1. THE MOLE Unit 7

2. One way to measure how much substance available is to count the # of particles in that sample –However, atoms & molecules are extremely small –Also, the # of individual particles in even a small sample is very large –Therefore, counting the # of particles is not a practical measure of amount To solve this problem, scientists developed the concept of the mole –It’s the “chemical counting unit” One way to measure how much substance available is to count the # of particles in that sample –However, atoms & molecules are extremely small –Also, the # of individual particles in even a small sample is very large –Therefore, counting the # of particles is not a practical measure of amount To solve this problem, scientists developed the concept of the mole –It’s the “chemical counting unit” How Scientists Keep Track of Atoms

3. Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000 –It is equal to that number no matter what kind of particles you’re talking about –It could be represent marbles, pencils, or bikes –usually deals with atoms and molecules The word “mole” was introduced about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.” The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance. Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000 –It is equal to that number no matter what kind of particles you’re talking about –It could be represent marbles, pencils, or bikes –usually deals with atoms and molecules The word “mole” was introduced about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.” The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance.

4. The mole, as a unit, is only used to count very small items –Represents a # of items, so, we can know exactly how many items are in 1 mole The experimentally determined number a mole is called, Avogadro’s Number. –Or 6.02x10 23 The term representative particle refers to the species present in a substance –Usually atoms –Molecules –Or formula units (ions) The mole, as a unit, is only used to count very small items –Represents a # of items, so, we can know exactly how many items are in 1 mole The experimentally determined number a mole is called, Avogadro’s Number. –Or 6.02x10 23 The term representative particle refers to the species present in a substance –Usually atoms –Molecules –Or formula units (ions)

5. REPRESENTATIVE PARTICLES & MOLES ATOMIC NITROGEN ATOMN 6.02x10 23 NITROGEN GAS MOLEC. N2N2N2N2 6.02x10 23 WATERMOLEC. H20H20H20H20 CALCIUM ION ION Ca 2+ 6.02x10 23 CALCIUM FLUORIDE FORMULA UNIT CaF 2 6.02x10 23

6. How Do We Use The Mole? We’d never use the mole to describe macroscopic or real world objects. –1 mole (6.02x10 23 ) of watermelon seeds would be found inside a watermelon the size of the moon. –1 mole (6.02x10 23 ) of donut holes would cover the earth and would be 5 miles deep. Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small. –1 mole (6.02x10 23 ) of water molecules would barely fill a shot glass We’d never use the mole to describe macroscopic or real world objects. –1 mole (6.02x10 23 ) of watermelon seeds would be found inside a watermelon the size of the moon. –1 mole (6.02x10 23 ) of donut holes would cover the earth and would be 5 miles deep. Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small. –1 mole (6.02x10 23 ) of water molecules would barely fill a shot glass

7. Using the mole in calculations #1 What number of moles of Mg is equivalent to 1.806x10 24 atoms of Mg? *Remember* 1 mol Mg = 6.02x10 23 atoms Mg *Remember* 1 mol Mg = 6.02x10 23 atoms Mg 6.02x10 23 atoms Mg 1 mole Mg X mole Mg 1.806x10 24 atoms Mg = = (6.02x10 23 atoms Mg)(X mole Mg) = (1.806x10 24 atoms Mg)(1 mole Mg) (6.02x10 23 atmMg)(X)=(1.806x10 24 atmsmolsMg) ( 6.02x10 23 atmMg ) X = 3.0 moles

8. Using the mole in calculations #2 If we had 2.5 moles of sugar, how many molecules of sugar is that equal to? *Remember* 1 mol sugar = 6.02x10 23 molecules sugar *Remember* 1 mol sugar = 6.02x10 23 molecules sugar 6.02x10 23 molec sugar 1 mole sugar 2.5 moles sugar X molec sugar = = (1mole sugar)(X molec sugar) = (6.02x10 23 molecs sugar)(2.5 mole sugar) (1molsugar)(X) = (1.505x10 24 molecsmols sugar) (1molsugar) X = 1.51x10 24 molecules of sugar

9. What if I asked you how many atoms are in a mole of a compound? –you must know how many atoms are in a representative particle or cluster of the compound. To do this you must know the chem formula –For example, each molecule of CO 2 is composed of 1 C + 2 O’s = 3 atoms 1 mole of carbon dioxide molecules contains avogadro’s number of carbon dioxide molecules. –Thus a mole of CO 2 contains three times avogadro’s number of atoms What if I asked you how many atoms are in a mole of a compound? –you must know how many atoms are in a representative particle or cluster of the compound. To do this you must know the chem formula –For example, each molecule of CO 2 is composed of 1 C + 2 O’s = 3 atoms 1 mole of carbon dioxide molecules contains avogadro’s number of carbon dioxide molecules. –Thus a mole of CO 2 contains three times avogadro’s number of atoms

10. To find the # of atoms in a mol of a compound, –You 1 st determine the # of atoms in a representative particle of that compound –And then multiply that # of atoms by avogadro’s # To find the # of atoms in a mol of a compound, –You 1 st determine the # of atoms in a representative particle of that compound –And then multiply that # of atoms by avogadro’s # Using the mole in calculations #3 How many atoms of carbon are in 2.12 mols of propane molecules (C 3 H 8 )? Useful Info: 1 mol C 3 H 8 = 6.02x10 23 molecules C 3 H 8 1molecule C 3 H 8 = 3 atoms of C Useful Info: 1 mol C 3 H 8 = 6.02x10 23 molecules C 3 H 8 1molecule C 3 H 8 = 3 atoms of C

11. 1 st we need to see how many molecules of propane we have if we have 2.12 moles. 6.02x10 23 molec C 3 H 8 1 mole C 3 H 8 2.12 moles C 3 H 8 X molec C 3 H 8 = = X = 1.276x10 24 molecules of C 3 H 8 (1molecC 3 H 8 )(X)=(1.276x10 24 molecmolsC 3 H 8 ) (1 molec C 3 H 8 )

12. 2 nd we need to see how many atoms of C if we have 1.276x10 24 molecs of C 3 H 8. 3 atoms of C 1 molecule C 3 H 8 1.276x10 24 molec C 3 H 8 X atoms C = = X = 3.83x10 24 atoms of Carbon (1 molec C 3 H 8 )(X)=(3.83x10 24 molec atoms C) (1 molec C 3 H 8 )

13. Do you know how to measure out 3 moles of sugar or salt or water? –The mole is a counting unit, so we would have to count out 6.02x10 23 particles of each substance. (no thank you) There are 2 ways we can use to measure out a number of moles of a substance. –Measure it in grams (a mass) –Or measure it in liters (a volume) Do you know how to measure out 3 moles of sugar or salt or water? –The mole is a counting unit, so we would have to count out 6.02x10 23 particles of each substance. (no thank you) There are 2 ways we can use to measure out a number of moles of a substance. –Measure it in grams (a mass) –Or measure it in liters (a volume) How we measure moles…

14. One of the units we can use to measure out a particular amount of moles is to weigh it out in grams? –The only problem with this method is that 1 mol of books will weigh more than 1 mol of pencils, since each book is heavier. –What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x10 6 Gtons. How much would 3.0 mols of pencils and 3 mols of books weigh? –500 Gtons * 3 mols = 1500 Gtons pencils –1x10 6 Gtons * 3 mols = 3x10 6 Gtons One of the units we can use to measure out a particular amount of moles is to weigh it out in grams? –The only problem with this method is that 1 mol of books will weigh more than 1 mol of pencils, since each book is heavier. –What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x10 6 Gtons. How much would 3.0 mols of pencils and 3 mols of books weigh? –500 Gtons * 3 mols = 1500 Gtons pencils –1x10 6 Gtons * 3 mols = 3x10 6 Gtons Using mass to measure moles…

15. To be able to measure out 1 mol of a substance we would need access to the known mass in grams of 1 mol of any substance in question –We would need a data table that provided all of these masses since every substance involved would have its own mass. Remember, we don’t use the mole to count anything but atoms, molecules, etc. –So we need a table that provides the mass 1 mole would weigh for every combination of atoms known to man. To be able to measure out 1 mol of a substance we would need access to the known mass in grams of 1 mol of any substance in question –We would need a data table that provided all of these masses since every substance involved would have its own mass. Remember, we don’t use the mole to count anything but atoms, molecules, etc. –So we need a table that provides the mass 1 mole would weigh for every combination of atoms known to man.

16. Using mass to measure moles… It just so happens that the periodic table provides us with some of that information. –The masses of each atom on the table is the equivalent to the mass of 1 mole of that atom –Every type of atom known to humankind is on that table. The mass on the periodic table is called the molar mass (units of g/mol), because it represents the mass of 1 mol of that atom –1 mole of Mg atoms weighs 24.305 g –1 mole of C atoms weighs 12.011 g It just so happens that the periodic table provides us with some of that information. –The masses of each atom on the table is the equivalent to the mass of 1 mole of that atom –Every type of atom known to humankind is on that table. The mass on the periodic table is called the molar mass (units of g/mol), because it represents the mass of 1 mol of that atom –1 mole of Mg atoms weighs 24.305 g –1 mole of C atoms weighs 12.011 g

17. Using mass to measure moles… That works well for atoms off of the periodic table, but how do we deal the molar masses of molecules and compounds? –Each of those compounds and molecules is composed of a combination of atoms –We have the molar masses for all of the atoms on the periodic table We need to be able to add up the total weight of all of the atoms in the compound or molecule given its formula. –For ex, what is the molar mass of H 2 O? That works well for atoms off of the periodic table, but how do we deal the molar masses of molecules and compounds? –Each of those compounds and molecules is composed of a combination of atoms –We have the molar masses for all of the atoms on the periodic table We need to be able to add up the total weight of all of the atoms in the compound or molecule given its formula. –For ex, what is the molar mass of H 2 O?

18. We just add the molar masses of each of the atoms that make up the molecule From the PT, we find that the molar mass of 1 mole of Hydrogen atoms is 1.0079 g. –We have 2 Hydrogen atoms per molecule of H 2 O, so our Hydrogen atoms total 2 * 1.0079 g or 2.0158 g per mole The mass of 1 mole of oxygen atoms is 15.999 g. –We have only 1 atom of oxygen per mole-cule of H 2 O so our total mass of oxygen is 1 * 15.999 g or just 15.999 g per mol Therefore 1 mole of H 2 O molecs would weigh, 2.0158g+15.999g= 18.0148g We just add the molar masses of each of the atoms that make up the molecule From the PT, we find that the molar mass of 1 mole of Hydrogen atoms is 1.0079 g. –We have 2 Hydrogen atoms per molecule of H 2 O, so our Hydrogen atoms total 2 * 1.0079 g or 2.0158 g per mole The mass of 1 mole of oxygen atoms is 15.999 g. –We have only 1 atom of oxygen per mole-cule of H 2 O so our total mass of oxygen is 1 * 15.999 g or just 15.999 g per mol Therefore 1 mole of H 2 O molecs would weigh, 2.0158g+15.999g= 18.0148g

19. What is the mass of 1 mole of C 6 H 12 O 6 ? Ex #2: Calculating molar masses using chemical formulas The overall mass of 1 mole of C 6 H 12 O 6 will be the molar mass of 6 Carbons + the molar mass of 12 Hydrogens + the molar mass of 6 Oxygens. 6 Carbons = 12.011 g 6 * 12 Hydrogens = 1.0079 g 12 * = 72.066 g = 12.095 g 6 Oxygens = 15.999 g 6 * = 95. 994 g 180.16 g/mole

20. Even though for compounds and molecules we have to calculate a molar mass using the periodic table, they are considered given or known values. We can use these molar masses in calculations in which we are either give moles and asked for its mass equivalent or given mass and asked for its mole equivalent. –If we are given an element we just use the mass from the periodic table –If we are given a formula instead we just calculate the molar mass of the molecule using the masses from the periodic table. Even though for compounds and molecules we have to calculate a molar mass using the periodic table, they are considered given or known values. We can use these molar masses in calculations in which we are either give moles and asked for its mass equivalent or given mass and asked for its mole equivalent. –If we are given an element we just use the mass from the periodic table –If we are given a formula instead we just calculate the molar mass of the molecule using the masses from the periodic table.

21. Using the mole in calculations #4 How much would 9.45 moles of N 2 O 3 weigh? How much would 9.45 moles of N 2 O 3 weigh? 2(14.007g)+3(15.999g) 1 mole N 2 O 3 9.45 moles N 2 O 3 X g N 2 O 3 = =

22. Using the mole in calculations #4 How much would 9.45 moles of N 2 O 3 weigh? How much would 9.45 moles of N 2 O 3 weigh? 76.011g N 2 O 3 1 mole N 2 O 3 9.45 moles N 2 O 3 X g N 2 O 3 = = (1mole N 2 O 3 )(X g N 2 O 3 ) = (9.45 moles N 2 O 3 )(76.011g N 2 O 3 ) X = 718 grams of N 2 O 3 (1 mol N 2 O 3 )(X) = (718 g mols N 2 O 3 ) (1 mol N 2 O 3 )

23. Using the mole in calculations #5 1(55.847g)+1(15.999g) 1 mole FeO X mols FeO 92.2 g FeO = = We have 92.2g of FeO, how many moles is the equivalent of the given mass?

24. Using the mole in calculations #5 71.846 g FeO 1 mole FeO X mols FeO 92.2 g FeO = = (71.846g FeO)(X mols FeO) = (1 mole FeO)(92.2 g FeO) X = 1.28 moles of FeO (71.846 g FeO)(X) = (92.2 gmols FeO) (71.846 g FeO)

25. The other unit we can use to measure out mols is to measure a gas in Liters –There is a standard volume that 1 mol of any gas will occupy called molar volume. –If we had 1 mol of Ne and 1 mol of CO 2 they would each contain 6.02x10 23 particles, and occupy the same volume under standard conditions (0°C, 1 atm). At STP or standard temp & press; 1 mol of any gas occupies 22.4 Liters of space –1 mol of He = 22.4 L of space –1 mol of N 2 = 22.4 L of space The other unit we can use to measure out mols is to measure a gas in Liters –There is a standard volume that 1 mol of any gas will occupy called molar volume. –If we had 1 mol of Ne and 1 mol of CO 2 they would each contain 6.02x10 23 particles, and occupy the same volume under standard conditions (0°C, 1 atm). At STP or standard temp & press; 1 mol of any gas occupies 22.4 Liters of space –1 mol of He = 22.4 L of space –1 mol of N 2 = 22.4 L of space Using volume to measure moles…

26. Using the mole in calculations #6 What volume, in Liters, would.500 mols of CO gas occupy at STP? 22.4 L CO 1 mole CO.500 mol CO X L CO = = *Remember* 1 mol CO = 22.4 L CO *Remember* 1 mol CO = 22.4 L CO (1 mol CO )(X L CO )= (.500 mol CO )(22.4 L CO (1 mol CO ) X = 12.2 L of CO

28. If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are in this piece of metal? You are given mass and asked for number of particles Let’s get some strategy You are given mass and asked for number of particles Let’s get some strategy Using the mole in calculations #7

30. We are given a mass

31. We are asked for atoms It’s going to take us 2 conversions, we just need to follow the arrowsIt’s going to take us 2 conversions, we just need to follow the arrows

32. 1 st we must convert our given mass of Chromium to moles of Chromium1 st we must convert our given mass of Chromium to moles of Chromium –So we need to use the periodic table to calculate the mass of 1 mole of Chromium 1 st we must convert our given mass of Chromium to moles of Chromium1 st we must convert our given mass of Chromium to moles of Chromium –So we need to use the periodic table to calculate the mass of 1 mole of Chromium 51.996g Cr 1 mole Cr X mol Cr 35.67g Cr = = (51.996gCr)(X mol Cr) = (35.67gCr)(1 mol Cr) X =.6860 mol Cr

33. 2 nd we must convert our newly found moles of Cr to atoms of Cr2 nd we must convert our newly found moles of Cr to atoms of Cr –So we need to remember that 1 mole of anything there are 6.02x10 23 particles 2 nd we must convert our newly found moles of Cr to atoms of Cr2 nd we must convert our newly found moles of Cr to atoms of Cr –So we need to remember that 1 mole of anything there are 6.02x10 23 particles 6.02x10 23 atoms Cr 1 mole Cr X atoms Cr.6860 mol Cr = = (1 mol Cr)(X atoms Cr) = (6.02x10 23 atoms Cr) (.6860 mol Cr) (6.02x10 23 atoms Cr) (.6860 mol Cr) X = 4.13x10 23 atoms Cr