Chemical Engineering Department

Chemical Engineering DepartmentCBB 2074 REACTION ENGINEERING

CHAPTER 5: COLLECTION AND ANALYSIS OF RATE DATA

1Determine the reaction order and reaction rate using the appropriate technique for a given experimental data set

2OBJECTIVES OF CHAPTER 5LECTURELEARNING OBJECTIVES1At the end of the lecture, students should be able to:Explain various method of data analysisPerform data analysis using the following techniques:Differential method of analysisIntegral method of analysisMethod of initial ratesMethod of half livesAnalyse data obtained from a differential reactor system3Learning objectivesAnalysis of Data to find Rate Law2 common reactors used to obtain rate data:Batch reactorDifferential reactor

Methods used to analyse rate data:Differential methodIntegral methodHalf live methodInitial rate methodLinear regressionNon-linear regressionConsider the following reaction:A Products

Mole balance:

Rate Law:

Stoichiometry:

Combine:Analysis of Data to find Rate Law

Analysis of Data to find Rate LawMETHOD 1: DIFFERENTIAL METHOD OF ANALYSIS6Take the log of

Plot graph of ln (-dCA/dt) vs. ln CA gives straight line graph with:Slope = Intercept = ln k

Analysis of Data to find Rate Law

Analysis of Data to find Rate LawMETHOD 2: INTEGRAL METHOD OF ANALYSIS8Need to guess reaction order and integrate the differential form of equation used to model the reactor used.If the right reaction order is assume, the plot of concentration time data should be linear3 examples will be considered:Zero orderFirst orderSecond order

Analysis of Data to find Rate LawZero order reaction:

Integration gives:Analysis of Data to find Rate Law~Integral method analysis~

t=CA0 / kSlope = -ktCACA0First order reaction:

Integration gives:Analysis of Data to find Rate Law~Integral method analysis~

tln CA0/CASlope = kSecond order reaction:

Integration gives:Analysis of Data to find Rate Law~Integral method analysis~

tSlope = kIntercept = 1/CA01/CAAnalysis of Data to find Rate LawMETHOD 3: METHOD OF INITIAL RATE13The presence of reverse reaction causes differential and integral method ineffective in analysing the rate dataPerform a series of experiment at different initial concentration, CA0, and evaluate the initial rate, -rA0 for each run.Analysis of Data to find Rate LawAnalysis of Data to find Rate LawMETHOD 4: METHOD OF HALF LIVES15Half-live, t1/2, is define as:

Consider:

Integration gives:

Half live, t1/2, occur at CA = CA0Analysis of Data to find Rate Law

Taking natural log gives:Analysis of Data to find Rate Law~Method of half-lives~

Slope = 1-ln CA0ln t1/2Differential reactorsNormally used to determine rate of reaction as a function of either concentration or pressureCriteria of a differential reactor:Conversion of reactant along catalyst bed is very smallConcentration change of reactant along catalyst bed is very smallLow conversion means heat release is small therefore reactor is essentially isothermal.Analysis of Data to find Rate LawANALYSING DATA FROM DIFFERENTIAL REACTOR19Design equation similar to CSTR due to gradientless criteriaDifferential reactorsLFA0FAeInert filingCatalyst

Example:The formation of methane form carbon monoxide and hydrogen using a nickel catalyst was studied by Pursley. The reaction, 3H2+COCH4+2H2O, was carried out at 500 F in a differential reactor where the effluent concentration of methane was measured. The exit volumetric flowrate was maintain at 300 dm3/min. The weight of catalyst is maintain at 10g. The partial pressure of H2 and CO was measured at reactor exit.Relate the rate of reaction to the exit methane concentrationDetermine the reaction order with respect to CO using data from Table E5-4.1 assuming the rate law is a function of rA=f(PCO)

Differential reactorsDifferential reactorsRunPCO (atm)PH2 (atm)CCH4 (g mol/dm3)11.01.02.44 x 10-421.81.034.081.041.00.151.00.561.04.0TABLE E5-4.1END OF LECTURE 23Example 5-1: Differential method of analysisThe following reaction takes place in an isothermal batch reaction system. The reaction scheme is given below and the experimental result is given in Table E5-1.1. Find the reaction rate constant of the reaction.

A + B C + DAnalysis of Data to find Rate Law~Differential method analysis~Time (min)Concentration (mol/dm3) x 1030.050503810030.615025.620022.225019.530017.4Table E5-1.1