Chapter 14 Kinetics - Houston Community College

Chapter 14 Kinetics - Houston Community College

Lecture Presentation Chapter 14 Chemical Kinetics 2015 Pearson Education, Inc. James F. Kirby Quinnipiac University Hamden, CT Chemical Kinetics

Chemical Kinetics In chemical kinetics we study the rate (or speed) at which a chemical process occurs. Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism, a molecular-level view of the path from reactants to products. Chemical Kinetics 2015 Pearson Education, Inc. Factors that Affect

Reaction Rates 1) 2) 3) 4) Physical state of the reactants Reactant concentrations Reaction temperature Presence of a catalyst Chemical Kinetics 2015 Pearson Education, Inc.

Physical State of the Reactants The more readily the reactants collide, the more rapidly they react. Homogeneous reactions are often faster. Heterogeneous reactions that involve solids are faster if the surface area is increased; i.e., a fine powder reacts faster than a pellet or tablet. 2015 Pearson Education, Inc. Chemical Kinetics

Reactant Concentrations Increasing reactant concentration generally increases reaction rate. Since there are more molecules, more collisions occur. Chemical Kinetics 2015 Pearson Education, Inc. Temperature

Reaction rate generally increases with increased temperature. Kinetic energy of molecules is related to temperature. At higher temperatures, molecules move more quickly, increasing numbers of collisions and the energy the molecules possess during the collisions. Chemical Kinetics 2015 Pearson Education, Inc. Presence of a Catalyst Catalysts affect rate without being in the

overall balanced equation. Catalysts affect the kinds of collisions, changing the mechanism (individual reactions that are part of the pathway from reactants to products). Catalysts are critical in many biological reactions. Chemical Kinetics 2015 Pearson Education, Inc. Reaction Rate Rate is a change in concentration over a time period: [ ]/t.

means change in. [ ] means molar concentration. t represents time. Types of rate measured: average rate instantaneous rate initial rate Chemical Kinetics 2015 Pearson Education, Inc. Following Reaction Rates Rate of a reaction is measured using

the concentration of a reactant or a product over time. In this example, [C4H9Cl] is followed. Chemical Kinetics 2015 Pearson Education, Inc. Following Reaction Rates The average rate is calculated by the (change in

[C4H9Cl]) (change in time). The table shows the average rate for a variety of time intervals. Chemical Kinetics 2015 Pearson Education, Inc. Plotting Rate Data A plot of the data gives more information about rate.

The slope of the curve at one point in time gives the instantaneous rate. The instantaneous rate at time zero is called the initial rate; this is often the rate of interest to chemists. This figure shows Note: Reactions instantaneous and initial rate typically slow down Chemical of the earlier example. Kinetics over time!

2015 Pearson Education, Inc. Relative Rates As was said, rates are followed using a reactant or a product. Does this give the same rate for each reactant and product? Rate is dependent on stoichiometry. If we followed use of C4H9Cl and compared it to production of C4H9OH, the values would be the same. Note that the change would have opposite signsone goes down in value, the other goes up. Chemical Kinetics

2015 Pearson Education, Inc. Relative Rates and Stoichiometry What if the equation is not 1:1? What will the relative rates be for: 2 O3 (g) 3 O2 (g) Chemical Kinetics 2015 Pearson Education, Inc. Determining Concentration Effect on Rate How do we determine what effect the

concentration of each reactant has on the rate of the reaction? We keep every concentration constant except for one reactant and see what happens to the rate. Then, we change a different reactant. We do this until we have seen how each reactant has affected the rate. 2015 Pearson Education, Inc. Chemical Kinetics An Example of How

Concentration Affects Rate Experiments 13 show how [NH4+] affects rate. Experiments 46 show how [NO2] affects rate. Result: The rate law, which shows the relationship between rate and concentration for all reactants: Rate = k [NH4+] [NO2] Chemical Kinetics 2015 Pearson Education, Inc. More about Rate Law The exponents tell the order of the reaction with

respect to each reactant. In our example from the last slide: Rate = k [NH4+] [NO2] The order with respect to each reactant is 1. (It is first order in NH4+ and NO2.) The reaction is second order (1 + 1 = 2; we just add up all of the reactants orders to get the reactions order). What is k? It is the rate constant. It is a temperature-dependent quantity. 2015 Pearson Education, Inc. Chemical Kinetics

First Order Reactions Some rates depend only on one reactant to the first power. These are first order reactions. The rate law becomes: Rate = k [A] Chemical Kinetics 2015 Pearson Education, Inc. Relating k to [A] in a First Order Reaction

rate = k [A] rate = [A] / t So: k [A] = [A] / t Rearrange to: [A] / [A] = k t Integrate: ln ([A] / [A]o) = k t Rearrange: ln [A] = k t + ln [A]o Note: this follows the equation of a line:

y = mx + b Chemical Kinetics So, a plot of ln [A] vs. t is linear. 2015 Pearson Education, Inc. An Example: Conversion of Methyl Isonitrile to Acetonitrile The equation for the reaction: CH3NC CH3CN It is first order. Rate = k [CH3NC] Chemical

Kinetics 2015 Pearson Education, Inc. Finding the Rate Constant, k Besides using the rate law, we can find the rate constant from the plot of ln [A] vs. t. Remember the integrated rate law: ln [A] = k t + ln [A]o The plot will give a line. Its slope will equal k. Chemical Kinetics 2015 Pearson Education, Inc.

Half-life Definition: The amount of time it takes for one-half of a reactant to be used up in a chemical reaction. First Order Reaction: ln [A] = k t + ln [A]o ln ([A]o/2) = k t + ln [A]o ln ([A]o/2) + ln [A]o = k t ln ([A]o / [A]o/2) = k t ln 2 = k t or t = 0.693/k 2015 Pearson Education, Inc.

Chemical Kinetics Second Order Reactions Some rates depend only on a reactant to the second power. These are second order reactions. The rate law becomes: Rate = k [A]2 Chemical Kinetics 2015 Pearson Education, Inc.

Solving the Second Order Reaction for A Products rate = k [A]2 rate = [A] / t So, k [A]2 = [A] / t Rearranging: [A] / [A]2 = k t Using calculus: 1/[A] = 1/[A]o + k t

Notice: The linear relationships for first order and second order reactions differ! Chemical Kinetics 2015 Pearson Education, Inc. An Example of a Second Order Reaction: Decomposition of NO2 A plot following NO2 decomposition shows that it must be second order because it is

linear for 1/[NO2], not linear for ln [NO2]. Equation: NO2 NO + O2 2015 Pearson Education, Inc. Chemical Kinetics Half-Life and Second Order Reactions Using the integrated rate law, we can see how half-life is derived: 1/[A] = 1/[A]o + k t

1/([A]o/2) = 1/[A]o + k t 2/[A]o 1/[A]o = k t t = 1 / (k [A]o) So, half-life is a concentration dependent quantity for second order reactions! 2015 Pearson Education, Inc. Chemical Kinetics Zero Order Reactions Occasionally, rate is

independent of the concentration of the reactant: Rate = k These are zero order reactions. These reactions are linear in concentration. 2015 Pearson Education, Inc. Chemical Kinetics

Factors That Affect Reaction Rate 1. 2. 3. 4. Temperature Frequency of collisions Orientation of molecules Energy needed for the reaction to take place (activation energy) Chemical Kinetics

2015 Pearson Education, Inc. Temperature and Rate Generally, as temperature increases, rate increases. The rate constant is temperature dependent: it increases as temperature increases. Rate constant doubles (approximately) with every 10 C rise.

Chemical Kinetics 2015 Pearson Education, Inc. Frequency of Collisions The collision model is based on the kinetic molecular theory. Molecules must collide to react. If there are more collisions, more reactions can occur. So, if there are more molecules, the reaction rate is faster. Also, if the temperature is higher, molecules move faster, causing more collisions and a

higher rate of reaction. Chemical Kinetics 2015 Pearson Education, Inc. The Collision Model In a chemical reaction, bonds are broken and new bonds are formed. Molecules can only react if they collide with each other. Chemical Kinetics

2015 Pearson Education, Inc. Orientation of Molecules Molecules can often collide without forming products. Aligning molecules properly can lead to chemical reactions. Bonds must be broken and made and atoms need to be in proper positions. Chemical Kinetics 2015 Pearson Education, Inc.

Energy Needed for a Reaction to Take Place (Activation Energy) The minimum energy needed for a reaction to take place is called activation energy. An energy barrier must be overcome for a reaction to take place, much like the ball must be hit to overcome the barrier in the figure below. Chemical Kinetics 2015 Pearson Education, Inc. Transition State (Activated Complex)

Reactants gain energy as the reaction proceeds until the particles reach the maximum energy state. The organization of the atoms at this highest energy state is called the transition state (or activated complex). The energy needed to form this state is called the activation energy. Chemical Kinetics 2015 Pearson Education, Inc. Reaction Progress Plots are made to show

the energy possessed by the particles as the reaction proceeds. At the highest energy state, the transition state is formed. Reactions can be endothermic or exothermic after this. 2015 Pearson Education, Inc. Chemical Kinetics

Distribution of the Energy of Molecules Gases have an average temperature, but each individual molecule has its own energy. At higher energies, more molecules possess the energy needed for the reaction to occur. Chemical Kinetics 2015 Pearson Education, Inc. The Relationship Between Activation Energy & Temperature Arrhenius noted relationship between activation

energy and temperature: k = AeEa/RT Activation energy can be determined graphically by reorganizing the equation: ln k = Ea/RT + ln A Chemical Kinetics 2015 Pearson Education, Inc. Law vs. Theory Kinetics gives what happens. We call the description the rate law. Why do we observe that rate law? We explain with a theory called a mechanism.

A mechanism is a series of stepwise reactions that show how reactants become products. Chemical Kinetics 2015 Pearson Education, Inc. Reaction Mechanisms Reactions may occur all at once or through several discrete steps. Each of these processes is known as an elementary reaction or elementary process.

Chemical Kinetics 2015 Pearson Education, Inc. Molecularity The molecularity of an elementary reaction tells how many molecules are involved in that step of the mechanism. Chemical Kinetics 2015 Pearson Education, Inc. Termolecular?

Termolecular steps require three molecules to simultaneously collide with the proper orientation and the proper energy. These are rare, if they indeed do occur. These must be slower than unimolecular or bimolecular steps. Nearly all mechanisms use only unimolecular or bimolecular reactions. Chemical Kinetics 2015 Pearson Education, Inc. What Limits the Rate? The overall reaction cannot occur faster than

the slowest reaction in the mechanism. We call that the rate-determining step. Chemical Kinetics 2015 Pearson Education, Inc. What is Required of a Plausible Mechanism? The rate law must be able to be devised from the rate-determining step. The stoichiometry must be obtained when all steps are added up. Each step must balance, like any equation.

All intermediates are made and used up. Any catalyst is used and regenerated. Chemical Kinetics 2015 Pearson Education, Inc. A Mechanism With a Slow Initial Step Overall equation: NO2 + CO NO + CO2 Rate law: Rate = k [NO2]2 If the first step is the rate-determining step, the coefficients on the reactants side are the same as the order in the rate law! So, the first step of the mechanism begins:

NO2 + NO2 Chemical Kinetics 2015 Pearson Education, Inc. A Mechanism With a Slow Initial Step (continued) The easiest way to complete the first step is to make a product: NO2 + NO2 NO + NO3 We do not see NO3 in the stoichiometry, so it is an intermediate, which needs to

be used in a faster next step. NO3 + CO NO2 + CO2 Chemical Kinetics 2015 Pearson Education, Inc. A Mechanism With a Slow Initial Step (completed) Since the first step is the slowest step, it gives the rate law. If you add up all of the individual steps (2 of them), you get the stoichiometry. Each step balances. This is a plausible mechanism.

Chemical Kinetics 2015 Pearson Education, Inc. A Mechanism With a Fast Initial Step Equation for the reaction: 2 NO + Br2 2 NOBr 2 NOBr The rate law for this reaction is found to be Rate = k [NO]2 [Br2] Because termolecular processes are rare, this rate law suggests a multistep mechanism. Chemical

Kinetics 2015 Pearson Education, Inc. A Mechanism With a Fast Initial Step (continued) The rate law indicates that a quickly established equilibrium is followed by a slow step. Step 1: NO + Br2 2 NOBr NOBr2 Step 2: NOBr2 + NO 2 NOBr Chemical Kinetics 2015 Pearson Education, Inc.

What is the Rate Law? The rate of the overall reaction depends upon the rate of the slow step. The rate law for that step would be Rate = k2[NOBr2] [NO] But how can we find [NOBr2]? Chemical Kinetics 2015 Pearson Education, Inc. [NOBr2] (An Intermediate)? NOBr2 can react two ways: With NO to form NOBr.

By decomposition to reform NO and Br2. The reactants and products of the first step are in equilibrium with each other. For an equilibrium (as we will see in the next chapter): Ratef = Rater 2015 Pearson Education, Inc. Chemical Kinetics The Rate Law (Finally!) Substituting for the forward and reverse rates:

k1 [NO] [Br2] = k1 [NOBr2] Solve for [NOBr2], then substitute into the rate law: Rate = k2 (k1/k1) [NO] [Br2] [NO] This gives the observed rate law! Rate = k [NO]2 [Br2] Chemical Kinetics 2015 Pearson Education, Inc. Catalysts Catalysts increase the rate of a reaction by decreasing the activation energy of the reaction.

Catalysts change the mechanism by which the process occurs. Chemical Kinetics 2015 Pearson Education, Inc. Types of Catalysts 1) Homogeneous catalysts 2) Heterogeneous catalysts 3) Enzymes Chemical Kinetics

2015 Pearson Education, Inc. Homogeneous Catalysts The reactants and catalyst are in the same phase. Many times, reactants and catalyst are dissolved in the same solvent, as seen below. Chemical Kinetics 2015 Pearson Education, Inc. Heterogeneous Catalysts

The catalyst is in a different phase than the reactants. Often, gases are passed over a solid catalyst. The adsorption of the reactants is often the ratedetermining step. 2015 Pearson Education, Inc. Chemical Kinetics

Enzymes Enzymes are biological catalysts. They have a region where the reactants attach. That region is called the active site. The reactants are referred to as substrates. Chemical Kinetics 2015 Pearson Education, Inc.

Lock-and-Key Model In the enzymesubstrate model, the substrate fits into the active site of an enzyme, much like a key fits into a lock. They are specific. Chemical Kinetics 2015 Pearson Education, Inc.

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