.MCAD 303010000 1 74 35 0 .CMD PLOTFORMAT 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 NO-TRACE-STRING 0 2 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 21 15 0 3 .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0 .CMD SET ORIGIN 0 .CMD SET TOL 0.001000000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 4 .CMD PRINT_SETUP 1.200000 0.983333 1.200000 1.200000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty* .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=2 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .TXT 2 1 30 0 Cg b73.000000,73.000000,288 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {\b \fs28 Activation Energy: Exponential Regression Analysis\par }{\par }{\i \fs24 }{\i \fs24 Zoran Zdravkovski, Institute of Chemistry, Skopje, Macedoni}{\i \fs24 a}{\par \par The rate constant is a function of the temperature and can be calculated from the }{\i Arrhenius }{equation: }} } .EQN 19 18 29 0 {0:k}NAME:{0:A}NAME*({0:e}NAME)^(-((({0:Ea}NAME)/({0:R}NAME*{0:T}NAME)))) .TXT 4 -18 28 0 Cg b73.000000,73.000000,832 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {\par The same formula can be used to calculate the activation energy }{\i E}{a from a set of experimentally determined rate constants at different temperatures. For example, in the hydrolysis of 2-chloro-2-methylpropane, the following data was obtained: \par \par }{\i T}{/K 30 298 293 288 283\par }{\i k}{*10^2 9.41 3.59 3.08 2.44 1.82\par \par The exponential equations can be converted to the linear form by taking the logarithm of both sides, which in our case would give: Plotting ln}{\i k}{ against 1/}{\i T}{ should give an approximately straight line relationship with a slope, }{\i E}{a/}{\i R}{ and an intercept, ln}{\i A}{. In this case the calculations involve the lnk values instead of the plain }{\i k}{ values, and the reciprocal values of the temperature.\par }} } .EQN 40 2 1 0 {0:k}NAME:({5,1}1.82*(10)^(-2)2.44*(10)^(-2)3.08*(10)^(-2)5.59*(10)^(-2)9.41*(10)^(-2)) .EQN 0 16 2 0 {0:T}NAME:({5,1}283288293298303) .TXT 5 13 19 0 Cg a9.500000,42.000000,15 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {gas constant}} } .EQN 0 13 3 0 {0:R}NAME:8.3136 .TXT 4 -13 18 0 Cg a5.800000,42.000000,10 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {counter}} } .EQN 0 13 4 0 {0:i}NAME:0;{0:last}NAME({0:T}NAME) .TXT 5 -44 32 0 Cg a17.500000,70.000000,33 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {natural logarithm of }{\i k}{:}} } .TXT 0 31 33 0 Cg a28.300000,39.000000,39 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {reciprocal value of the temperature:}} } .EQN 4 -28 5 0 ({0:lnk}NAME)[({0:i}NAME):{0:ln}NAME(({0:k}NAME)[({0:i}NAME)) .EQN 0 36 6 0 ({0:Tr}NAME)[({0:i}NAME):(1)/(({0:T}NAME)[({0:i}NAME)) .TXT 8 -39 34 0 Cg a41.100000,72.000000,55 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {the correlation is between these transformed values:}} } .EQN 4 0 7 0 {0:corr}NAME({0:Tr}NAME,{0:lnk}NAME)={18996}?_n_u_l_l_ .EQN 3 0 8 0 {0:a}NAME:{0:slope}NAME({0:Tr}NAME,{0:lnk}NAME) .EQN 0 20 10 0 {0:Ea}NAME:-{0:a}NAME*{0:R}NAME .TXT 0 20 26 0 Cg a13.500000,33.000000,20 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {activation energy}} } .EQN 0 17 11 0 {0:Ea}NAME={0}?_n_u_l_l_ .EQN 5 -57 12 0 {0:lnA}NAME:{0:intercept}NAME({0:Tr}NAME,{0:lnk}NAME) .EQN 0 18 13 0 {0:lnA}NAME={0}?_n_u_l_l_ .EQN 0 13 14 0 {0:A}NAME:({0:e}NAME)^({0:lnA}NAME) .TXT 0 9 27 0 Cg a14.700000,33.000000,21 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {Arrhenius constant}} } .EQN 0 17 15 0 {0:A}NAME={0}?_n_u_l_l_ .EQN 7 -56 24 0 {0:Tg}NAME:283,283.2;303 .TXT 0 19 22 0 Cg a13.100000,60.000000,19 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {regression curve}} } .EQN 0 16 23 0 {0:kr}NAME({0:Tg}NAME):{0:A}NAME*({0:e}NAME)^(-(({0:Ea}NAME)/({0:R}NAME*{0:Tg}NAME))) .EQN 3 -35 20 0 0.1&0&(_n_u_l_l_&_n_u_l_l_)&({0:k}NAME)[({0:i}NAME),{0:kr}NAME({0:Tg}NAME)@310&280&(_n_u_l_l_&_n_u_l_l_)&({0:T}NAME)[({0:i}NAME),{0:Tg}NAME 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 32 17 0 3 .TXT 31 -1 35 0 Cg a70.300000,71.000000,422 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {\b References}{:\par \par 1. Z. Zdravkovski, Mathcad in Chemistry Calculations, }{\i J. Chem. Ed.}{ }{\b 1991}{, }{\i 68}{, A95 and }{\b 1992}{, }{\i 69}{, A240.\par \par 2. T. R. Dickson, The Computer and Chemistry, W. H. Freeman, San Francisco, 1968 .\par \par 3. P. W. Atkins, Physical Chemistry, W. H. Freeman, New York, 4th Ed., 1990.\par \par 4. J. Freund, Modern Elementary Statistics, Prentice-Hall, Englewood Cliffs, 1979.\par \par }} }