Kinetics

Kinetics

Reaction Rates, Rate Law, Collision Theory and Activation Energy (PLN 7-

10)

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)

Basic Kinetics

• Reaction Rate – Speed that reactants disappear and products form– How fast reactants become/form products

Examples:

• Very Fast Rates (Almost Instantaneous):– Most Acid-Base Reactions

– Some Precipitation Reactions• Slower Reaction Rates:– Rusting

What Determines the Rate?

• Temperature• Pressure• Concentration• Catalyst (PLN 12)– Lowers activation energy

• Surface Area– Not going to be covered on this test

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

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

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

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

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)

PLN 8

• Important Concepts:– Rate Laws– Rate Constant (k)– Order of Reaction– Initial Rate Method

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.

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

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

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

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

The Initial Rate Method

• By determining the ratio of Δrate to Δ[reactant] between 2 experiments

• Solve for the exponents for each reactant

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

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

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:

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

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

First Order Reactions

• Basic Example:

• Which can be rewritten as:

• And simply by cross-multiplying, you can get:

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.

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:

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:

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 :

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

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

What Affects Reaction Rates, Again?

• Reaction rates are dependent upon:– Temperature– Pressure– Concentration– Catalyst– Surface Area

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:

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

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

Importance of Correct Orientation

• For the reaction: • Consider two possible ways for the reactant

molecules to collide:

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

Calculating EA for an Equation

• By subtracting: • From: • We get:

• (ln A – ln A) = 0, simplify ln x – ln y and combine like terms :

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

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

Transition State

• For:

• Where a temporary complex:

• Is formed, before the • bond is broken• and the bond• is completely formed

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 ()

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