Second order reactions: I

<BODY LANG="EN"> <HR><center> <table border=1> <td><A NAME="tex2html48" HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A NAME="tex2html54" HREF="node2.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html56" HREF="node5.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR><H2><A NAME="SECTION00022000000000000000">Second order reactions: I</A></H2> <P> For a bimolecular reaction involving a single species <I>A</I> where <P> <P> <IMG WIDTH=324 HEIGHT=15 ALIGN=BOTTOM ALT="displaymath107" SRC="img4.gif" > <P> <P> in a single elementary step, the rate law is <P> <P> <IMG WIDTH=302 HEIGHT=35 ALIGN=BOTTOM ALT="displaymath109" SRC="img5.gif" > <P> <P> Several types of non-linear equations require loading of a special Mathematical library. Do this for the rest of this session by executing the command: <P> <table><td valign=top><a href="/hamlet-bin/qhandler/send5.hamlet?execute" target="results"><img height=24 width=24 alt="EXECUTE" src="/UCESIcons/tools/execute.gif"></a></td><td valign=top><code> <<Calculus`DSolve`;</code></td></table> <P> Now modify the DSolve command for the first order reaction above to solve for this case.....be sure to clear the constants <I>k</I> and <I>a</I>0, or your will not get a "general"solution. To see what this means. You could "not" clear <I>k</I> and <I>a</I>0, run DSolve, and then clear them and repeat....what is the difference? Does this make sense? A bit later we will see that working with the general solution (i.e. the solution expressed in terms of the arbitrary constants <I>k</I> and <I>a</I>0) is rather more useful than one expressed in terms of specific pre-set values. <P> <I>Q: Determine the half-life from a plot generated for the case <I>a</I>0=1.0 and for the case <I>a</I>0=10.0. Is there a definite half-life for this reaction? Namely, does the half life in this case depend on <I>a</I>0? How does this differ from the first order case? If you only had experimental data for the concentration of the chemical <I>A</I> at various times, what kind of graph would tell whether the reaction is first order or second order? Illustrate with a plot for each case.</I> <P> <HR><center> <table border=1> <td><A NAME="tex2html48" HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A NAME="tex2html54" HREF="node2.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html56" HREF="node5.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I>Hannes Jonsson<BR> Modified by Thomas L. Marchioro II<BR> and the <A NAME="tex2html1" HREF="/UCES/">Undergraduate Computational Engineering and Science project</A> </I> </ADDRESS> </BODY>