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北京化工大学:《物理化学》课程教学资源(双语实践教学)kinetics the iodine clock reaction

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Experiment Kinetics:The lodine Clock Reaction Obiectives Introduction In virtually every facet of chemical research.the ability to discover the kinetics of the reaction being studied is the key to understanding the overall chemistry.In a kinetic study,one investigates the rates at which reactions occur and how those rates are affected by changes in the concen and the presence of catalysts.Once factors are In this experiment,the reaction between iodide,and peroxydisulfate,SOis studied 3I(aq)+S,O-(aq)I(aq)+2S,O-(aq) The reaction kinetics will be investigated by the method,that is,measuring the amount if time that it takes for a certain fixed amount of the reactants to react.By measuring the time interval under various conditions of concentration and temperature,the rate law can be determined. For in,the rate depends upo a number of factors,the most imporant being of the and the rate constant,The rate econstant,in turn,depends on the reaction under study,but for any given reaction,varies only with temperature The rate is calculated as a change in concentration over a time interval (At)and has the units mol Lsec During each of several runs under different conditions,we will determine the length of time(At)required for the concentration of one of the reactants (S)to change by a certain fixed amount ()This is similar to timing runers inrace.By measuring the amount of tom it takes each runne rto run 1000 meters,we can calculate their running rates [A(distance)/A(time)] units of meters sec Determining the Order of Reaction What va riables eed tobe considered?The kinetics of be using the general rate law Rate=k[[S,O where a andare termed the orders of reaction with respect to iodide and peroxydisulfate.The maters the reactionrinh ow oncnrio ioe compi ha ing five variables (the twe oncentrations, a,b,and the rate and a known concentration of peroxydisulfate (S).The change in the peroxydisulfate concentration with time(which is the rate)can be calculated from the elapsed time for the reaction.This eliminates two variables,leaving three unknowns in the rate equation(a,b and the PDF文件使用"pdfFactory Pro”试用版本创建ww,fineprint.com,cn

Experiment Kinetics: The lodine Clock Reaction Objectives • To determine the kinetic parameters (rate, order, rate constant) of a reaction. • To examine the effect of a catalyst on the rate of reaction. Introduction In virtually every facet of chemical research, the ability to discover the kinetics of the reaction being studied is the key to understanding the overall chemistry. In a kinetic study, one investigates the rates at which reactions occur and how those rates are affected by changes in the temperature, pressure, concentration, and the presence of catalysts. Once these factors are understood, the conditions may be optimized to speed up or slow down a reaction as desired. In this experiment, the reaction between iodide, I- , and peroxydisulfate, 2 S O2 8 - is studied: - 2 - 2 2 8 3 2 4 3I (aq)+S O (aq) I (aq) 2S O (aq) - - + The reaction kinetics will be investigated by the method of initial rates, that is, measuring the amount if time that it takes for a certain fixed amount of the reactants to react. By measuring the time interval under various conditions of concentration and temperature, the rate law can be determined. For reactions occurring in solution, the rate depends upon a number of factors, the most important being the concentration of the reactants and the rate constant, k. The rate constant, in turn, depends on the reaction under study, but for any given reaction, varies only with temperature. The rate is calculated as a change in concentration over a time interval (Δ[ ]/ Δt) and has the units mol L-1 sec -1 . During each of several runs under different conditions, we will determine the length of time (Δt) required for the concentration of one of the reactants ( 2 S O2 8 - ) to change by a certain fixed amount (Δ[ ]). This is similar to timing runners in a race. By measuring the amount of tome it takes each runner to run 1000 meters, we can calculate their running rates [Δ(distance)/Δ(time)], units of meters sec -1 . Determining the Order of Reaction What variables need to be considered? The kinetics of this reaction can be approximated using the general rate law: -1 a 2 R 2 8 ate=k[I ] S O - é ù ë û where a and b are termed the orders of reaction with respect to iodide and peroxydisulfate. The above rate law is fairly complex, having five variables (the two concentrations, a, b, and the rate constant). To simplify matters, the reactions is run staring with a known concentration of iodide (I-) and a known concentration of peroxydisulfate ( 2 S O2 8 - é ù ë û ). The change in the peroxydisulfate concentration with time (which is the rate) can be calculated from the elapsed time for the reaction. This eliminates two variables, leaving three unknowns in the rate equation (a, b and the PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

rate constant) What happens if two erimental runs are performed atroom temperature.and ony one concentration,say,[]is varied?For the first run, R=kI-S,O and for the second trial R=k[TSO:T Suppose that the in run 1 is twice that of run 2([),and the recall that S,Ois the same in both runs.Substituting into the first rate equation, R=k(21)[S.O:-T If we then divide the first ratequation by the second.we get the following expression =2 R Since both Rand R are known,this equation has only one unknown and can be solved for,the order of reaction with respect to a=In(R/R) In2 The order of b can be calculated in a similar manner by comparing the rates of two runs where only the S.Ochanges. Determining the Rate Constant Once a and b are known,the original rate equation has one unknown,the rate constant,k.It can then be determined directly.It should be remembered that the rate constant varies with temperature.This dependency may be investigated by performing similar runs(with the same initial concentrations)at several different temperatures.The relationship betweenk and temperature has the orm k=Ae-E This equation is known as the Arrhenius equation,where R is the gas law constant,T is temperature in K.E is the activation energy of the reaction.and A is the Arrhenius proportiornaiyfactorlum A more useful form of the Arrhenius equation can be arrived at by taking the natural logarithm of both sides and comparing it to the equation of a straight line: E Ink InA- RT Since we are interestedin howk varies with we cn rearrange this to become PDF文件使用"pdfFactory Pro”试用版本创建wnw,fineprint,com,cn

rate constant). What happens if two experimental runs are performed at room temperature, and only one concentration, say, [I- ], is varied? For the first run, b 2 1 2 8 1 S O a R k I - - = é ù é ù ë û ë û and for the second trial, b 2 2 2 8 2 S O a R k I - - = é ù é ù ë û ë û Suppose that the [I- ] in run 1 is twice that of run 2 ([I- ]1 = 2[I- ]2), and the recall that 2 S O2 8 - is the same in both runs. Substituting into the first rate equation, ( ) a b 2 1 2 8 2 R k I 2 S O - - = é ù é ù ë û ë û If we then divide the first rate equation by the second, we get the following expression: 1 2 (2) R a R = Since both R1 and R2 are known, this equation has only one unknown and can be solved for a, the order of the reaction with respect to [I- ]. 1 2 ln( / ) ln 2 R R a = The order of b can be calculated in a similar manner by comparing the rates of two runs where only the 2 S O2 8 - é ù ë û changes. Determining the Rate Constant Once a and b are known, the original rate equation has one unknown, the rate constant, k. It can then be determined directly. It should be remembered that the rate constant varies with temperature. This dependency may be investigated by performing similar runs (with the same initial concentrations) at several different temperatures. The relationship between k and temperature has the form / Ea RT k Ae- = This equation is known as the Arrhenius equation, where R is the gas law constant, T is temperature in K, Ea is the activation energy of the reaction, and A is the Arrhenius proportionality factor (unique to each reaction). The activation energy is the minimum amount of energy required for a collision between reactions to result in products. A more useful form of the Arrhenius equation can be arrived at by taking the natural logarithm of both sides and comparing it to the equation of a straight line: Ea ln k ln A RT = - Since we are interested in how k varies with T, we can rearrange this to become a 1 ln ln E k A R T æ ö = - + ç ÷ è ø PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

y=mx+b Thus,a plot of Ink(y axis)versus 1/T(x axis)gives a straight line with a slope equal to-Ea/R and a y intercept equal to In 4. In this experiment.we will determine the kinetic parameters of the reaction between iodide metal cationsact as catalysts in reactions,largely because they canexist different oxidation states.They can easily gain an election from one reactant and pass it on to another.The effect of the catalyst will be calculated by comparing runs with identical concentrations and temperatures,with and without the catalyst.Catalysts are very important in industrial applications,as they can greatly speed up a process or allow it to run at lower temper tures or pressure The main difficulty in performing a kinetics experiment is to devise a means by which to measure the rate of the reaction,that is,a way to signal when the reaction has progressed to a certain point.If this can be done accurately,then the SOwill be constant In that case. all we need todo it is measure the time it takesfor each rial toreach that pont. The reaction sequence in this experiment is 31 +S2O))+2S0 (1) Ivm +2S0 3+S.O (2) Starch+Starch-licomplex (3) Reaction2 occurs as long as thiosulfate (SO is present in solution.It reacts with the triiodide ions produced in Reaction I and converts them back to iodide.When the thiosulfate is used up.triiodide will start to accumulate and Reaction curs,producing a dark blue some time interva )thereisngin cormn (Shas reached the desired level.Since the same amount of thiosulfate is added toeachrun the same amount of peroxydisulfate is used up in each run,making A constant for all runs.Since rate=ASO/Atime,if two runs have similar times,their times indicate faster rates. Experimental Procedure PDF文件使用"pdfFactory Pro”试用版本创建wm,fineprint,com,cn

y = + mx b Thus, a plot of ln k (y axis) versus 1/T (x axis) gives a straight line with a slope equal to –Ea/R and a y intercept equal to ln A. In this experiment, we will determine the kinetic parameters of the reaction between iodide and peroxydisulfate. We will also examine the effect of a catalyst on the rate of the reaction. Many metal cations act as catalysts in reactions, largely because they can exist in solution in two or more different oxidation states. They can easily gain an election from one reactant and pass it on to another. The effect of the catalyst will be calculated by comparing runs with identical concentrations and temperatures, with and without the catalyst. Catalysts are very important in industrial applications, as they can greatly speed up a process or allow it to run at lower temperatures or pressures. The main difficulty in performing a kinetics experiment is to devise a means by which to measure the rate of the reaction, that is, a way to signal when the reaction has progressed to a certain point. If this can be done accurately, then the 2 D S O2 8 - é ù ë û will be constant. In that case, all we need to do it is measure the time it takes for each trial to reach that point. The reaction sequence in this experiment is - 2 - 2 (aq) 2 8 (aq) 3(aq) 4 (aq) 3I +S O I 2SO - - + (1) - 2 - 2 3(aq) 2 3 (aq) (aq) 4 6 (aq) I +2S O 3I S O - - + (2) - - S (aq) 3(aq) 3 tarch +I Starch-I complex (3) Reaction 2 occurs as long as thiosulfate ( ) 2 S O2 3 - is present in solution. It reacts with the triiodide ions produced in Reaction 1 and converts them back to iodide. When the thiosulfate is used up, triiodide will start to accumulate and Reaction 3 occurs, producing a dark blue starch-complex. Thus, two colorless solutions will be mixed together, and at some time interval (15 seconds to 4 minutes), there is a sharp change in color from clear to dark blue, indicating that ( ) 2 S O2 8 - has reached the desired level. Since the same amount of thiosulfate is added to each run, the same amount of peroxydisulfate is used up in each run, making 2 D S O2 8 - é ù ë û constant for all runs. Since 2 2 8 rate D D S O / time - = é ù ë û , if two runs have similar times, their times indicate faster rates. Experimental Procedure PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

Note:This experiment is most conveniently performed with partners.The concentrations in the tables are stock concentrations.The effective initia concentrations of I-and S must be caleulated,taking into accoun the dilution factor. Part A:Determining the Order of Reaction with Respect to lodide Refer to Table 1 for the amounts of reagents to be used for each run.The first four reagents (starch,NaSO,KI,KNO)should be pipetted into one 13x100mm test tube. Pour the contents of the second test tube into the first.noting the time of mixing to the nearest second.Pour back and forth between the test tubes three times to thoroughly mix the two solutions When the colorle mixture tums dark blue.note the elapsed time from the first mixing Discard the contents of the tube in a proper waste container.Each run should be done in duplicate Times for duplicate runs should be within 10%ofeach other. Part B:Determining the Order of Reaction with Respect to Peroxydisulfate Refer to Table 2 fo OF. ents to be used for e ach Part A.performing each run in duplicate.Times for duplicate runs should be within 0%of each other. Table 1. Reagent volumes for Determining the Order with respect to Idodide Reagents used (mL +0.01mL) 0.20M Run No.0.2%Starch 0.012M NazS2O3 KI (NH)2S2Os ( 010 02 0.10 0.20 0.40 0.40 0.40 0.40 3 0.10 0.20 0.20 0.60 0.40 0.40 0.10 0.20 0.10 0.70 0.40 0.40 Table 2. Reagent volumes for Determining the Order with respeet to Peroxydisulfate Reagents used (mL 0.01mL) 0.20M Run No.0.2%Starch 0.012M NazS2O3 KI KNO3 (NHA)2S2Os (NHa)2SO. 0.10 0.20 0.40 0.40 0.80 0.00 6 0.10 0.20 0.40 0.40 040 0.40 7 0.10 0.20 0.40 0.40 0.20 0.60 8 0.10 0.20 0.40 0.40 0.10 0.70 Part C:Determining the Activation Energy of the Reaction(Runs 9-12 Refer to Run 7 for the amounts of reagents to be used for each temperature run.Follow the PDF文件使用"pdfFactory Pro”试用版本创建n,fineprint,com,cn

Part A: Determining the Order of Reaction with Respect to Iodide Refer to Table 1 for the amounts of reagents to be used for each run. The first four reagents (starch, Na2S3O3, KI, KNO3) should be pipetted into one 13×100mm test tube. Pour the contents of the second test tube into the first, noting the time of mixing to the nearest second. Pour back and forth between the test tubes three times to thoroughly mix the two solutions. When the colorless mixture turns dark blue, note the elapsed time from the first mixing. Discard the contents of the tube in a proper waste container. Each run should be done in duplicate. Times for duplicate runs should be within 10% of each other. Part B: Determining the Order of Reaction with Respect to Peroxydisulfate Refer to Table 2 for the amounts of reagents to be used for each run. Follow the procedure in Part A, performing each run in duplicate. Times for duplicate runs should be within 10% of each other. Table 1. Reagent volumes for Determining the Order with respect to Idodide Reagents used (mL, ±0.01mL) 0.20M Run No. 0.2% Starch 0.012M Na2S2O3 KI KNO3 (NH4)2S2O8 (NH4)2SO4 1 0.10 0.20 0.80 0.00 0.40 0.40 2 0.10 0.20 0.40 0.40 0.40 0.40 3 0.10 0.20 0.20 0.60 0.40 0.40 4 0.10 0.20 0.10 0.70 0.40 0.40 Table 2. Reagent volumes for Determining the Order with respect to Peroxydisulfate Reagents used (mL, ±0.01mL) 0.20M Run No. 0.2% Starch 0.012M Na2S2O3 KI KNO3 (NH4)2S2O8 (NH4)2SO4 5 0.10 0.20 0.40 0.40 0.80 0.00 6 0.10 0.20 0.40 0.40 0.40 0.40 7 0.10 0.20 0.40 0.40 0.20 0.60 8 0.10 0.20 0.40 0.40 0.10 0.70 Part C: Determining the Activation Energy of the Reaction (Runs 9-12) Refer to Run 7 for the amounts of reagents to be used for each temperature run. Follow the Note: This experiment is most conveniently performed with partners. The concentrations in the tables are stock concentrations. The effective initial concentrations of I- and 2- S O2 8 must be calculated, taking into account the dilution factor. PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

600mLbea er of cold water),at room temperature (already done in Run 7),and at 10C and 20C (in a 600mL beaker of warm water)above room temperature. Insert the two test tubes with the pipetted reagents into the water bath for 5 minutes prior to mixing to allow the temperatures to equilibrate.After mixing,reinsert the full test tube into the vater duplicate runs sh Part D:Determining the Effect of a Catalyst(Runs 13-16) Refer to Runs 5-8 the amounts of reagents to be used for each run.Add 1 drop of .0020M Cu(NO to the test tube containing the peroxydisufate prior to mixing Follow the procedure e runs should be within Calculations NOTE:Before coming to laboratory,calculate the initial and S,using M:V;=M:V:for all runs,where V,is the volume of r or S,O used and V:is the total vlume.Record these on the data sheets. 1.Calculate the change in theS.The change is the same for all runs.(Hints:It is not equal to SO) M((.ImoIS,O 4[S,0g1= 2molS.O2 AV=1.all runs 2.Calculate the rate SOA for each run,using the average time for the duplicate runs. 3.Calculate a for Runs a and 2,2 and 3,and 3 and 4.Determine the average value. 4.Calculate b similarly for runs 5-8 5.Calculatek for all runs(k should be approximately the same for all uncatalyzed runs at room temperature). 6.If desired,the energy of activation may be determined in the following way,using the PDF文件使用"pdfFactory Pro”试用版本创建ww,fineprint.com,cn

procedure in Part A for pipetting the reagents. Do runs at about 10℃ below room temperature (in a 600mLbeaker of cold water), at room temperature (already done in Run 7), and at 10℃ and 20℃ (in a 600mLbeaker of warm water) above room temperature. Insert the two test tubes with the pipetted reagents into the water bath for 5 minutes prior to mixing to allow the temperatures to equilibrate. After mixing, reinsert the full test tube into the water bath, noting the elapsed time when it turns blue. Perform each trial in duplicate. Times for duplicate runs should be within 10% of each other. Record the temperature to ±0.1℃. Part D: Determining the Effect of a Catalyst (Runs 13-16) Refer to Runs 5-8 the amounts of reagents to be used for each run. Add 1 drop of 0.0020M Cu(NO3)2 to the test tube containing the peroxydisufate prior to mixing. Follow the procedure described in Part A, performing each run in duplicate. Times for duplicate runs should be within 10% of each other. Calculations 1. Calculate the change in the 2 S O2 8 - é ù ë û . The change is the same for all runs. (Hints: It is not equal to 2 S O2 8 - é ù ë û .) 2 2 2 2 8 2 3 2 3 2 2 2 8 2 8 total 1molS O (S O ) (S O ) 2molS O S O M V V D - - - - - × é ù = ë û DVtotal =1.9×10-3 Lfor all runs. 2. Calculate the rate ( ) 2 D D S2 8 O / t - é ù ë û for each run, using the average time for the duplicate runs. 3. Calculate a for Runs a and 2, 2 and 3, and 3 and 4. Determine the average value. 4. Calculate b similarly for runs 5-8. 5. Calculate k for all runs (k should be approximately the same for all uncatalyzed runs at room temperature). 6. If desired, the energy of activation may be determined in the following way, using the NOTE: Before coming to laboratory, calculate the initial [I- ] and 2 S O2 8 - é ù ë û using M1V1=M2V2 for all runs, where V1 is the volume of I￾or 2 S O2 8 - é ù ë û used and V2 is the total volume. Record these on the data sheets. PDF 文件使用 "pdfFactory Pro" 试用版本创建 ÿwww.fineprint.com.cn

Arrhenius equation(which is the equation of a straight line) nk=贸9}nd 7.Note the effect of adding a catalyst by comparing the averagek for Runs 5-8 with that of the catalyzed Runs 13-16.If the ratio=2.the catalyst causes the rate to double,for example. PDF文件使用"pdfFactory Pro”试用版本创建n,fineprint,com,cn

Arrhenius equation (which is the equation of a straight line): 1 ln ln Ea k A R T æ ö = + ç ÷ è ø 7. Note the effect of adding a catalyst by comparing the average k for Runs 5-8 with that of the catalyzed Runs 13-16. If the ratio cat uncat k k/ 2 = , the catalyst causes the rate to double, for example. PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

Pre-Laboratory Question: 1.Two kinetics runs are performed at the same temperature withS held constant and thein the first run being four times that in the second.Ifthe change in the concentration is 5x10M of S,and the reaction times are 20 seconds(Run 1)and 82 seconds(Run 2) what is theorder with respect to iodideon? 2.How cou on determine that the Cuionin the catalyst is the active species,rather than the nitrate ion? 3.Explain why the relationship M(S()molS 4「S,01= 2molS,O is correct. Name: Data: Section: PDF文件使用”pdfFactory Pro”试用版本创建wmw,fineprint..com,cn

Pre-Laboratory Question: 1. Two kinetics runs are performed at the same temperature with 2 S O2 8 - é ù ë û held constant and the [I-] in the first run being four times that in the second. If the change in the concentration is 5×10-5M of 2 S O2 8 - é ù ë û , and the reaction times are 20 seconds (Run 1) and 82 seconds (Run 2), what is the order with respect to iodide ion? 2. How could one determine that the Cu2+ ion in the catalyst is the active species, rather than the nitrate ion? 3. Explain why the relationship 2 2 2 2 8 2 3 2 3 2 2 2 8 2 8 total 1molS O (S O ) (S O ) 2molS O S O M V V D - - - - - × é ù = ë û is correct. Name:_______________________________________________________________________ Data:___________________ Section:______________________________________________ PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

Data Sheet,p.1 AS,M(same for all runs) A:Order of Reaction with Respect to Iodide Run No. Time(sec) Rate 「s,og1 (Triall) B:Order of Reaction with Respect to Peroxydisulfate Run No. Time(sec) Rate 「s,og1 Trial1)Trial2)4「s,0gVw C:Determination ofActivation Energy Run No. Temperature Time(sec) Rate (Trial 1)(Trial 2)AS,-/A 三三目 PDF文件使用"pdfFactory Pro”试用版本创建n,fineprint,com,cn

Data Sheet, p.1 2 D S O2 8 - é ù ë û _______M (same for all runs) A: Order of Reaction with Respect to Iodide Run No. Time (sec) Rate - [I ] 2 S O2 8 - é ù ë û (Trial 1) (Trial 2) 2 D D S2 8 O / t - é ù ë û 1 ________ _________ _________ _ ________ _________ 2 ________ _________ _________ _ ________ _________ 3 ________ _________ _________ _ ________ _________ 4 ________ _________ _________ _ ________ _________ B: Order of Reaction with Respect to Peroxydisulfate Run No. Time (sec) Rate - [I ] 2 S O2 8 - é ù ë û (Trial 1) (Trial 2) 2 D D S2 8 O / t - é ù ë û 5 ________ _________ _________ _ ________ _________ 6 ________ _________ _________ _ ________ _________ 7 ________ _________ _________ _ ________ _________ 8 ________ _________ _________ _ ________ _________ C: Determination of Activation Energy Run No. Temperature Time (sec) Rate (Trial 1) (Trial 2) 2 D D S2 8 O / t - é ù ë û 9 ____________ ________ ________ ________ 10 ____________ ________ ________ ________ 11 ____________ ________ ________ ________ 12 ____________ ________ ________ _ _______ Name:_______________________________________________________________________ Data:___________________ Section:______________________________________________ PDF 文件使用 "pdfFactory Pro" 试用版本创建 ÿwww.fineprint.com.cn

Data Sheet,p.2 D:Run with Catalyst Run No. Time Time Time (Trial 1)(Trial2) Uncatalyzed(from Part B) 15 Determine the rate law (clearly indicating the orders and rate constant)for this reaction from the lata in Part Aand B Compare the rate constant for Runs 5-8 with those Runs 13-16.What was the effect of adding a catalyst? Name: Data: Section: PDF文件使用"pdfFactory Pro'试用版本创建m,fineprint.con,cn

Data Sheet, p.2 D: Run with Catalyst Run No. Time Time Time (Trial 1) (Trial 2) Uncatalyzed (from Part B) 13 ________ _________ _______________ 14 ________ _________ _______________ 15 ________ _________ _______________ 16 ________ _________ _______________ Determine the rate law (clearly indicating the orders and rate constant) for this reaction from the data in Part A and B. Compare the rate constant for Runs 5-8 with those Runs 13-16. What was the effect of adding a catalyst? Name:_______________________________________________________________________ Data:___________________ Section:______________________________________________ PDF 文件使用 "pdfFactory Pro" 试用版本创建 ÿwww.fineprint.com.cn

Data Sheet,p.3 E:Temperature Relationships From the data in Part C,determine the relationship between k and T.Attach a graph of Ink vs.1/T, and from the slope,determine the slope,determine Ea Show the calculation of the slope and Ea below.What are the units of the slope? Name:_ Data: Section: PDF文件使用"pdfFactory Pro”试用版本创建www.fineprint..com.cn

Data Sheet, p.3 E: Temperature Relationships From the data in Part C, determine the relationship between k and T. Attach a graph of lnk vs. 1/T, and from the slope, determine the slope, determine Ea. Show the calculation of the slope and Ea below. What are the units of the slope? Name:_______________________________________________________________________ Data:___________________ Section:______________________________________________ PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn

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