ÿþ<html> <head> <title>The Mole: Calculating moles, atoms, molecules and grams </title> <script language="JavaScript"> <!-- Begin function move_in(img_name,img_src) { document[img_name].src=img_src; } function move_out(img_name,img_src) { document[img_name].src=img_src; } // --> <!-- Begin image1 = new Image(); image1.src = "step.1.1.gif"; image2 = new Image(); image2.src = "step.1.2.gif"; image3 = new Image(); image3.src = "step.2.1.gif"; image4 = new Image(); image4.src = "step.2.2.gif"; image5 = new Image(); image5.src = "step.3.1.gif"; image6 = new Image(); image6.src = "step.3.2.gif"; image7 = new Image(); image7.src = "step.4.1.gif"; image8 = new Image(); image8.src = "step.4.2.gif"; image9 = new Image(); image9.src = "step.5.2.gif"; image10 = new Image(); image10.src = "step.6.2.gif"; // End --> </script> <script language='javascript'> function popup_window( url, id, width, height ) { popup = window.open( url, id, 'toolbar=no,scrollbars=no,location=no,statusbar=no,menubar=no,resizable=no,width=' + width + ',height=' + height + '' ); popup.focus(); } </script> </head> <body> <center><table width=500> <tr><td colspan=2><hr color=#990000></td></tr> <tr><td><img src="danalysis.gif" width=200 alt="dimensional analysis"></td> <td><font size=5 color=#990000>Lecture 2:<br>Calculating moles, atoms, molecules and grams </font><br><br> To calculate the relationship between moles-atoms-molecules and grams, many skills must be mastered. While there are many approaches to the solution, dimensional analysis or the factor-label method is best to use. To successfully use this method, one must also be able to use a scientific calculator and express the answer in the proper form. </td></tr> <tr><td colspan=2> <font face=arial color=#990000 size=4>Dimensional Analysis:</font><br><br> Dimensional analysis is a method by which many chemistry problems can be solved. Also known as factor-label, this process involves the multiplication of a number by a conversion factor that is equal to one so that labels are canceled. This process continues until the desired answer is achieved. The idea is that a given number and unit can be multiplied by a conversion factor so that the unit can be canceled. Because the conversion factor is always equal to one, this process is mathematically correct. For instance:<br><br> <center><A HREF="#"onmouseover="move_in('step1','pencils.1.2.gif')" onmouseout="move_out('step1','pencils.1.1.gif')"> <IMG NAME="step1" SRC="pencils.1.1.gif" border=0 ALT="Image"></A></center><br> It's true! A box of five dozen, is equal to 60 pencils. Pass the cursor over the problem and see that the labels cancel. This process can work in the reverse as well, inverting the conversion factor. For instance:<br><br> <center><A HREF="#"onmouseover="move_in('step2','pencils.2.2.gif')" onmouseout="move_out('step2','pencils.2.1.gif')"> <IMG NAME="step2" SRC="pencils.2.1.gif" border=0 ALT="Image"></A></center><br> For more complex problems many conversion factors may be used, the rule of thumb, "whatever goes on the top, goes on the bottom." Here is an example involving several conversion factors.<br><br> <font face=arial size=3><b>How many inches are in 2.5 yards?</b></font><br> <center><img src="dim_analysis_ex1.gif" width=500></center><br> <center><a href="dim_analysis_ex1/dim_analysis_ex1.htm" target=new>Show Me How This Is Done!</a></center> The factor-label method is particularly suited for converting from english to metric units. To convert from english length units, say 1 foot, to metiric units, say meters, the conversion 1 inch = 2.54 centimeters can be used.<br><br> <center><A HREF="#"onmouseover="move_in('step3','metric.1.2.gif')" onmouseout="move_out('step3','metric.1.1.gif')"> <IMG NAME="step3" SRC="metric.1.1.gif" border=0 ALT="Image" width=500></A></center><br> While you can memorize all the english to metric conversions, only three need be committed to memory. One for each of the types of measurements; mass, length and volume. For this class you are responsible for three conversions:<br><br> <center><table width= 450 border=1 bgcolor=lightyellow> <tr><td><center>Type</center></td><td><center>English</center></td><td><center>Metric</center></td></tr> <tr><td><center>Mass</center></td><td><center>2.2 lb</center></td><td><center>1 kg</center></td></tr> <tr><td><center>Volume</center></td><td><center>1 gal</center></td><td><center>3.78 lt</center></td></tr> <tr><td><center>Length</center></td><td><center>1 in</center></td><td><center>2.54 cm</center></td></tr> </table></center><br><br> The steps for dimensional analysis are:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <a href="dim_analysis_ex1/dim_analysis_ex1.htm" target=new>Show Me This in Action!</a><br><br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1. ask the question with units<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2. write what is given<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3. whatever label goes on the top, goes on the bottom<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4. plug in the conversion numbers<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5. cancel any labels<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6. check the label<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7. if it is the same, stop and multiply<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8. if it is different go back to step 3<br><br> In table form: <br><br> <center><img src="da_flow_chart.gif"></center><br> <center><font face=arial size=3><b>Flow Chart for Dimensional Analysis</b></font></center><br> Master dimensional analysis by completing Task 1: Converting English to Metric<br><br> <font face=arial color=#990000 size=4>Calculating<br>Atoms-Molecules-Moles:</font><br><br> To apply the factor-label method to calculations between moles-atoms-molecules and grams, the relationship between these units must be understood. From Unit 1, one mole of any element is equal to the rounded atomic mass. For example: 1 mole of <a href="javascript:popup_window( 'oxygen.htm', 'mole_grams', 150, 225 );">oxygen</a> is equal to 16 grams, 1 mole of <a href="javascript:popup_window( 'nitrogen.htm', 'mole_grams', 150, 225 );">nitrogen</a> is equal to 14 grams. As a conversion then, 1 mole = 16 g or:<br><br> <center> <table> <tr><td><img src="conversion1a.gif" width=50></td><td width=100 valign=center><center><b>or</b></center> </td><td><img src="conversion1a.gif" width=50></td> </tr></table></center><br><br> Graphically:<br><br> <center><img src="relationship.gif"><br><font face=arial size=2><b>Stoichiometric Relationships</b></font></center><br><br> Also from Unit 1, one mole is equal to Avagadro s number, 6.02 x 10<sup>23</sup>. So <br>1 mole = 6.02 x 10<sup>23</sup> atoms or if it is a compound, 1 mole = 6.02 x 10<sup>23</sup>.<br><br> Graphically:<br><br> <center><img src="relationship2.gif"><br><font face=arial size=2><b>Stoichiometric Relationships</b></font></center><br><br> With these conversions in mind, find solutions to the following problems:<br><br> <font face=arial size=2><b>Example 1: How many grams are in 2.5 moles of iron (Fe)?</b></font><br><br> <center><table border=0><tr><td> <center><img src="example1.gif" height=50></center><br><br></td></tr> <tr><td> <UL> <font face=arial size=2><b>Steps</b></face><br> Step 1: Write what is needed<br> Step 2: Equals to what<br> Step 3: What ever goes on the top, goes to the bottom<br> Step 4: Moles go to grams<br> Step 5: Add the number values from the periodic table<br> Step 6: Cancel the labels<br> Step 7: Check the labels and stop or continue<br> Step 8: Labels the same, stop and calculate<br> </ul> </td></tr> </table></center> <br><br> <font face=arial size=2><b>Example 2. How many atoms are in 5 g of calcium (ca)?</b></font><br><br> <center><table border=0><tr><td> <center><img src="example2.gif" height=50></center><br><br></td></tr> <tr><td> <UL> <font face=arial size=2><b>Steps</b></face><br> Step 1: Write what is needed<br> Step 2: Equals to what<br> Step 3: What ever goes on the top, goes to the bottom<br> Step 4: Moles go to grams<br> Step 5: Add the number values from the periodic table<br> Step 6: Cancel the labels<br> Step 7: Check the labels and stop or continue<br> Step 8: Labels are not the same, continue<br> Go Back to Step 3<br> Step 13: Labels the same, stop and calculate<br> </ul> </td></tr> </table></center> <br><br> In the last example, inputing 6.02 x 10<sup>23</sup> may have been a problem! For review <a href="calculator.htm" target=new>show me how to use my calculator!</a> Before completing Task 2, <a href="javascript:popup_window( 'atomsmoles.htm', 'mole_grams', 650, 400 );">test my knowledge</a> for mole to gram conversions. Once you have gain confindence, complete Task 2 and take the unit quiz.<br><br> <font face=arial color=red size=4>How to Express My Answer:</font><br><br> All answers will be expressed in scientific notation with three significan digits. <a href="sigfig.htm" target=new>What are significant Digits?</a> To express your answer in the proper form, first round to three significant digits. Then move the decimal point so that it is between the first and the second significant digits. Multiply the three significant digits by 10 to the power of the spaces that the decimal point was moved. Remember moving to the left is always good, so the exponant will be positive. Moving to the right, is always bad so the exponant will be negative. Always box your answer! <a href="javascript:popup_window( 'sci_notation.htm', 'sci_notation', 650, 400 );">Show Me How This Works!</a><br><br> <font face=arial size=3><b>Example:</b></font> <br> </td></tr> <tr><td colspan=2> <hr color=#990000><br> <font size=5 color=#990000>Readings:</font><br><br> <a href="http://www.chemistrycoach.com/use.htm" target=new>Dimensional Analysis</a><br> <a href="http://wine1.sb.fsu.edu/chm1045/notes/Intro/Dimanal/Dimanal.htm" target=new>Dimensional Analysis</a><br> <a href="http://www.ncsu.edu/felder-public/kenny/papers/units.html" target=new>One of These Things is Not Like the Other</a><br> <br><br> <hr color=#990000><br> </td></tr> <tr><td colspan=2> <font size=5 color=#990000>Tasks:</font><br><br></td></tr> <tr><td colspan=2> Task 1: <a href="conversion.htm" target="new">English-Metirc Conversions</a><br><br> Task 2: <a href="atom-mole-gram.htm" target="new">Atoms-Moles-Grams</a><br><br> <br><hr color=#990000> </td></tr> <tr><td colspan=2><center><a href="mole2quiz.html"><font size=5 color=#990000>Take The Unit 2 Quiz</font></a></center><hr color=#990000></td></tr> </table></center> </body> </html>