Download - Kinetics
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Kinetics
Reaction Rates, Rate Law, Collision Theory and Activation Energy (PLN 7-
10)
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PLN 7
• Important Concepts:– Reactions can occur at different rates– Factors that help determine the reaction rate– Reaction characteristics:• Mechanism of reaction (PLN 11)• Rate of Reaction• Rate Law (PLN 8)
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Basic Kinetics
• Reaction Rate – Speed that reactants disappear and products form– How fast reactants become/form products
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Examples:
• Very Fast Rates (Almost Instantaneous):– Most Acid-Base Reactions
– Some Precipitation Reactions• Slower Reaction Rates:– Rusting
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What Determines the Rate?
• Temperature• Pressure• Concentration• Catalyst (PLN 12)– Lowers activation energy
• Surface Area– Not going to be covered on this test
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Mechanism of Reaction
• Lists the individual steps of a reaction• Describe reactions at a molecular level• Not all reactions occur in one step or all at
once• Chemical equation is overall summary of the
reaction
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Rate of Reaction
• The calculated rate at which reactants are used up/disappear or products are formed/appear
• For general reaction:
Where a, b, c and d are coefficients,
𝑅𝑎𝑡𝑒=− 1𝑎∆ [𝐴 ]∆𝑡
=− 1𝑏∆ [𝐵 ]∆ 𝑡
=1𝑐∆ [𝐶 ]∆ 𝑡
= 1𝑑∆[𝐷 ]∆ 𝑡
𝑎𝐴+𝑏𝐵→𝑐𝐶+𝑑𝐷
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Rate Law
• Mathematic expression for the rate of reaction– Expressed in terms of the concentrations of the
reactants• For a reaction:A + B C + D
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Reaction Rates
• Definition:– The rate of a reaction is the change in molar
concentration of a reactant or product per unit of time in a reaction
• Example:• Rate of decomposition of • However, this gives the average rate over the
period of time Δt• The instantaneous rate can be calculated as the
slope of the tangent line at a given point
2𝑁2𝑂5(𝑔)→ 4𝑁𝑂2(𝑔)+𝑂2(𝑔)
𝑁 2𝑂5=−∆[𝑁 2𝑂5]∆ 𝑡
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Overall Rate of Reaction
• The rate of reaction is more commonly described in terms of the equation
• For the reaction:• For every 2 moles of N2O5 lost: – 4 moles of NO2 is formed
– And 1 mole of O2 is formed
Note: The negative sign placed in front of the reactants is to count for the fact that their concentrations are decreasing
𝑅𝑎𝑡𝑒=−12
∆ [𝑁2𝑂5 ]∆ 𝑡
=14
∆ [𝑁𝑂2 ]∆ 𝑡
=11
∆[𝑂2]∆𝑡
2𝑁2𝑂5(𝑔)→ 4𝑁𝑂2(𝑔)+𝑂2(𝑔)
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PLN 8
• Important Concepts:– Rate Laws– Rate Constant (k)– Order of Reaction– Initial Rate Method
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Rate Laws for Chemical Reactions
• Rates depend on concentrations of certain reactants and the concentration of the catalyst, if there is one
• Definition:– A Rate Law is an equation that relates the rate of a
reaction to the concentrations of the reactants (and catalyst, if used) raised to various powers, or exponents.
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𝑅𝑎𝑡𝑒=𝑘[ 𝐴 ]𝑚 [𝐵]𝑛• Rate – Expressed in mol/L/time or M/time• k – Rate constant
– Specific to a certain reaction at a specific temperature– Units depend on the overall reaction order (explained later)
• [A] & [B] – Concentrations of reactants as mol/L or M
• m & n – Orders of reaction with respect to reactants
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k
• The reaction constant, k, is called the rate constant and is dependent on the particular reaction as well as the specific temperature at which the reaction takes place
• The units of k depend on the order of reaction
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Orders of Reaction
• The rate law exponents are determined using experimental data
• Examples:
• The overall order of reaction is the sum of all orders with respect to each reactant
• So for the example, where the rate is 2nd order with respect to NO and first order with respect to H2:
• The overall order of reaction is 2 + 1 = 3, or a 3rd order reaction
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Determining the Rate Law Experimentally
• The Initial Rate Method– Uses the relationship between the measured
initial rate of a reaction and the concentrations of each reactant
• The Integrated Rate Law Method– Uses the relationship between reactant or product
concentration and its changes over time
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The Initial Rate Method
• By determining the ratio of Δrate to Δ[reactant] between 2 experiments
• Solve for the exponents for each reactant
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The Initial Rate Method – Data Collection
1. Determine the initial rate of reaction, fixing the concentration of all reactants except one
2. Repeat step 1, fixing the concentration of each reactant in turn
Example:
Experiment [NH4NCO]M
Rate of loss of NH4NCOM/min
1 0.14 2.2 × 10-4
2 0.28 8.8 × 10-4
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The Initial Rate Method – Calculations
• The reaction is 2nd order with respect to NH4NCO• The reaction is also 2nd order overall, since
NH4NCO is the only reactant and there is no catalyst
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Initial Rate Method – Rate Law and k
• Given NH4NCO is 2nd order, we can now determine the rate law to be:
• Using this rate law and the experimental data, the rate constant can also be calculated:
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PLN 9
• Important Concepts:– Integrated Rate Law Method• 0th, 1st and 2nd order reactions
– Half-Life• 0th, 1st and 2nd order reactions
– Units for k• 0th, 1st and 2nd order reactions
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The Integrated Rate Law Method
• Initial Rate Method describes change of rate as we change initial reactant concentrations
• Using integral calculus, we can convert Rate Laws into equations that can give us concentrations of the reactant(s) or product(s) at anytime during the reaction
• The Integrated Rate Law Method fits experimental data to a mathematical relationship
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First Order Reactions
• Basic Example:
• Which can be rewritten as:
• And simply by cross-multiplying, you can get:
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First Order Reactions (cont.)
• This setup allows integration of both sides:
Note: The k can be pulled out of the integral since it is a constant.
• Rearranging: Note: The next two slides detail all the steps in the integration process and may be skipped if you already understand the integration done here.
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Explaining the Integration: 1st Order• Beginning with: • The integral of is written as:
• And is solved as:
Note: In calculus, the notation “” means that you plug in b for x and plug in a for x and subtract the second equation (one with the a’s) from the first (one with the b’s)
• So, using our equation, the integration of just the left side looks like this:
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Explaining the Integration: 1st Order (cont.)• Beginning with: • The integral of 1 on the interval from a to b is written as:
• And is solved as:
• So, using our equation, the integration of just the right side looks like this:
• The final equation:
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Half-Life of a Reaction
• Definition– The half-life of a first order reaction is the time
taken for the reactant amount to reach one-half of its initial (or previous) value
• This is saying that
• Using substitution into the integrated rate law for 1st order reactions, we get time of half life :
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Rate Law, k, Integrated Rate Law and Half-Life for 1st, 2nd and 3rd Order
Order Rate Law k Integrated Rate Law Half-Life n (number of half lives)
0 Rate = k
1 Rate = k [B]
2𝑅𝑎𝑡𝑒=𝑘 [𝐶 ]2
𝑚𝑜𝑙𝐿×𝑡𝑖𝑚𝑒1
𝑡𝑖𝑚𝑒
𝐿𝑚𝑜𝑙× 𝑡𝑖𝑚𝑒
[ 𝐴 ]𝑡− [ 𝐴 ]0=−𝑘𝑡
ln[𝐵]0[𝐵]𝑡
=𝑘𝑡
1[𝐶 ]𝑡
−1
[𝐶 ]0=𝑘𝑡
𝑡 12
=1𝑘
[𝐴 ]02
𝑡 12
=ln 2𝑘
𝑡 12
=1
𝑘[𝐶 ]0
2−𝑛=( 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑙𝑒𝑓𝑡 )
• For only 1st order reactions: The half-life doesn’t depend on the initial concentration
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PLN 10
• Important Concepts:– Collision Theory• Pre-exponential constant (A)• fKE
– Importance of Correct Orientation– Arrhenius Equation– Activation Energy (EA)– Transition State Theory– Potential Energy Diagrams
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What Affects Reaction Rates, Again?
• Reaction rates are dependent upon:– Temperature– Pressure– Concentration– Catalyst– Surface Area
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How Temperature influences Reaction Rates
• Sometimes the influence temperature has on the rate of reaction can be quite dramatic, for:
• Data:At 25°C: At 35°C:
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Collision Theory
• The Collision Model says that, in order to react, molecules have to collide, both:– With enough energy– And with correct orientation
• In the Collision Model, k depends on 3 factors:– Z = Collision frequency– fraction of collisions that occur with the molecules
properly oriented– fraction of molecules having or exceeding the
required activation energy
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Changes in Temperature
• Z and forient are generally combined into one– Pre-exponential constant = A
• A is essentially independent of any temperature change, so fKE is the critical factor of k when it comes to changes in temperature
• where:– R = ideal gas constant in terms of
• 8.314
– T = temperature in kelvin– EA = Activation Energy for the process
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Importance of Correct Orientation
• For the reaction: • Consider two possible ways for the reactant
molecules to collide:
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Arrhenius Equation
• Taking the natural log of both sides:
• Rearranged: looks somewhat similar to: • In fact, it is a linear equation if you plot – Where the – And the
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Calculating EA for an Equation
• By subtracting: • From: • We get:
• (ln A – ln A) = 0, simplify ln x – ln y and combine like terms :
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Example
• For:
• Plug in values for k1, k2, T1 and T2 into the equation:
• Solve for EA:
k (L mol-1 s-1) T (°C)1.1 5506.4 625
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Transition State Theory
• Transition State Theory describes what happens to the reactant molecules as a reaction proceeds
• When the reactants collide, they form a temporary “substance” composed of a combination of the two reactants– This temporary “substance” is called the transition
state or activated complex
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Transition State
• For:
• Where a temporary complex:
• Is formed, before the • bond is broken• and the bond• is completely formed
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Transition States (cont.)
• The double dagger (‡) indicates a transition state
• The transition state is a step in-between forming a bond and breaking another– Can be thought of as one half broken bond and
one half formed bond• The partially formed and partially broken
bonds are denoted with ()
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Potential Energy Diagrams
• A graph of Potential Energy vs. the Reaction Coordinate– The reaction coordinate is essentially the progress
of the reactionExothermic Reaction Endothermic Reaction