 1.6 kg candle?
• 1.6 kg paraffin wax at 42 MJ kg-1 can release 67.2 MJ
• Candle flame has a heat release rate of 80 W (80 Js-1)
s840000Js80J67.2x10
Js80MJ67.2time(s) 1
6
1
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A candle bomb?
• NASA are researching the paraffin rocket!!
• How can this work?• Increase rate of combustion
– Increase concentration of the oxidant; use 100% oxygen
– Paraffin as small liquid droplets
• Study of the rates of reaction - kinetics
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Factors affecting the rate of a chemical reaction
1. Concentration (hydrogen peroxide demo)
2. Pressure (gases)
3. Temperature (glowstick)
4. Surface area (dust explosion)
5. Catalysis
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Measuring Reaction Rate• Use a characteristic of the products or the reactants
that can be used as a measure of amount.– Volume of gas– Change in mass– Absorption of light
• rate of decrease of reactant or rate of increase of a product
DCBA
tD
tC
tB
tARate
ΔΔ
ΔΔ
ΔΔ
ΔΔ
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H2O2(l) H2O(l) + ½O2(g)
0
50
100
150
200
0 50 100 150Time (s)
Amou
nt of
H2O
2 rem
aini
ng (x
105 m
ol)
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Calculating Rate of ReactionThe gradient of tangent to the curve is the rate of reactionWhat happens to the reaction rate with time?
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 50 100 150
Time (s)
Conc
entra
tion
of H
2O2 (
mol
dm-3
)
Concentration = 0.3 mol dm-3 s-1
Rate = gradient = 0.0068 mol dm-3 s-1
Concentration = 0.1 mol dm-3 s-1
Rate = gradient = 0.0023 mol dm-3 s-1
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A Mathematical Relationship
• Select two other points on the curve and calculate the rate of reaction at that concentration of H2O2
• Plot a graph of Rate of Reaction as a function of H2O2 concentration
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Rate plot for the decomposition of hydrogen peroxide
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Hydrogen Peroxide concentration (mol dm-3)
Rate
of R
eacti
on (m
ol d
m-3 s-1 )
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What does the graph show?• Graph is a straight line through the origin
• The two variables have a linear mathematical relationship
• We can say: Rate of Reaction is directly proportional to Hydrogen Peroxide concentration
122OHRateα 122OHkRate
− Easy to predict what happens to reaction when [H2O2] is changed− [H2O2] x2 Rate x 2− First Order with respect to H2O2
− k is the rate constant; first order reaction has units of s-1 when the rate of reaction is measured in mol dm-3 s-1. Show this by rearranging the rate equation and why are the units of rate important.
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Rate of reaction can be measured from the rate that oxygen gas is produced.
50
40
30
20
10
0
Yeast suspension +hydrogen peroxide solution
Inverted burette
Water
0
5
10
15
20
25
30
0 50 100 150 200
Time (s)
Volu
me O
2 /cm
2
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Vary the starting concentration and measure the initial rate
[H2O2]= 0.40 mol dm-3
[H2O2]= 0.32 mol dm-3[H2O2]= 0.24 mol dm-3[H2O2]= 0.16 mol dm-3[H2O2]= 0.08 mol dm-3
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Initial Rate can be measured
0
5
10
15
20
25
30
0 50 100 150 200Time (s)
Volu
me
O2/c
m-3
Initial gradient 0.51cm3s-1
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Plot Initial Rate as a function of starting concentration
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4Conc of Hydrogen peroxide (mol dm-3)
Rate
of re
actio
n (c
m2 (O
2)s-1 )
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Summary– Decomposition of H2O2 can be followed by
measuring the decrease in H2O2 concentration or the volume of O2 evolved.
– Rate of reaction can be calculated from the progress curve at different times or initial rate measurements.
– Plots of rate as a function of reagent concentration can be used to determine the mathematical relationship
– Order of reaction can be determined– Rate equation can be written
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For you to do: Initial rate data[H2O2]/mol dm-3 Rate/cm3 O2 s-1
0.08 0.10.16 0.2150.24 0.320.32 0.410.4 0.51
Determine the order of reaction with respect to hydrogen peroxide and calculate the value of the rate constant.
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General Rate equations
kAkRate 0
nAkRate
2AkRate
Zero orderUnits of k ?
First orderUnits of k ? AkAkRate 1
Second orderUnits of k ?
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Further Analysis of data• Logarithms can be very useful• Plot of log rate as a function of log
concentration (p439 Housecroft)
nAkRate
AnloglogkAloglogkAlogklogRate nn
Gradient is n; Intercept is log kUse this method on the initial rate data in slide 21 to determine order and the value of k
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Half-lifeTime taken for the concentration of reactant A at time t, [A]t to fall to half its value.
kt21ln
ktAAln
0
t
0.693kt k0.693t
A constant half-life for a first order reactionProgress curve and measure t½ at several different
points.
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Constant half-life
0
50
100
150
200
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180Time (s)
Amou
nt of
H2O
2 rem
aini
ng (x
105 m
ol)
27s 27s
26s
Going from 200 x 10-5 mol to 100 x 10-5 mol takes 27s
Going from 100 x 10-5 mol to 50 x 10-5 mol takes 27s
Going from 50 x 10-5 mol to 25 x 10-5 mol takes 26s
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Using Luminol to detect blood stainsExponential decay curveFirst order write rate equationCalculate half-life and why is it important Video clip or demo
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Reactions with more than one reactant
A + B → products
mn BAkRatee.g. C12H22O11 + H2O → C6H12O6 + C6H12O6
sucrose glucose fructose
OHOHCkRate 2112212
First order with respect to each reactant Second order reaction (sum of orders in rate equation)
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Determining order and rate equations
Difficulties with more than one reactant?
•Initial rate method•Isolation method
Experimental DesignPrincipleVary one concentration and keep other(s) constant while measuring rate.
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An Example Reactionperoxodisulfate (VI) and iodide
ions2
24
282 I2SO2IOS
Design the experiment1. initial rate method (vary each concentration)2. Plot a graph of log rate as a function of log initial concentration for each reactant. Gradient of each line is order of reaction for each reactant.
3. k is determined by rearranging the rate equation.
11282 IOSkRate
Task: Determine the rate equation and a value for k
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Iodine clock data from experiment
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Collision theory• Molecules have to collide if they are to
react – increasing frequency of collisions?• Increasing concentration increases the
frequency of collisions• Increasing pressure increases frequency
of collisions• Increasing temperature increases
frequency of collision• But not just about rate of collisions – how
do we explain slow reactions?
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Activation Energy (Enthalpy)
Ea
• Energy of the collision must be above a certain value for reactants to react
• Why? Energy is needed to break bonds (remember bond enthalpies)
• This then creates reactive species to make new bonds
• The minimum energy required for a collision to result in chemical reaction is Ea
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Only those molecules with sufficient energy can react
Num
ber o
f mol
ecul
es w
ith
kine
tic e
nerg
y E
Kinetic energy (E)
Activation enthalpy Ea =50kJ mol-1
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Increasing Temperature increases Rate of Reaction
Num
ber o
f mol
ecul
es w
ith
kine
tic e
nerg
y E
Kinetic energy (E)
Activation enthalpy Ea =50kJ mol-1
Number of molecules with energy greater than 50kJ mol-1 at 300 K
Number of molecules with energy greater than 50kJ mol-1 at 310 K
300 K
310 K
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Back to petrol• Petrol vapour reacts with oxygen (air)• But not spontaneous at room temperature• Needs ignition. What does ignition do?
– Provides energy to break bonds (endothermic)– Creates reactive species (free radicals)– Self-sustaining (can remove ignition source and
it carries on). Why????– Energy released from the reaction breaks more
bonds and the reaction continues
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Combining Activation Energy and enthalpy
Draw a diagram for an endothermic reaction
Both can be shown on an enthalpy level diagram
Add Ea to the diagram
A+B
C+D
ΔHPo
sitiv
e en
thal
pyNe
gativ
e en
thal
py
Reaction coordinate
Exothermic reaction
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Rate equations and Temperature
RTEa
Aek
k is the rate constant; A is the pre-exponential factor; Ea is the activation energy; R is the molar gas constant (8.314 J mol-1 K-1); T is the absolute temperature (Kelvin).
increase temperature increase k increase ratedecrease Ea increase k increase rate
The Arrhenius equation
How does it work?
mn BAkRate
RTE
Ak AlnlnIt might be easier to do this
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The well known ‘rule of thumb’• Reaction rate doubles if temperature
is increased by 10 oC
Temp/K Ea/kJ mol-1 A/L mol-1 s-1 k/L mol-1 s-1
313 54 8.7 x 106 8.5 x 10-3
323 54 8.7 x 106 1.6 x 10-2
Check the values of k by calculating them from the Arrhenius equation using the other values in the tableCalculate k at 333 K. What is happening to the value of k? How will this affect the rate of this reaction?
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An experiment to determine Ea
• Determine order and rate equation for the reaction
• Measure the rate of reaction at different temperatures keeping the initial concentrations the same
• Calculate k at the different temperatures
RTElnAlnk ART
Ea
Aek
Plot lnk against 1/T: gradient = -EA/R; intercept = lnA
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Calculating Ea
Temperature/K
k/dm3 mol-1 s-1
296 2.9 x 10-3
302 4.2 x 10-3
313 8.3 x 10-3
323 1.9 x 10-2
Use the data below to calculate a value for the activation energy for this reaction
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How do we explain catalysis?
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What are catalysts?
Definition and some examples; reactions and catalystsHydrogen peroxide , metals and natural substancesEnzymesGases on metal surfacesWhat is a different reaction route?
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A catalyst provides an alternative path for the reaction with a lower
activation enthalpyEn
thal
py
Progress of reaction
Reactants
Products
Activation enthalpy of catalysed reaction
Activation enthalpy of uncatalysed reaction
Uncatalysed reaction
Catalysed reaction
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Acknowledgements• JISC• HEA• Centre for Educational Research and
Development• School of natural and applied sciences• School of Journalism• SirenFM• http://tango.freedesktop.org