1. 1 Prepared for SSAC by Rachel Wang – Spokane Falls Community College © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2005. How do we determine “quantity” in everyday life? How do we generally keep track of items too small and too numerous to count one-by-one? Supporting Quantitative Skills Scientific Notation Significant figures SSAC2005.QD461.RW1.1 How do you determine the number of atoms or molecules in everyday items? The Mole in Chemistry Core Quantitative Concept Unit Conversions

2. 2 Slides 3 & 4 provide a brief review of atoms, molecules, significant figures and scientific notation. Slides 5-7 spreadsheet1* & 2.connect conventional ways of determining quantity to what we do in chemistry with atoms and molecules by drawing a parallel between “dozen” (a lump sum of 12) and “mole” (a lump sum of 6.022 x 10 23, called Avogadro’s number) through exercises in spreadsheet 1* & 2. Slides 8-11 examine the origin of Avogadro’s number and how this number facilitates moles  grams conversions through exercises in spreadsheets 3 & 4. Slide 12 presents a composite diagram in spreadsheet 5 summarizing all the conversions: grams  moles  numbers of atoms or molecules. Slides 13-15 address the question “how do you determine the number of atoms or molecules present in everyday items?” with a sample problem concerning paper clips. Slides16 and 17 Slides 16 and 17.lists the assignment to hand in. * An Excel  file is inserted in Slide 6. You may activate / download it by double-clicking the icon in the NORMAL view (view menu). Overview of Module

3. 3 Review: Atoms and Molecules 1.All matter is composed of small representative units of atoms and/or molecules. (Atomic Theory) 2.The mass of an atom (atomic mass) is reported in the atomic mass unit (amu),which is approximately the mass of a proton. This is experimentally determined as: 2.The mass of an atom (atomic mass) is reported in the atomic mass unit (amu), which is approximately the mass of a proton. This is experimentally determined as:  1 amu = 1.66058 x 10 -24 grams 3.The periodic table displays the average atomic mass of each element. For example:  Hydrogen (H) = 1.01 amu, and oxygen (O) = 16.00 amu. 4.The formula mass ofcompound is the sum of all the atomic masses in the formula. For example: 4.The formula mass of a compound is the sum of all the atomic masses in the formula. For example:  mass of H 2 SO 4 = 2 (H) + (S) + 4(O) = 2(1.01) + (32.06) + 4(16.00) = 98.08 amu

4. 4 How to format cells for scientific notation within a spreadsheet: Left-click the cell  Click Format on toolbar  number  scientific  decimal places = [Decide based on significant figures.] Example: To keep the 5 significant figures in this number: 0.0035090, you will select 4 decimal places to display: 3.5090E-3 in the cell. 1.An answer derived by multiplication or division should not have more significant figures than any of the data used to derive it. 2.All non-zero digits in a measurement are significant. A zero digit is significant if it is a “captive” between two non-zero digits or if it is at the end of a number behind the decimal point. Example: The number 0.0035090 has a total of five significant figures, shown underlined. The zeros in front are NOT significant digits. scientific notation, 3.In scientific notation, the number in front includes all the significant digits. The power of ten shows magnitude. For example: 0.0035090 in scientific notation is 3.5090 x 10 -3 (which shows up as: 3.5090E-3 in a spreadsheet cell.) Review: Significant Figures & Scientific Notation

5. 5 quantity We will first consider how people normally keep track of quantity in everyday life. There are generally three ways to do this: by number (1)Counting  by number of units. Example: oranges priced by number. lump sum. If a single unit is too small, we devise a lump sum. Example: eggs are priced by the dozen, which is a lump sum of 12 units. by weight or mass. (2) Weighing  by weight or mass. Example: meat is priced by the pound. by volume. (3) Measuring  by volume. This is easier to use with liquids or gases. Example: gasoline is priced by the gallon. How we determine quantity: Counting, Weighing or Volume Measurements Is it surprising to you that we employ similar ways in chemistry to keep track of atoms and molecules as described above? But, indeed we do. mole The next two slides compare two parallel ways of counting by number of units: As we count small items by the “dozen” in everyday life, we count atoms and molecules by the “ mole ” in chemistry.

6. 6 = given values. Start with these. = answers calculated by cell equations. Express all numbers in scientific notation and correct number of significant figures. Double-Click the Excel icon in normal view and complete Sheet 1. Instructions: Input a cell equation in D6 using D3 as absolute reference ($D$3). Click & drag its anchor to input similar equations in subsequent Cells D7-D9. Follow similar procedures with C10 and then C11-13. Counting by the dozen

7. 7 1.Print a hardcopy later. 1.Print a hardcopy (or save your work on a disk) of the spreadsheet you just completed on “counting by the dozen” for submission later. mole. “mole(s)” 6.022x10 23 12 2.Go to Sheet 2 of your downloaded Excel file and complete the spreadsheet table on “counting by the mole.” Note that Rows 1 through 13 of Sheet 2 exactly duplicate those of Sheet 1, except that the word “dozen(s)” is replaced with “mole(s)” everywhere. Note the dramatic change in your answers when the numerical value of 6.022x10 23 is used as the lump sum instead of 12. mole(s)These four exercises are added to the “counting by the mole(s)” worksheet. Complete the cells under Columns D, E, and F with appropriate values, units or equations. Print a hardcopy molePrint a hardcopy (or save your work on a disk) when you complete the “counting by the mole” spreadsheet. Remember to use scientific notations with correct number of significant figures! Counting by the Counting by the mole

8. 8 Avogadro’s number Named Avogadro’s number in honor of Amedeo Avogadro (1776-1856) mole Slides 6 and 7 showed how counting eggs in dozens is similar to counting atoms by the mole. We use similar math equations for both mole  number conversions and dozen  number conversions. Avogadro’s number amugram, But why do we use Avogadro’s number, 6.022 x 10 23, for one mole? Did he invent the number? No, neither he nor anyone else did. The number is defined by how the mass units, amu and gram, relate to each other: 1 amu = 1.66058 x 10 -24 grams Since everyday items contain astronomical numbers of atoms and molecules, it is easier to count them by a huge lump sum: 1 mole = 6.022 x 10 23. Pictured on the right are 1 mole each of H 2 O molecules and Fe atoms (in the pile of staples). 1 Mole = 6.022 x 10 23

9. 9 Complete this table in Sheet 3 of your downloaded Excel file. Print a hardcopy or save it on a disk. = given values. Start with these. = answers calculated by cell equations. Complete Column C with values of atomic mass from your periodic table. If one K atom weighs 39.01 amu, how much would 1 mole of K atoms weigh: amu (column D) in amu (column D)? grams (column E) In grams (column E)? atomic mass (amu)  molar mass (gram) BCDE 2 1 amu =1.66058E-24grams 3 quantity of atoms1 mole = 6.02200E+23 4 element 1 atom mass (amu) 1 mole atoms (amu) molar mass (grams) 5 potassium,K 3.91E+01 2.35E+25 3.90E+01 6 sodium, Na 2.299E+01 7 hydrogen, H 1.01E+00 8 oxygen, O 1.600E+01 9 nitrogen, N 1.401E+01 10 iron, Fe 11 aluminum, Al 12 carbon, C 13 zinc, Zn 14 sulfur, S HINT: $C$2 and $D$3 are absolute references. Input appropriate equations in cells D5 and E5 that produce the numbers in those cells shown here. Then Click and drag anchors to add similar equations in the other cells.

10. 10 Examine the spreadsheet you prepared in Slide 9. How do the numerical values in Column C and those in Column E compare for each element? Are they exactly the same? They should be, as Avogadro’s number is defined by the way amu and gram relate to each other. Experimental data: 1 amu1.66058 x 10 -24 grams 1 amu = 1.66058 x 10 -24 grams leads to this equality: 6.022 x 10 23 amu= 1 gram 6.022 x 10 23 amu = 1 gram 11.66058 x 10 -24 ) = 6.022 x 10 23 because: 1  (1.66058 x 10 -24 ) = 6.022 x 10 23 One H 2 O molecule 18.00 amu = 18.00 amu Avogadro’s number 6.022 x10 23 H 2 O molecules mole H 2 O One mole H 2 OMolecules 18.00 gram = 18.00 gram Weighing in Grams and the Mole

11. 11 Complete this table in Sheet 4 of your downloaded Excel file. Print a hardcopy or save it on a disk. Express all numbers in scientific notation and the correct number of significant figures. = given values. Start with these. = answers calculated by cell equations. Grams Mole Conversions Grams  Mole Conversions 1 mole of any element = molar mass in grams from the periodic table.

12. 12 number of atoms and moleculesmolesgrams Print a hardcopy of the completed sheet or save it on a disk. This composite diagram in Sheet 5 of the Excel file summarizes all conversions among number of atoms and molecules, moles, and grams. Supply cell equations to answer the questions given on the sheet. Print a hardcopy of the completed sheet or save it on a disk. No. of atoms Mole  Grams Conversions No. of atoms  Mole  Grams Conversions The color coding of yellow, green, blue, and brown cells is shown on the spreadsheet.

13. 13 Given the chemical composition of an everyday item, we can easily determine the number of atoms or molecules present in it by applying the conversions we have practiced in the previous slides: grams moles numbers of atoms or molecules grams  moles  numbers of atoms or molecules. mass in gramsmoles, numberof atoms or moleculesIf the item is more or less “pure” in that it has only one type of element or compound, we can readily determine the number of atoms or molecules in it by (a) weighing the item to obtain its mass in grams, (b) converting grams to moles, using the periodic table for molar mass, and then (c) converting moles to number of atoms or molecules, using Avogadro’s number. Examples in this category include: distilled water (H 2 O), regular staples (Fe) and table sugar (sucrose, C 12 H 22 O 11 ). mass of each element or compoundmolesatoms or molecules.If the item is a mixture, we may need to do some chemical analyses to determine the mass of each element or compound. After finding the respective mass of each element or compound, we can readily convert that to moles and atoms or molecules.. About the problem of determining the number of atoms or molecules in everyday items …

14. 14 How many atoms are there in a paper clip? One of the most important problem-solving strategies is to frame the problem so that it can be answered under conditions consistent with available information. Because the question did not specify any details, it is obviously not looking for an exhaustive answer about every paper clip in the world. Can you frame the problem by defining some conditions that are reasonable for you to obtain a satisfactory answer and be consistent with a ‘generic’ paper clip in common use? Paper clips vary in style, size and chemical composition. The familiar Gem style pictured above varies in size from over 2 inches to less than 1 inch long. The wire itself differs in thickness. Though paper clips may be made of colorful plastics or brass, most are made of steel (>99.7% iron). To prevent rusting, they often have a thin surface coating of zinc. If you immerse a zinc-coated clip in dilute acid, the reactive zinc metal will readily oxidize and dissolve away to reveal the iron. Iron, being less active, does not react as zinc does.

15. 15 Use the spreadsheet on sheet 6 of your downloaded spreadsheet to determine the number of iron and zinc atoms in a hypothetical paper clip given the data below: 0.403g Original mass of the paper clip = 0.403 g. 0.365 g Mass after removing zinc with 1 M HCl = 0.365 g Fe = 0.367 gram  moles Fe  atoms Fe Zn = 0.403– 0.367 = 0.0363 gram  moles Zn  atoms Zn How many atoms are there in a paper clip? For some interesting paper clip history, check out this web site: http://www.ideafinder,com/history/inventions/paperclip.htm

16. 16 End-of-Module Assignments Submit answers to the following: 1.How many water (H 2 O) molecules are there in the cup of coffee pictured on the right? 2.Two teaspoons each of table sugar and a non-dairy creamer are in the coffee. How many sucrose molecules are there? 3.How many carbon atoms are present in your body? Discuss whether these C atoms are sufficient to make a 5-carat diamond? (Hint: 18% body weight is C; 1 carat = 205 mg.) Frame each problem by specifying reasonable conditions. Specify the sources of all data, which can be from your own experiment, a publication and/or a product label, etc. Show calculations and report answers in correct significant figures and scientific notation. 4. Submit the spreadsheets completed in Slides 6, 7, 9, 11 & 12.

17. 17 5.Conduct your own lab experiment to determine the number of zinc and iron atoms present in a paper clip. Your must: a)Specify the conditions under which you can determine the number of atoms present in a paper clip. b)Conduct experiments and collect data on this paper clip using available supplies and equipment in the Chem lab. c)Submit a brief one-page summary report of your lab results and calculations in answer to the question. End-of-Module Assignments Continued