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# Intro to kinetics

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Zumdahl Chemistry, 4th ed. Kinetics overview,

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### Intro to kinetics

1. 1. Kinetics: Zumdahl Chapter12L. AllenStonington High School
2. 2. Chapter objectives (lots!) Identify factors that influence reaction rates Calculate rate of consumption of a reactant or ofcreation of a product from stoichiometry Write the rate law for a reaction Determine the rate law of a reaction from data Determine the order of a reaction from time/ratedata Solve for the rate constant from time/rate data Determine the instantaneous rate of a reaction Create graphs to determine order of a reaction Use the integrated rate law to determineconcentration at time t Determine half life of a reaction Determine the activation energy for a reaction
3. 3. Didn’t we already figure out if areaction would runspontaneously? Remember the rule fromthermochemistry – spontaneous doesnot mean fast! Just because areaction is energetically favored, doesnot mean it will run in a reasonableamount of time. Thermochemistrytakes into account the energy of theproducts and of the reactants, not anyactivation energy required to run areaction.
4. 4. Factors that influence reactionrates Concentration – the more particlesbump into each other, the more likelythey are to react Temperature – the more particlesmove, the more they bump into eachother Increasing surface area – powderedaluminum is much more interestingthan a chunk of aluminum Addition of a catalyst – determinedexperimentally
5. 5. Effect of a catalyst on activationenergyReactions can beendothermic orexothermic – eitherway, a catalyst canfacilitate overcomingthe activation energy“bump”
6. 6. Simple stoichiometry In the reaction: N2 + 3 H2 2NH3, what is the relationship betweenthe rate of production of NH3 and therate of consumption of H2? In any given amount of time, twice asmuch NH3 is created as nitrogen gasdisappears. Its RATE of generation istwice as great. Its rate of generationis 2/3 that of hydrogen’sdisappearance.
7. 7. Chapter objectives (lots!) Identify factors that influence reaction ratesDONE Calculate rate of consumption of a reactant or ofcreation of a product from stoichiometry DONE Write the rate law for a reaction Determine the rate law of a reaction from data Determine the order of a reaction from time/ratedata Solve for the rate constant from time/rate data Determine the instantaneous rate of a reaction Create graphs to determine order of a reaction Use the integrated rate law to determineconcentration at time t Determine half life of a reaction Determine the activation energy for a reaction
8. 8. Determine the rate law of areactionFirst,Notice that Zumdahlonly selects examplesof reactions that havea good reason not torun both ways.Usually, it is that oneof the products is agas that escapes.Thus, only reactantsare considered inelementary kinetics.Next,Notice that we arebeginning withdecompositionreactions, in whichthere is only onereactant. This meanswe are only looking atthe rate of change ofone substance – theproduct concentrationsare stoichiometricallydependent on thereactant anyway.
9. 9. 2NO2(g)  2NO(g) + O2(g) See page 551 for table ofconcentrations as a function of time The rate of change is going to bedefined as the change inconcentration over the elapsed time.The instantaneous rate is graphicallythe slope of the line tangent to thecurve. You will NOT have to calculatethe slope of that tangent yourselfwhen the graph is a curve.
10. 10. “WRITE THE RATE LAW FOR THIS REACTION”RATE = K[NO2]NFor the reaction2NO2(g)  2NO(g) + O2(g) This k is NOT the same k as we used inequilibrium. Sorry! N is an exponent – this tells us whether thedisappearance of NO2 is directly related toconcentration (n=1), exponentially related(n=2) or not based on concentration at all(n=0) The concentrations of the products are notincluded because the reverse rate of thereaction is not significant in this case – infact, you will never need to consider anequilibrium situation for these problems.
11. 11. 2N2O5 (aq)  4NO2(aq) + O2(g) Notice in thisproblem, the oxygenleaves – no worriesabout the reversereaction On page 557, Z hascut to the chase – theconcentration of N2O5and the instantaneousrate are presentedtogether As the concentrationdoubles, theinstantaneous ratedoubles. No moremath required; youknow that the value ofthe exponent is 1 rate = k[N2O5]n Now plug in n=1, anyconcentration ofN2O5, and solve for k You can now find therate at anyconcentration of N2O5
12. 12. Sneaky sneaky Zumdahl… Notice that on page 552, you get a biggorgeous graph of the concentrations of allthe substances in this reaction as a functionof time. The tangents at specific points arecalculated for you In a tiny table on page 553, you get therate/time data, but even that is notinstantaneous. If you graphed the change of theinstantaneous velocities, you would get astraight line – this means it is a first orderreaction, although Zumdahl never tells youthat. In fact, he moves to a different equation
13. 13. Chapter objectives (makingprogress!) Identify factors that influence reaction ratesDONE Calculate rate of consumption of a reactant or ofcreation of a product from stoichiometry DONE Write the rate law for a reaction DONE Determine the rate law of a reaction fromdataDONE Determine the order of a reaction from time/ratedata Solve for the rate constant from time/rate data Determine the instantaneous rate of a reaction Create graphs to determine order of a reaction Use the integrated rate law to determine
14. 14. Reactions with two reactants NH4+(aq) + NO2-(aq)  N2(g) + 2H2O(l) Notice that the N2(g) leaves. Z provides initial instantaneous ratesfrom 3 different experiments on page559. Spend a minute reading the table –see if you can reach any conclusionswithout a lot of math about therelationships between concentrationand rate for each reactant.
15. 15. Need a hand? Look at the initial concentration ofammonium ions. Do you see howexperiment 2 and 3 are related? Notice that the NO2- does not changebetween experiment 2 and 3. Thismeans the change in the rate isexclusively dependent on the ammoniumconcentrations Notice the difference betweenconcentrations in experiments 1 and 2. Can you establish the exponent for eachreactant in the rate law now?
16. 16. rate = k[NH4+ ]n[NO2-]m The rate doubles as the concentrationof NH4+ doubles. Therefore, n=1 The rate doubles as the concentrationof NO2- doubles. Therefore, m=1 Now you can plug in any of the valuesfor one experiment and calculate k. Calculating k from different initialconcentrations should NOT yielddifferent k values.
17. 17. WHAT DOES IT MEANWHEN THEY SAY….?Dealing with the words Write the rate law for a reactionrate = k[NH4+ ]n[NO2-]m Determine the rate law of a reaction fromdatarate = k[NH4+ ]1[NO2-]1 Determine the order of a reaction fromtime/rate data1 + 1 = 2 so the overall order of a reaction is 2 Determine the instantaneous rate of areaction Solve for the rate constant from time/rate
18. 18. WHAT DOES IT MEANWHEN THEY SAY….?Dealing with the words Write the rate law for a reactionrate = k[NH4+ ]n[NO2-]m Determine the rate law of a reaction from datarate = k[NH4+ ]1[NO2-]1 Determine the order of a reaction from time/rate data1 + 1 = 2 so the overall order of a reaction is 2 Solve for the rate constant from time/ratedata k = rate/ [NH4+ ][NO2-] Determine the instantaneous rate of areaction◦ Plug in your new k into the reaction◦ rate = k[NH4+ ] [NO2-] for any concentrations of thereactants
19. 19. Chapter objectives (makingprogress!) Identify factors that influence reaction rates DONE Calculate rate of consumption of a reactant or ofcreation of a product from stoichiometry DONE Write the rate law for a reaction DONE Determine the rate law of a reaction fromdataDONE Determine the order of a reaction from time/ratedata DONE Solve for the rate constant from time/rate dataDONE Determine the instantaneous rate of a reactionDONE Create graphs to determine order of areaction Use the integrated rate law to determine
20. 20. HOMEWORK End of chapter 12, numbers21, 24, 25, 29, 30, 36, 39, 40, 46, 66 Due next class – Friday April 26 Also, read to the end of chapter12, and come prepared to askquestions or to solve problems!
21. 21. Which data am I being given?Initial concentrations andratesConcentrations andtime In this case, look forpatterns that will tell youif the exponent in the ratelaw is a zero, 1, or 2 No additional calculatedvalues are necessary tofind the rate order In this case, add 2 morecolumns of data Include 1/[A] and ln[A]columns of data whenpresented withconcentration and time
22. 22. 2C4H6C8H12Given[C4H6] timeCalculatedTime 1/ [C4H6] ln[C4H6] .01000 0 .00625 1000 .00476 1800 .00370 2800 .00313 3600 .00270 4400 .00241 5200 .00208 6200 0 100 -4.605 1000 160 -5.075 1800 210 -5.348 2800 270 -5.599 3600 320 -5.767 4400 370 -5.915 5200 415 -6.028 6200 481 -6.175
23. 23. Using the inverse and the ln A graph of [A] over time will be astraight line for zero order reactions. One other data set you will need is thenatural log of the concentration. A graph of ln[A] over time will be astraight line for first order reactions. The third data set you will need is thereciprocal of the concentration. A graph of 1/[A] vs. time will be astraight line for second orderreactions.
24. 24. Graph each data set with time onthe x axis The graph of [C4H6] is not a straight line. This is not a zero order reaction. The graph of the ln [C4H6] is not astraight line. The reaction is not firstorder for [C4H6] REJECT the data set of ln [C4H6]. The graph of 1/[C4H6] is a straight line.Therefore, the reaction is second orderfor [C4H6].
25. 25. Finding k Rate = k[C4H6]2 The k is actually the slope of thegraph. To find slope, calculate y/ xfrom your graph. Alternately, pick two values off yourdata table to calculate the slope from. Visually, I used (0, 100) and(5000, 400) and got k=.06 Z did it with the data points and got 6.14 e -2
26. 26. Chapter objectives (makingprogress!) Identify factors that influence reaction rates DONE Calculate rate of consumption of a reactant or of creation of a product fromstoichiometry DONE Write the rate law for a reaction DONE Determine the rate law of a reaction from dataDONE Determine the order of a reaction from time/rate data DONE Solve for the rate constant from time/rate data DONE Determine the instantaneous rate of a reaction DONE Create graphs to determine order of areaction DONE Use the integrated rate law to determineconcentration at time t Determine half life of a reaction
27. 27. The integrated rate law Take a look at page 562, equation 12.2and at the AP “cheat sheet” pageii, kinetics section. Note that the form of the integrated ratelaw on the cheat sheet is somewhatdifferent than in Z. It is only marginallydifferent. This form of the integrated rate law isonly applied to first order reactions. Ifyou use it to work with zero or 2nd orderreactions, you will mess up!! Thelesson? Establish the order before you
28. 28. Why is Zumdahl right thistime? Zumdahl has organized his version ofthe integrated rate law into y=mx+bformat. Y= ln[A] M = -k X = time B = ln[A]o THAT is cool!
29. 29. Integrated rate law for secondorder reactions Page 567, eq’n 12.5 Again, Z uses y=mx+b format, and theAP cheat sheet does not.
30. 30. Chapter objectives (makingprogress!) Identify factors that influence reaction rates DONE Calculate rate of consumption of a reactant or of creation of a product fromstoichiometry DONE Write the rate law for a reaction DONE Determine the rate law of a reaction from dataDONE Determine the order of a reaction from time/rate data DONE Solve for the rate constant from time/rate data DONE Determine the instantaneous rate of a reaction DONE Create graphs to determine order of areaction DONE Use the integrated rate law to determineconcentration at time t DONE Determine half life of a reaction
31. 31. Half life – not as simple as youthought! The traditional concept of half life – theamount of time it takes for half of asample to convert to some other form –is based on first order reactions only In first order reactions, half life follows asimple equation T1/2= .693/k This is NOT on the AP cheat sheet! This equation was derived on page 565using the integrated rate law for firstorder reactions. Follow the logic, andyou can reconstruct it if you need it.
32. 32. Half life problem – first order See Z page 566 Solve for k Solve for time to a particularconcentration Solve for a concentration at a giventime Plug and chug… not difficult, exceptthat you must use the right equations!
33. 33. What you should notice aboutthat half life equation This is NOT dependent onconcentration! To calculate specificconcentrations at time t, you will needthe initial concentration, but you do notneed it to calculate k or t1/2
34. 34. Half life of a second orderreaction t1/2 = 1/k[A]0 This is specific to second orderreactions. It is not on the AP cheatsheet, but can be derived from theintegrated rate law for second orderreactions. This IS dependent on initialconcentration. Unlike simple first order half life, secondorder half lives do not mean half thematerial changes in a set amount oftime. For these reactions, each half lifetakes twice as long.
35. 35. So to quoteZumdahl, “Spontaneous doesnot mean fast.” But time IS something that we can useto learn more about a reaction, whatits mechanism is, and how it is likely toproceed. We can calculate with it.We can graph stuff.