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Prepared for SSAC byRachel Wang – Spokane Falls Community College

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *YEAR*

● 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?

● Can we adapt conventional methods to deal with atoms and molecules?

● What experimental data are necessary to determine, for example, the number of atoms

present in a paper clip?

Quantitative Concepts and SkillsUnit ConversionsScientific NotationSignificant figures

Module RW-1

How do you determine the number of atoms or molecules in everyday items?

The Mole in Chemistry

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Slides 3 & 4Slides 3 & 4 • provide a brief review of atoms, molecules, significant figures and scientific

notation. Slides Slides 5-7 5-7 • 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 1023, called Avogadro’s number) through exercises in spreadsheetspreadsheet 1* & 2.1* & 2.

SlideSlidess 8-118-11 • examine the origin of Avogadro’s number and how this number facilitates

moles grams conversions through exercises in spreadsheets 3 & 4spreadsheets 3 & 4. Slide Slide 1212 • presents a composite diagram in spreadsheet 5spreadsheet 5 summarizing all the conversions:

grams moles numbers of atoms or molecules.SlideSlidess 13-1513-15 • address the question “how do you determine the number of atoms or molecules

present in everyday items?” with a sample problem concerning paper clips.SlidesSlides 1616 • lists the assignment to hand in.. * An Excel* An Excel file is inserted in Slide 6. You may activate / download it by file is inserted in Slide 6. You may activate / download it by

double-clicking the icon in the NORMAL view (view menu). double-clicking the icon in the NORMAL view (view menu).

Overview of Module

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1.1. All matter is composed of small representative All matter is composed of small representative unitsunits of of atoms atoms and/or moleculesand/or molecules. (Atomic Theory). (Atomic Theory)

2.2. The mass of an atom (The mass of an atom (atomic massatomic mass) is reported in the ) is reported in the atomic atomic mass unitmass unit ( (amu),amu), which is approximately the mass of a protonwhich is approximately the mass of a proton. . This is experimentally determined as:This is experimentally determined as:

1 amu1 amu == 1.66058 x 10 1.66058 x 10-24-24 grams grams

3.3. The The periodic tableperiodic table displays the average atomic mass of each displays the average atomic mass of each elementelement. . For example:For example:

Hydrogen (H) = 1.01 amu, and oxygen (O) = 16.00 amu.

4.4. The formula mass ofThe formula mass of a compoundcompound is the sum of all the atomic is the sum of all the atomic masses in the formula. For example:masses in the formula. For example:

mass of H2SO4 = 2 (H) + (S) + 4(O)= 2(1.01) + (32.06) + 4(16.00)

= 98.08 amu

Review: Atoms and Molecules

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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.

3. In sscientific notationcientific 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

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We will first consider how people normally keep track of quantity quantity in everyday life. There are generally three ways to do this:

(1) Counting by by numbernumber of units. Example: oranges priced by number. If a single unit is too small, we devise a lump sumlump sum. . Example: eggs are priced by the dozen, which is a lump sum of 12 units.

(2) Weighing by by weightweight or or massmass. . Example: meat is priced by the pound.

(3) Measuring by by volume. 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.

•The next two slides compare two parallel ways of counting by number of units: As we count small items by the “dozendozen” in everyday life, we count atoms and molecules by the “molemole” in chemistry.

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= given values. Start with these.

= answers calculated by cell equations.

Express all numbers in scientific notation and correct number of significant figures.

Double-Click Double-Click ththee Excel Excel icon in normal view andicon in normal view and

complete Sheet 1.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 theCounting by the dozen dozen

B C D E23 lump sum 1 dozen = 12

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5practice exercise

quantity in lump sum

quantity in number

type of item

6How many eggs are there in 15 dozens of eggs? 1.5E+01 1.8E+02 eggs

7How many donuts are there in 2.6 dozen donuts? 2.6E+00 3.1E+01 donuts

8How many atoms are there in 57 dozens of Al atoms?

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How many molecules are there in 9.6 dozens of H2O molecules?

10How many dozens of eggs are there in 15 eggs? 1.3E+00 1.5E+01 eggs

11How many dozens of donuts are there in 26 donuts? 2.2E+00 2.6E+01 donuts

12How many dozens of atoms are there in 1.8x105 Fe?

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How many dozens of molecules are there in 4.6x1018 CO2?

Microsoft Excel Worksheet

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1.1. PPrint a hardcopyrint a hardcopy (or save your work on a disk) of the spreadsheet you just completed on “counting by the dozendozen” for submission later. later.

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)”“dozen(s)” is replaced with “mole(s)”“mole(s)” everywhere. Note the dramatic change in your answers when the numerical value of 6.022x106.022x102323 is used as the lump sum instead of 1212.

• These four exercises are added to the “counting by the molemoles”s” worksheet.

• Complete the cells under Columns D, E, and F with appropriate values, units or equations.

• Print Print a hardcopya hardcopy (or save your work on a disk) when you complete the “counting by the molemole”” spreadsheet.

Remember to use scientific notations with correct number of significant figures!

14How many moles of eggs are there in 2.60x1023 eggs?

15How many moles of atoms are there in 4.60x1024 atoms?

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How many pennies are there in 0.557 moles of pennies?

17How many moles are there in 2.60x1023 water molecules?

Counting by theCounting by the molemole

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Named Avogadro’s numberAvogadro’s number in honor of Amedeo Avogadro (1776-1856)

Slides 6 and 7 showed how counting eggs in dozens is similar to counting atoms by the molemole. We use similar math equations for both mole number conversions and dozen number conversions.

But why do we use Avogadro’sAvogadro’s numbernumber, 6.022 x 1023, for one mole? Did he invent the

number? No, neither he nor anyone else did. The number is defined by how the mass units,

amuamu and gram, gram, relate to each other:

1 amu1 amu == 1.66058 x 10 1.66058 x 10-24-24 grams 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 1023.

Pictured on the right are 1 mole each of H2O molecules and Fe atoms (in the pile of staples).

1 Mole = 6.022 x 10231 Mole = 6.022 x 1023

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Complete tComplete this his table in Stable in Sheetheet 3 of your downloaded Excel file 3 of your downloaded Excel file.. Print a Print a hardcopy or save it on a disk.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:in amu (column D)amu (column D)? In grams (column E)grams (column E)?

atomic mass atomic mass (amu) (amu) molar massmolar mass (gram)(gram)

B C D E2 1 amu = 1.66058E-24 grams

3 quantity of atoms 1 mole = 6.02200E+23

4 element1 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, Fe11 aluminum, Al12 carbon, C13 zinc, Zn14 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.

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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 amu and gramgram relate to each other.Experimental data: 1 amu1 amu = 1.66058 x 101.66058 x 10-24-24 grams grams leads to this equality: 6.022 x 106.022 x 102323 amuamu = 1 gram= 1 gram because: 11 (1.66058 x 101.66058 x 10-24-24)) == 6.022 x 106.022 x 102323

OneOne H H22O O

molecule molecule

= 18.00 amu18.00 amu

Avogadro’s number

6.026.0222 x10 x102323

H2O molecules

One mole Hmole H22OO

MoleculesMolecules

= 18.0018.00 gramgram

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15

10

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Weighing in GramsWeighing in Grams and the MoleMole

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Complete Complete this this table in Stable in Sheetheet 4 of your downloaded Excel file 4 of your downloaded Excel file. . Print aPrint a hardcopy hardcopy or save it on a disk. 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.

GramsGrams MoleMole ConversionsConversions

1 mole of any element = molar mass in grams from the periodic table.

B C D E2

3practice exercise

molar mass

(g)

quantity

(Mol)

quantity

(g)

4How many grams are there in 15.0 moles of Al atoms?

2.698E+01 1.50E+01 4.05E+02

5How many grams are there in 2.60 moles of Fe atoms?

6How many grams are there in 2.6 moles FeO?

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How many grams are there in 1.23 moles Br2?

8How many moles are there in 57.0 grams of Al atoms?

2.698E+01 2.11E+00 5.70E+01

10How many moles are there in 9.60 grams H2O molecules?

11How many moles are there in 15.7 grams Carbon atoms?

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How many moles are there in 264g Br2?

Une the periodic table to find molar mass.

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number mole gram

74.3

1.297

4.30E+28

lump sum: 1 mole =

molar mass =

Use Avogadros' number for atoms - mole conversions

Use molar mass for grams-mole conversions

Answer these questions concerning sucrose (C12H22O11) using this spreadsheet.1. How many moles are there in 74.3 gr sucrose? How many molecules are there?2. How many grams are there in 1.297 moles of sucrose? How many molecules are threre?3. How many moles are in 4.30x1028 molecules of sucrose? How many grams are there?

Input cell equation here to find answer.

Start here if given # atoms or molecules.

Start here if given moles.Start here if given

grams.

This composite diagram in Sheet 5 of

the Excel file summarizes all

conversions among number of atoms number of atoms and moleculesand molecules,

molesmoles, and gramsgrams. Supply cell equations

to answer the questions given on the

sheet. Print a Print a hardcopy of the hardcopy of the

completed sheet or completed sheet or save it on a disk.save it on a disk.

No. of atomsNo. of atoms MoleMole GramsGrams ConversionsConversions

The color coding of yellow, green, blue, and brown cells is shown on the spreadsheet.

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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 grams moles moles numbers of atoms or moleculesnumbers of atoms or molecules.

• If 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 gramsmass in grams, (b) converting grams to moles, moles, using the periodic table for molar mass, and then (c) converting moles to numbernumber of atoms or moleculesof atoms or molecules, using Avogadro’s number. Examples in this category include: distilled water (H2O), regular staples (Fe) and table sugar (sucrose, C12H22O11).

• 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 mass of each element or compoundcompound, we can readily convert that to molesmoles and atoms or atoms or molecules.molecules..

About the problem of determining the number of About the problem of determining the number of atoms or molecules in everyday items …atoms or molecules in everyday items …

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A Sample Problem: How many atoms are there in a paper clip?A Sample Problem: 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.

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Sample data and calculations for a hypothetical paper clip: Original mass of the paper clip = 0.403 0.403 gg. Mass after removing zinc with 1 M HCl = 0.365 g 0.365 g Adapt the composite diagram in slide 12 (Sheet 5 of the Excel file) to convert grams moles atoms :

Fe = Fe = 0.365 gram0.365 gram moles Femoles Fe atoms Featoms FeZn = 0.403– 0.365 = Zn = 0.403– 0.365 = 0.038 gram0.038 gram moles Znmoles Zn atoms Znatoms Zn

A Sample Problem: How many atoms are there in a paper clip? A Sample Problem: How many atoms are there in a paper clip?

(Continued from slide 14) Your task is to:• Specify the conditions under which you can determine the

number of atoms present in a paper clip.• Conduct experiments and collect data on this paper clip

using available supplies and equipment in the Chem lab.• Submit a brief one-page summary report of your lab results

and calculations in answer to the question.

For some interesting paper clip history, check out this web site: http://www.ideafinder,com/history/inventions/paperclip.htm

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End-of-Module Assignments

Submit answers to the following: 1. How many water (H2O) 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.

• Also submit the spreadsheets completed in Slides 6, 7, 9, 11 & 12 and the summary report in Slide 15.