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Kinetics
How fast does your reaction go?
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Reaction rates
• Rate is how fast a process occurs
• Rates are measured in units of
Results
Time
• Example: speed is measured in m/s (or mi/hr). A remote control car covers 125 meters in 15 seconds. What is its rate of speed?
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Reaction rates
• Example #2: Lucy wraps chocolates at a rate of 5 pieces/minute. The conveyor belt moves chocolates by at a rate of 9 pieces/minute. At what rate does Lucy have to eat chocolates to keep them from piling up on the conveyor belt?
• Chemical reaction rates are often mol/s or mol/Ls.
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Reaction rates
• Average rate is the (total results)/(total time).
• MgO + H2 Mg + H2O
• Average rate =
([H2Ofinal]-[H2Oinitial])/(tf-ti)
= [H2O]/t
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Reaction rates
• Instantaneous rate is the results for an infinitesimally small amount of time divided by that time
• Instantaneous rate = d[H2O]/dt
• Rates can also be for the disappearance of reactants
• Average rate = -[H2]/t
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Reaction rates
• Measured in units of
amount of product formed
time
• The amount of product can be any convenient unit (grams, moles, liters of gas, etc.)
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Reaction rates
• Example:
MgO + H2 Mg + H2O
• If the concentration of water vapor in the above reaction increases from 1.0x10-3 moles/liter to 8.8x10-3 moles/liter in 3.5 seconds, What would be the average reaction rate?
• (8.8-1.0)x10-3/3.5 = 2.2x10-3 mol/L∙s
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Graphing rates
• Results (dependent variable) are plotted on the y axis, and time (independent variable) is plotted on the x axis.
• The rate at any time is the slope of the graph at that time.
• The rate of a straight line plot is just the slope of the whole line (rise/run).
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Graphing rates
• Curved plots– Instantaneous rate at any time is the
slope of the tangent to the curve at that point.
– Average rate for any time period is the slope of the straight line connecting the two desired time points on the graph.
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Collision theory
• Particles must collide in order to react.
• Particles must be oriented correctly when colliding in order to react
• Correct orientation results in a temporary high-energy arrangement called an activated complex or transition state.
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Collision theory
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Collision theory
Activated complex for SN2 substitution of bromomethane with hydroxide to make methanol
• Transition state may form products or break apart and re-form reactants
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Activation energy
• Particles must collide with sufficient energy to cause a reaction
• Activation energy is the difference in energy between the reactants and the transition state
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Activation energy
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Activation energy
• If reactants do not have enough kinetic energy, the reaction will not start.
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Factors affecting reaction rates• Free energy and reaction rate are
unrelated
• Surface area– More surface area (smaller pieces or
finer powder) means a faster reaction. All reactions involving a solid phase take place at the surface of the solid.
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Factors affecting reaction rates• Concentration
– Higher concentration means a faster reaction.
• Nature of reactants– Rate of reaction depends on what is
reacting.
• Temperature – The activation energy is supplied by
the kinetic energy of the particles.
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Factors affecting reaction rates
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Factors affecting reaction rates• Higher temperature means that
more particles will have enough energy to react.
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Catalysts
A reaction will proceed faster in the presence of a catalyst because the activation energy is lowered.
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Catalysts
• A catalyst speeds a reaction without being used up.
• Transition metals and their oxides often have catalytic properties – used in catalytic converters in automobiles
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Catalysts
• For solid catalysts, the reaction usually takes place on the surface of the catalyst, therefore the more surface area the catalyst has, the faster the reaction
• Biological catalysts are called enzymes
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Rate Laws
• Rate varies with concentration of reactants
A B
Rate = k[A]
where k is the rate constant. • The rate constant is temperature
dependent.• Rate constant is experimentally
determined.
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Reaction order
• Expresses how rate depends on concentration as an exponent
• Zero order: rate = k[A]0 = k
• First order: rate = k[A]
• Second order: rate = k[A]2
• Reactions beyond second order in one reactant are extremely rare.
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Reaction order
A + B AB
Rate = k[A][B]
• Reaction is first order in A, first order in B and second order overall.
• In a simple reaction the order represents the molecularity of the reaction.
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Reaction order
• Molecularity is the number of particles that have to collide to make a reaction
• Zero order – generally reactions that happen at a surface and depend only on surface area.
• First order – depends only on concentration of reactant
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Reaction order
• Second order
Rate = k[A]2
• Two molecules of A must collide.• Probability of a collision is n(n-1)/2. If
the concentration is doubled to 2n (and n is large) the probability increases by a factor of four, so the rate depends on the square of the concentration.
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Determining reaction order
• Method of initial rates– Reaction is run for short periods of time and
stopped before reactant concentrations change much
– Initial concentrations are changed and rates compared
– If initial concentration is doubled, the rate will• zero order: not change • first order: 2x • second order: 4x
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Determining reaction order
• Rate constant can also be determined
• Example. A + B C
Determine rate law for this reaction, rate constant, and rate when [A] = 0.050 M and [B] = 0.100 M
Experiment [A] [B] Initial rate (M/s)
1 0.100 0.100 4.0x10-5
2 0.100 0.200 4.0x10-5
3 0.200 0.100 16.0x10-5
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Determining reaction order
• Rate law for B: Use exp. 1 & 2• Rate2/rate1 = 4.0x10-5/4.0x10-5
= k(0.100)m(0.200)n = 1 k(0.100)m(0.100)n
• Rate law for A: Use exp. 1 & 3 • Rate2/rate1 = 16.0x10-5/4.0x10-5 = 4
= k(0.200)m(0.100)n k(0.100)m(0.100)n
• rate = k[A]2[B]0 = k[A]2
n = 0
m = 2 = 2m = 4
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Determining reaction order
• Determining k: use any experiment
• k = rate/[A]2 = 4x10-5/0.1002 = 4.0x10-3M-1s-1
• Rate at given concentrations: Use the rate law equation
• rate = k[A]2 = (4x10-3)(0.200)2 = 1.6x10-4 M/s
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Determining reaction order
• Example:
2NO + 2H2 N2 + 2H2O
Determine the rate law and rate constant, and the rate when [NO] =
0.050 M and [H2] = 0.150 MExperiment [NO] [H2] Initial rate (M/s)
1 0.10 0.10 1.23x10-3
2 0.10 0.20 2.46x10-3
3 0.20 0.10 4.92x10-3
Answer: rate = k[NO]2[H2]; k = 1.2 M-2s-1; rate = 4.5x10-4M/s
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Integrated rate laws
• Concentration expressed in terms of time
• Zero order: • [A] = -kt + [A]0
• Graph of [A] vs t is a straight line.• 1st order: • ln[A] = -kt + ln[A]0
• Graph of ln[A] vs t is a straight line.
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Integrated rate laws
• 2nd order:
• 1/[A] = kt + 1/[A]0
• Graph of 1/[A] vs t is a straight line.
• 3rd order reactions are practically non-existent.
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Reaction mechanisms
• Complex reactions are made of several simple steps.
• Example:
NO2 + CO NO + CO2 occurs in two steps:
i. NO2 + NO2 NO3 + NO
ii. NO3 + CO NO2 + CO • Overall process is sum of steps.
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Reaction mechanisms
• Intermediates are short-lived species that are temporarily formed as the reaction proceeds.
• The rate-determining step is the slowest step of the mechanism.
• Intermediates are short-lived species that are temporarily formed as the reaction proceeds.
• The rate-determining step is the slowest step of the mechanism.
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Reaction mechanisms
• Changing components of this step changes the reaction rate; changing components of other steps does not.
• Rate laws for complex reactions include the components of the slow step and critical components of earlier steps.
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Reaction mechanisms
• Example: 2NO + 2H2 N2 + 2H2Ooccurs in three steps:
2NO N2O2 (fast)N2O2 + 2H2 N2O + H2O (slow)
N2O + H2 N2 + H2O (fast)• Rate law is rate = k[NO]2[H2]. [H2]
appears in the slow step, and [N2O] depends on [NO]2, so [NO]2 appears in the rate law as well.
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Reaction mechanisms
• Further examples:• Example 1
HBr + O2 2H2O + 2Br2
Step 1 (slow)
HBr + O2 HOOBrStep 2
HOOBr + HBr 2HOBrStep 3
2HOBr+ 2HBr 2H2O + 2 Br2
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Reaction mechanisms
• Choose the most likely rate law:
a. rate = [HBr]
b. rate = [O2]
c. rate = [HBr][O2]
d. rate = [HBr]2
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Reaction mechanisms
• Example 2
(CH3)3CBr + H2O (CH3)3COH + HBr