7.02 Atomic Vs. Macroscopic Scale Counting By Weighing Atoms, Molecules, Moles and Grams Dr. Fred O. Garces Chemistry 100 Miramar College 1 Atomic Vs. Macroscopic Scale
Atomic Mass Unit What is the mass of an object that cannot be seen? What scale / units of mass is used for such small objects? Unit of mass that is comparable to object of that size. atomic mass unit (amu) has been used as a standard for a mass of an atom. 1 amu = 1.66 10-27 Kg = 1/12 mass of 12 C Atoms: Atomic mass one atom of potassium 39 K weighs 39 amu. one atom of zinc 65 Zn weighs 65 amu. Molecule: Molecular mass one water (H 2 O) molecule one glucose (C 6 H 12 O 6 ) molecule: 6C, 12H, 6O 2-H, 1-O = 2amu + 16amu = 18 amu = [6 C 12amu] + [12 H 1 amu] + [6 O 16amu] = 180 amu 2 Atomic Vs. Macroscopic Scale
Isotopic Distribution Isotopic Distribution: Question comes to mind: Why is the mass of carbon 12.011 according the periodic table? Why is the mass of chlorine 35.453? That of copper 63.546? Is not the mass of an atom reflected on the number of protons and neutrons an atom possesses? If so, is there such a thing as 0.011 amu of subatomic proton or neutron for carbon or 0.453 in chlorine and 0.546 in copper? Atomic mass, as shown in the periodic table, is the average of all isotope found in nature. Atomic mass is the weighted average mass for the isotropic distribution (found in nature) for that element. Weighted atomic mass average for the copper atom: Copper has two stable isotope: 63 Cu - 72.70 %, and 65 Cu - 27.30 % 63 amu (0.7270) + 65 amu (0.2730) = 63.546 amu 3 Atomic Vs. Macroscopic Scale
Weighted Average The mass of the elements from the periodic table is actually the weighted average. Consider the following: 8 : 7 : 6 : 6 - What is the average? (Four points each rep 25%) 8 + 7 + 6 + 6 = 27 g 27 / 4 = 6.75 or 8 (.25) + 7(.25) + 6(.25) + 6(.25) = 2 + 1.75 +1.5 + 1.5 = 6.75 (Also called a weighted average) Now what is the atomic mass for chlorine which exist in the following abundance: Cl-35 (75.53 % ) & Cl-37( 24.47 %) At. Wt = 35(.7553) + 37(.2447) = 26.44 + 9.05 = 35.49 g/mol 4 Atomic Vs. Macroscopic Scale
The Mole: A rice story The mole (a story of numbers) Moral of story: Rufus favorite food is rice. But he rarely eats it even though it is economical and easily prepared. He knows it is healthy for him and he was told once that it takes one serving is 12000 grains. So every time Rufus wants to eat rice he has to prepare 3 hr ahead of time and count out 12000 grains. How can we help my friend Rufus? 1 grain of rice weights an average of 19 mg. Count rice by weighing Mass = 12000 grains Mass rice for 1 serving = 8.0 oz 19 mg 1 grain 1 g 16 oz 1000mg 454 g Weighs out 8.0 oz. hand full rice = 1 cup 5 Atomic Vs. Macroscopic Scale
Method of Counting by mass Counting by mass In chemistry we deal with such small particles we need a way to count these particles. Like in Rufus case, the most efficient way of counting very small items is by counting by mass. As it turns out if we take 6.02 10 23 atoms of carbon-12, 12 C and weight this amount, it weights exactly 12 grams. Similarly, 6.023 10 23 35 Cl atoms weighs exactly 35 g. 6.023 10 23 16 O atoms weighs exactly 16 g. It follows that if we take 6.023 10 23 O 2 molecules made from oxygen-16, that weighs 32 g O 2. This 6.02 10 23 is call 1 mole. It is a chemist dozen. 1 mole of substance is equal to its formula weight in grams 6 Atomic Vs. Macroscopic Scale
Size of a mole Size of one mole; 1 mole of sand fill city of SD 5 miles deep. Take 1 moles of pennies, distribute these to all 5 billion humans, we'd all be trillionaire. If placing these pennies end to end, it would stretch... (how far?) 1 penny = 2.0 cm Length of 1 mole of penny = = 2.0 cm 6.02 1023 s 1 hr day yr 3 1010 cm 3600s 24 hr 365 day = 1, 268, 391.7 light - years = 1.3 million light - years A mole is a quantity 7 Atomic Vs. Macroscopic Scale
Atomic Vs Macroscopic Scale What path relates the atomic scale to our Macroscopic scale? Atomic Magnifier Macroscopic (amu) (grams) Atoms N av moles Atomic Wt grams Molecules N av moles Molar mass grams formula unit N av moles Formula wt grams 8 Atomic Vs. Macroscopic Scale
Questions Relating Atomic to Macroscopic Scale How many Carbon atoms (or molecules) in a certain mass of sample? 12 g C D 1mole D 6.02 10 23 atoms 6 g C D 0.5 mole D 3.01 10 23 atoms 200 g C D? mole D? Atoms Calculation- 200g C 1mole 12g C 23 6.02 10 1mole C = 1.0 1025 C atoms 9 Atomic Vs. Macroscopic Scale
Atomic Scale Vs. Macroscopic Scale Atomic Scale D Macroscopic Scale Atoms Magnifier Grams Molecules pounds 12 C 1-atoms 12 C 1-mole 12amu 12 grams H 2 O 1-molecule H 2 O 1-mole 18.0 amu 18.0 grams NaCl 1-Formula Unit NaCl 1-mole 58.5 amu 58.5 grams 10 Atomic Vs. Macroscopic Scale
What is a mole? Defining the MOLE SI base unit for amount. 6.02 10 23 anything. a magnifier between the atomic scale and macroscopic scale. a conversion factor. a chemist dozen. the sum of the atomic mass of all elements in a substance when the mass is expressed in grams. (Molar Mass) the ratio of elements in a substance as indicated by its chemical formula. C 7 H 5 N 3 O 6 the ratio of elements combining in a chemical reaction as indicated by the balance equation. 4 KOH (aq) + 3 O 2 (g) g 4 KO 2 (s) + 1 H 2 O 11 Atomic Vs. Macroscopic Scale
Questions Relating- Number of Molecules to Mass How much will 5.0 10 26 molecules of H 2 O weight (g)? Data: MW: = Nav: = 18.0 gh 2 O 1mole H 2 O 1mole H 2 O 6.02 10 23 molecules H 2 O 5.0 10 26 molecule H 2 O 5.0 10 26 molecule H 2 O 1mole H 2 O 6.02 10 23 molecules H 2 O 18.0 gh O 2 1 mole H 2 O = 14,950 g What volume is this (L)? Data: Density : 1.0 g = 1 ml 1000ml = 1ml 14, 950 g H 2 O 1ml 1.0 g 1L 1000ml = 15L 12 Atomic Vs. Macroscopic Scale
Questions Relating Number of Molecules to Mass How much will 5.0 10 26 molecules of H 2 O weight? Data: MW: = Nav: = 18.0 gh 2 O 1mole H 2 O 1mole H 2 O 6.02 10 23 molecules H 2 O 5.0 10 26 molecule H 2 O 5.0 10 26 molecule H 2 O 1mole H 2 O 6.02 10 23 molecules H 2 O 18.0 gh O 2 1 mole H 2 O = 14,950 g What volume is this? Data: Density : 1.0 g = 1L 1000ml = 1ml 14, 950 g H 2 O 1ml 1.0 g 1L 1000ml = 15L 13 Atomic Vs. Macroscopic Scale
Mole Relationship to Mass and Elements (p261) Atoms in the compound Compounds* W B Y D X C * Including elemental compounds, i.e., O 2, S 8, Fe 14 Atomic Vs. Macroscopic Scale
Question Relating Number of molecules to moles of Substance i. What is the number of molecules in 2.9 moles of TNT? TNT = C 7 H 5 N 3 O 6 Mol.Wt. = 227.0 g/mol g 227.0 g = 1 mol ii How much will this amount of TNT weigh (g)? iii How many N-atoms are in 1.0 g of TNT? Note that in TNT: 1 mole C 7 H 5 N 3 O 6 @ 7 mol C @ 5 mol H @ 3 mol N @ 6 mol O 15 Atomic Vs. Macroscopic Scale
Mole Relationship to Mass and Elements (p261) W B i What is the number of molecules in 2.9 moles of TNT? TNT = C 7 H 5 N 3 O 6 Mol.Wt. = 227.0 g/mol D C Y D ii How much will this amount of TNT weigh? D B X C iii How many N-atoms are in 1.0 g of TNT? Note that in TNT: 1 mole C 7 H 5 N 3 O 6 @ 7mol C @ 5mol H @ 3mol N @ 6mol O B D Y X 16 Atomic Vs. Macroscopic Scale
Question Relating Number of molecules to moles of Substance i. What is the number of molecules in 2.9 moles of TNT? TNT = C 7 H 5 N 3 O 6 Mol.Wt. = 227.0 g/mol g 227.0 g = 1 mol D 2.9mol TNT 6.02 1023 molc'tnt 1 mole TNT C = 1.75 10 24 molc'= 1.8 10 24 molc' ii How much will this amount of TNT weigh? D 2.9mol TNT 227.0 gtnt 1 mole TNT B = 658.3 g TNT = 660 g TNT iii How many N-atoms are in 1.0 g of TNT? Note that in TNT: 1 mole C 7 H 5 N 3 O 6 @ 7 mol C @ 5 mol H @ 3 mol N @ 6 mol O B 1.0g TNT 1mole TNT 227g TNT 3mol N 1mol TNT 6.02 10 23 atoms 1mol N = X D Y =7.96 10 21 N atoms=8.0 10 21 N atoms 17 Atomic Vs. Macroscopic Scale
Question Relating Number of molecules to moles of Substance i. What is the number of molecules in 2.9 moles of TNT? TNT = C 7 H 5 N 3 O 6 Mol.Wt. = 227.0 g/mol 2.9mol TNT 6.02 1023 molc'tnt 1 mole TNT = 1.75 10 24 molc'= 1.8 10 24 molc' ii How much will this amount of TNT weigh? 2.9mol TNT 227.0 gtnt = 658.3 g TNT = 660 g TNT 1 mole TNT iii How many N-atoms are in 1.0 g of TNT? Note that in TNT: 1 mole C 7 H 5 N 3 O 6 @ 7 mol C @ 5 mol H @ 3 mol N @ 6 mol O 1.0g TNT 1mole TNT 227g TNT 3mol N 1mol TNT 6.02 10 23 atoms 1mol N = =7.96 10 21 N atoms=8.0 10 21 N atoms 18 Atomic Vs. Macroscopic Scale
Moles and Molar Mass: Example #7.61-Ebbing a) Calculate the moles of chloride ions in 1.11 g of magnesium chloride. b) How many chloride ions are present? 1mole MgCl 2 @ 1mol Mg +2 @ 2mol Cl - Mg - 24.3 g/mol = 24.3 g/mol 2 Cl - 35.45 g/mol 2 = 70.9 g/mol 1mol Molar Mass (MgCl 2 ) 95.2 g = a)! " B # $! " D # $! " # $ = & " Answer Y ' $ b)! " Y! # # " $ $! # " $ = & Answer W ' " $ State the path 19 Atomic Vs. Macroscopic Scale
Moles and Molar Mass: Example #7.61-Ebbing a) Calculate the moles of chloride ions in 1.11 g of magnesium chloride. b) How many chloride ions are present? 1mole MgCl 2 @ 1mol Mg +2 @ 2mol Cl - Mg - 24.3 g/mol = 24.3 g/mol 2 Cl - 35.45 g/mol 2 = 70.9 g/mol Molar Mass (MgCl 2 ) = 95.2 g/mol a) D 1.1 g MgCl 2 1mole MgCl - 2 2mol Cl B = 0.0231 mol Y Cl - ions 95.2g MgCl 2 1mol MgCl 2 b) 0.0231 mol Cl - ions 6.02 1023 Cl - ions Y 1mol Cl - ions = 1.39 10 22 Cl - ions W 20 Atomic Vs. Macroscopic Scale
Counting by Mass: A Review One mole substance equivalent to: Atomic Weight (in grams) - atoms Molecular Weight (in grams) - molecules Formula Weight (in grams) - ionic Compounds Atoms Compound mole mass C 6 H 12 O 6 C 6 H 12 O 6 180 g molecule 1 mole (1 mol) C 6-C atoms 6 mol C 6(12.0) = 72g C H 12-H atoms 12 mol C 12(1.0) = 12g H O 6-O atoms 6 mol O 6(16.0) = 96g O 180 g total From Chemical Formula we obtain the conversion factors: 1 molecule C 6 H 12 O 6 c 6C atoms @ 12H atoms @ 6 O atoms or 1 mole C 6 H 12 O 6 c 6 C moles @ 12 H moles @ 6 O atoms 21 Atomic Vs. Macroscopic Scale
Percent Composition by Mass What is meant by %? Consider the % of male in this class # male = 9 Total class size = 20: % =9/20 100 = 45% % Composition c [part/whole] 100 Similarly for a compound the % composition (by mass) of each element can be determine by part/whole analysis. C 6 H 12 O 6 - glucose Consider 100 g Sample What is % C, H and O? i) Atomic basis: % C atom = [6/24] 100 = 25%; % H atom = [12/24] 100 = 50%; % O atom = [6/24] 100 = 25% ii) Mass basis: C: 6 (12.0g/mol) = 72 g/mol H: 12 (1.0g/mol) = 12 g/mol O: 6 (16.0g/mol) = 96 g/mol Total mass = 180 g/mol %C = 72g/mol 180 g/mol %H = 12g/mol 180 g/mol %O = 96g/mol 180 g/mol 100 = 40% 100 = 6.7% 100 = 53% 22 Atomic Vs. Macroscopic Scale
Formula Composition from % Composition Suppose given % composition, What is the chemical formula? Actually can only calculate Empirical (simplest) formula. What is the Chemical formula for with 40% C; 6.7%H and 53% O -Assume 100 g mass. 100 g CxHyOz g 40 g C; 6.7g H; 53g O mol C = 40 g C mol = 3.3 mol C 12.0 g mol H = 6.7 g C mol = 6.7 mol H 1.0 g mol O = 53 g C mol = 3.3 mol O 16.0 g Note: 1.0 g of H not H 2!! Ratio: C 3.3 H 6.7 O 3.33 Reduce to simplest whole # ratio divide by 3.33 e C 1 H 2 O 1 Note the best formula that can be obtain is the simplest (Empirical) formula without other information such as the Molar mass or the total number of atoms in the compound. 23 Atomic Vs. Macroscopic Scale
Counting and Weighing Atoms and Molecules Summary Counting by Weighing at a Glance: Formula Mass The sum of the atomic masses of atoms in a formula. The formula mass of glucose is: (6.0amu 12C) + (1.0amu 12H) + (16.0amu 6O) = 1.80 102 amu Mole Mole = Avogadro s number of particles = 6.02 10 23 1 Mole glucose = 6.02 10 23 molc Molar Mass The formula mass of a substance in grams; containing = 6.02 10 23 atoms or molecules or formula unit Molar mass of glucose = 180 g / mole. C 6 H 12 O 6 Glucose Atomic Mass Unit 1 g = 6.02 10 23 atomic mass unit 1 amu = 1/1 the mass of one 12 C atom 24 Atomic Vs. Macroscopic Scale