(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 123433, 3004]*) (*NotebookOutlinePosition[ 124292, 3033]*) (* CellTagsIndexPosition[ 124248, 3029]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Computing the Enthalpy of a Reaction", FontSize->18], StyleBox["\n", FontSize->24], StyleBox["Theresa Julia Zielinski\nMonmouth University\nDepartment of \ Chemistry\nWest Long Branch, NJ 07764\ntzielins@monmouth.edu", "Text", FontSize->14] }], "Text", TextAlignment->Center], Cell["\<\ \[Copyright] Copyright Theresa Julia Zielinski, 2004. All rights \ reserved.You are welcome to use this document in your own classes but \ commercial use is not allowed without the permission of the author.\ \>", "Text"], Cell[TextData[{ "This document is based on the ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook directions given in \"Physical Chemistry Using ", StyleBox["Mathematica\"", FontSlant->"Italic"], " by Joseph H. Noggle; Harper Collins College Publishers, New York, 1996, \ pp151-5. Data used in the calculations were prepared by Dr. Noggle using \ Tables from his Physical Chemistry textbook. The data files were updated to \ work with ", StyleBox["Mathematica", FontSlant->"Italic"], " 5. These data tables must be loaded before using the processes in this \ notebook. The data files are FRXDATA.ma and CPDATA.ma. \n" }], "Text"], Cell["\<\ First set the values for the gas constant and the reference temperature.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(R = 8.314; \ Tref = 298.15\)\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(298.15`\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Next make sure that you have both this notebook file \ and the data files FXDATA and CPDATA in the same directory. Use SetDirectory \ so that it matches the directory name on your system. 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FontVariations->{"Underline"->True}], ButtonFunction:>( Internal`PutInformation[ #, LongForm -> False]&), ButtonEvaluator->Automatic, ButtonData:>{"Info3286089724-2123795", "Global`fxSO3Ion"}, ButtonFrame->"None", ButtonNote->"Global`"], ""} }, RowMinHeight->{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1.05}]} }, RowSpacings->{2, 3}, ColumnAlignments->{Left}, ColumnsEqual->True]], "Print", CellMargins->{{20, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, CellFrameMargins->{{Inherited, Inherited}, {14, 14}}, Background->RGBColor[0.964706, 0.929412, 0.839216], ButtonBoxOptions->{Active->True}] }, Open ]], Cell[TextData[{ "\nAbove we see that we have the data for a large number of compounds.\n\ These data can be used to find the enthalpy of reaction for many reactions \ under condiditons\nwhere ", Cell[BoxData[ \(TraditionalForm\`C\_\(\(P\)\(\ \)\)\)]], "is a constant or where ", Cell[BoxData[ \(TraditionalForm\`C\_P\)]], " is a function of tempera\nB", Cell[BoxData[ \(TraditionalForm\`oth\ types\ of\ calculation\ will\ be\ shown\ in\ \ this\ \(\(notebook\)\(.\)\(\ \)\)\)]] }], "Text", PageWidth->WindowWidth], Cell[TextData[{ "\nCompute the heat of reaction for CO(g) +", Cell[BoxData[ FormBox[ RowBox[{\(1\/2\), " ", StyleBox["O", FontSlant->"Plain"]}], TraditionalForm]]], " ", Cell[BoxData[ \(TraditionalForm\`\_2\)]], "(g) = ", Cell[BoxData[ \(TraditionalForm\`CO\_2\)]], "(g)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(TableForm[{fxCO, \ fxO2, \ fxCO2}, TableHeadings -> {{"\", \*"\"\<\!\(O\_2\)\>\"", \*"\"\<\!\(CO\_2\)\ \>\""}, {\*"\"\<\!\(\[CapitalDelta]\_f\)H\>\"", \*"\"\<\!\(\[CapitalDelta]\_f\ \)G\>\"", \*"\"\<\!\(S\_f\^0\)\>\"", \*"\"\<\!\(C\_P\)\>\""}}\ ]\)\)\)], \ "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\"\>", "\<\"\\!\\(\[CapitalDelta]\\_f\\)H\"\>", "\<\"\\!\\(\ \[CapitalDelta]\\_f\\)G\"\>", "\<\"\\!\\(S\\_f\\^0\\)\"\>", \ "\<\"\\!\\(C\\_P\\)\"\>"}, {"\<\"CO\"\>", \(-110.525`\), \(-137.168`\), "197.674`", "29.142`"}, {"\<\"\\!\\(O\\_2\\)\"\>", "0", "0", "205.138`", "29.355`"}, {"\<\"\\!\\(CO\\_2\\)\"\>", \(-393.509`\), \(-394.359`\), "213.74`", "37.11`"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableHeadings -> {{"CO", "\!\(O\_2\)", "\!\(CO\_2\)"}, { "\!\(\[CapitalDelta]\_f\)H", "\!\(\[CapitalDelta]\_f\)G", "\!\(S\_f\^0\)", "\!\(C\_P\)"}}]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(rxndata = fxCO2 - fxCO - 1/2 fxO2\)], "Input"], Cell[BoxData[ \({\(-282.98400000000004`\), \(-257.191`\), \(-86.503`\), \ \(-6.7095`\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(datatable = TableForm[{fxCO2 - fxCO - 1/2 fxO2}, TableHeadings \[Rule] {None, {\*"\"\<\!\(\[CapitalDelta]\_rx\)H in kJ\ \>\"", \*"\"\<\!\(\[CapitalDelta]\_rx\)G in kJ\>\"", \*"\"\<\!\(\ \[CapitalDelta]\_rx\)\!\(S\^0\) in J/K\>\"", \*"\"\<\!\(\[CapitalDelta]C\_P\) \ in J/K\>\""}}]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\\!\\(\[CapitalDelta]\\_rx\\)H in kJ\"\>", "\<\"\\!\\(\ \[CapitalDelta]\\_rx\\)G in kJ\"\>", \ "\<\"\\!\\(\[CapitalDelta]\\_rx\\)\\!\\(S\\^0\\) in J/K\"\>", "\<\"\\!\\(\ \[CapitalDelta]C\\_P\\) in J/K\"\>"}, {\(-282.98400000000004`\), \(-257.191`\), \(-86.503`\), \ \(-6.7095`\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableHeadings -> {None, { "\!\(\[CapitalDelta]\_rx\)H in kJ", "\!\(\[CapitalDelta]\_rx\)G in kJ", "\!\(\[CapitalDelta]\_rx\)\!\(S\^0\) in J/K", "\!\(\[CapitalDelta]C\_P\) in J/K"}}]]]], "Output"] }, Open ]], Cell["\<\ This table contains the thermodynamic properties at Tref. Next we will calculate the heat of reaction at 1000 K. But first convert \ values to J/mol.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(DHrx = rxndata[\([1]\)]*1000\[IndentingNewLine] DCprx = rxndata[\([4]\)]\)\)\)], "Input"], Cell[BoxData[ \(\(-282984.00000000006`\)\)], "Output"], Cell[BoxData[ \(\(-6.7095`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(DHatT = DHrx + Integrate[DCprx, {T, Tref, T}]\)\)\)], "Input"], Cell[BoxData[ \(\(-280983.56257500005`\) - 6.7095`\ T\)], "Output"] }, Open ]], Cell[TextData[{ "\nThis result is the expression for the temperature dependence of \ \[CapitalDelta]", Cell[BoxData[ \(TraditionalForm\`\(\_rx\) H\^0\)]], "in joules. Notice the function is linear. However, this result uses \ constant C", Cell[BoxData[ \(TraditionalForm\`\_P\)]], "values. It would be better to use C", Cell[BoxData[ \(TraditionalForm\`\_P\)]], "(T) to get a general function for C", Cell[BoxData[ \(TraditionalForm\`\_P\)]], " to use in the integration. We do this by attaching the CPDATA file. \n " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(<< CPDATA.ma\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ \("Symbols cpm*"\)], "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(?cpm*\)\)\)], "Input"], Cell[BoxData[GridBox[{ { StyleBox["Global`", FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold"]}, {GridBox[{ { ButtonBox[ StyleBox["cpmBr2gas", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}], ButtonFunction:>( Internal`PutInformation[ #, LongForm -> False]&), ButtonEvaluator->Automatic, ButtonData:>{"Info3286089724-1913632", "Global`cpmBr2gas"}, ButtonFrame->"None", ButtonNote->"Global`"], ButtonBox[ StyleBox["cpmC2H4", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}], ButtonFunction:>( Internal`PutInformation[ #, LongForm -> False]&), ButtonEvaluator->Automatic, ButtonData:>{"Info3286089724-1913632", "Global`cpmC2H4"}, ButtonFrame->"None", 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This list consists of the gaseous compounds only. Solids \ and liquids do not change heat capacity as a function of temperature \ significantly. The heat capacity of gases, on the other hand, are vary \ strongly with temperature. \n \n Now we will compute the function for \ \[CapitalDelta]C", Cell[BoxData[ \(TraditionalForm\`\_P\ for\ the\ reaction\ of\ CO\ with\ \ \(\(oxygen\)\(.\)\)\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(DCpT = Simplify[cpmCO2 - cpmCO - 1/2 cpmO2]\)\)\)], "Input"], Cell[BoxData[ \(\(\(0.6499999999999968`\)\(\[InvisibleSpace]\)\) - 762500.`\/T\^2 + 0.004475`\ T - 1.0200000000000002`*^-6\ T\^2\)], "Output"] }, Open ]], Cell["\<\ The result is a function of temperature and very easy to use. Next we check \ this function by computing the heat capacity for the reference temperature. \ \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\({\ DCpT /. T -> Tref}\)\)\)], "Input"], Cell[BoxData[ \({\(-6.684137552081664`\)}\)], "Output"] }, Open ]], Cell["\<\ Compare this to the previous value. What is the percent difference between \ the two approaches to computing the heat capacity for the reaction at the \ reference temperature. What can you say about the simpler method for \ evaluating heat capacity? Is a function of temperature needed for \ calculations at the reference temperature? Next compute the heat of reaction for the combustion of CO using heat \ capacities as a function of temperature. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(DHTT = DHrx + Integrate[DCpT, {T, \ Tref, \ T}, Assumptions \[Rule] \ T > 0]\)\)\)], "Input"], Cell[BoxData[ \(\(-282984.00000000006`\) - \(3.4000000000000003`*^-7\ \ \((\(-6680.750313607696`\) + T)\)\ \((\(-880.5776607570656`\) + T)\)\ \ \((\(-298.15`\) + T)\)\ \((\(\(1278.5956214235853`\)\(\[InvisibleSpace]\)\) + \ T)\)\)\/T\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(tlist = {Tref, 500, 750, 1000, 1250, 1500, 1750, 2000}\)\)\)], "Input"], Cell[BoxData[ \({298.15`, 500, 750, 1000, 1250, 1500, 1750, 2000}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(TableForm[{{T, DHatT/1000, DHTT/1000} /. 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{\(-283.3057999324888`\)}, {\(-282.61512284915545`\)}, {\(-281.67059159915544`\)}, {\(-280.55491451582213`\)}, {\(-279.3217523134412`\)}, {\(-278.01387284915546`\)} }, RowSpacings->0.25, ColumnSpacings->1, RowAlignments->Baseline, ColumnAlignments->{Left}]} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Center}], TableForm[ {{{298.14999999999998, 500, 750, 1000, 1250, 1500, 1750, 2000}, {-282.98400000000004, -284.33831257500003, \ -286.01568757500007, -287.69306257500006, -289.37043757500004, \ -291.04781257500008, -292.72518757500006, -294.40256257500005}, \ {-282.98400000000004, -283.55824784915546, -283.30579993248881, \ -282.61512284915545, -281.67059159915544, -280.55491451582213, \ -279.32175231344121, -278.01387284915546}}}, TableHeadings -> {None, {"Temp", "\[CapitalDelta]H constant \!\(C\_P\)", "\[CapitalDelta]H \!\(C\_\(\(P\)\(\\ \)\)\)as a function of T"}}]]], \ "Output"] }, Open ]], Cell[TextData[{ "The table above contains the heat of reaction computed with ", Cell[BoxData[ FormBox[ SubscriptBox["C", StyleBox["P", FontSlant->"Plain"]], TraditionalForm]]], StyleBox[" ", FontSlant->"Italic"], "constant and with ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["C", RowBox[{ StyleBox["P", FontSlant->"Plain"], " "}]], "as", " ", "a", " ", "function", " ", "of", " ", \(\(temperature\)\(.\)\(\ \)\)}], TraditionalForm]]], "How do these compare as temperature increases?\n" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(plot1 = Plot[{DHrx/1000, DHatT/1000, DHTT/1000}, {T, \ Tref, \ 1000}, AxesLabel \[Rule] {"\", \ \ \*"\"\<\!\(\[CapitalDelta]H\_rx\)/kJ\>\""}]\)\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont 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The \ linear line sloping downward is the ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_rx\)]], "H when the heat capacity is constant. The curved line is the heat of \ reaction when the heat capacity is a function of temperature. The curved line \ is the heat of reaction when the heap capacity is a function of temperature. \ How does the enthalpy of a reaction change as a function of temperature? Is \ the approxomation holding the heat capacity constant good, bad, or \ indifferent?\n\n", StyleBox["Mastery Exercise", FontWeight->"Bold"], ": Repeat the steps in this notebook for the formation of HCl from \ component gases. Compare the results for HCl to that shown here for carbon \ dioxide. For which reaction is the assumption of constant heat capacity most \ valid? Justify your answer by specific reference to plots generated during \ completion of the exercise.\n", Cell[BoxData[ FormBox[ StyleBox[\(\(\ \)\(\[IndentingNewLine]\)\), "Text"], TraditionalForm]]] }], "Text"] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 991}, {0, 662}}, AutoGeneratedPackage->Automatic, ScreenStyleEnvironment->"Working", PrintingStyleEnvironment->"Printout", WindowToolbars->"RulerBar", WindowSize->{983, 628}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, ShowSelection->True ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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