1 The Mole 6.02 X X 10 23

2 STOICHIOMETRYSTOICHIOMETRY - the study of the quantitative aspects of chemical reactions.

3 The Mole A counting unit Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000, X Amedeo Avogadro (1776 – 1856)This number is named in honor of Amedeo Avogadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present in a given volume

4 Just How Big is a Mole? 6.02 x sheets of paper stacked on top of each other would reach beyond the solar system x unpopped popcorn kernels spread across the United States would cover the country in popcorn to a depth of over 9 miles. If a computer were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

5 Everybody Has Avogadro’s Number! But Where Did it Come From? It was NOT just picked! It was MEASURED. One of the early methods of measuring this number was the Millikan Oil Drop Experiment It links the weight of particles in amu’s to their weight in grams

6 The Mole 1 dozen cookies = 12 cookies 1 mole of cookies = 6.02 X cookies 1 dozen cars = 12 cars 1 mole of cars = 6.02 X cars 1 dozen Al atoms = 12 Al atoms 1 mole of Al atoms = 6.02 X atoms Note that the NUMBER of items is always the same, but the MASS is very different! Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

7 = 6.02 x C atoms = 6.02 x H 2 O molecules = 6.02 x NaCl formula units (ionic compounds are not molecules, they are called formula units) So one mole of NaCl contains: 6.02 x Na + ions and 6.02 x Cl – ions A Mole of Particles A Mole of Particles Contains 6.02 x particles 1 mole C 1 mole H 2 O 1 mole NaCl

x particles 1 mole or 1 mole 6.02 x particles Note that a particle could be an atom OR a molecule! Using Avogadro’s Number as a Conversion Factor

9

10 1. Number of atoms in mole of Al 2.Number of moles of S in x S atoms Learning Check

11 It’s A Matter Of Amount If you have a single molecule or atom, mass is measured in amu’s If you have a larger amount of a substance, mass is measured in grams The mole represents the number of particles that takes us between amu’s and grams!

12 The mass of 1 mole of a substance (in grams) Molar mass of an element is equal to the numerical value of the atomic mass (retrieved from periodic table) 1 atom of C = 12.0 amu 1 mole of C atoms= 12.0 g (the molar mass of carbon is 12 g) 1 atom of Mg= 24.3 amu 1 mole of Mg atoms =24.3 g (the molar mass of magnesium is 24.3 g) Molar Mass

13 Molecular/Formula Mass of a compound is the sum of the atomic masses of the atoms in a molecule or formula unit (in amu s ). Molar Mass of a compound is the weight (in grams) of 1 mole of the compound Methane (CH 4 ) 1 C (atomic mass = 12) →12 amu 4 H (atomic mass = 1) →_4 amu Molecular Mass of methane = 16 amu (One molecule of methane has a mass of 16 amu) Molar Mass of methane = 16 grams (One mole of methane molecules has a mass of 16 grams)

14 Molecular mass of CO 2 Molar mass of CO 2

15 Formula mass of KCl Molar mass of KCl

16 Molar Mass (other terms you may hear) Gram atomic mass (gam) –Mass of 1 mole of an element Gram formula mass (gfm) –Mass of 1 mole of an ionic compound Gram molecular mass (gmm) –Mass of 1 mole of a molecular compound Note: We will round atomic masses and molar masses off to the nearest 10 th

17 To find the molar mass of a compound, add up the number of grams of each element in one mole of the compound. Molar mass of Ca Cl 2 : 1 mole Ca x 40.1 g/mol = 40.1 g + 2 moles Cl x 35.5 g/mol= 71.0 g 1 mole of CaCl 2 = g The molar mass of CaCl 2 is g/mol Molar Mass of Molecules and Compounds

18 Find the molar mass of Mg(NO 3 ) 2 : Element # moles molar mass__________ Mg 1x24.3g/mol= N2x14.0g/mol= O6x16.0g/mol= Note: We will round molar masses off to the nearest 10 th Learning Check!

19 A.Molar Mass of K 2 O = ? g/mole B. Molar Mass of Al(OH) 3 = ? g/mole Learning Check!

20

21 We can use the mole in a conversion factor to go from number of particles to mass of particles. Example: Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? 3.00 moles Al ? g Al Converting Moles and Grams

22 Question: 3 moles of Aluminum = ? Grams Al 1. Molar mass of Al1 mole Al = 27.0 g Al 2. Conversion factors for Al 27.0g Al or 1 mol Al 1 mol Al 27.0 g Al 3. Setup3.00 moles Al x 27.0 g Al 1 mole Al Answer = 81.0 g Al

23 Learning Check How many grams are in 14.8 mole of copper?

24 Learning Check 2.3 g NaCl = ?? mol

25 The Mole-Volume Relationship Avogadro’s hypothesis states that equal volumes of gas at the same temperature and pressure contain the same number of particles 1 liter of oxygen gas has the same number of oxygen molecules as 1 liter of methane gas has of methane molecules – even though the molecules are of very different sizes.

26 The Mole-Volume Relationship The molar volume of a substance is the volume occupied by 1 mole of that substance at a given temperature and pressure. At standard temperature and pressure (STP), 1 mol of any gas occupies a volume of 22.4 L, therefore: The molar volume of a gas at STP is 22.4L STP is defined as 0 o C and 1 atm pressure (101.3 kPa)

27

28 Learning Check What is the volume, in liters, of 1.5 mol Cl 2 at STP?

29 Learning Check 15 L of H 2 gas contains how many moles of H 2 ? How many moles of H?

30 Learning Check The density of a gas containing carbon and oxygen is found to be g/L at STP. What is the molar mass of the compound?

31 Atoms/Molecules and Grams We can convert number of atoms/molecules to their weight in grams using Avogadro’s number However You can’t go directly from atoms to grams!!!! You MUST go thru MOLES. It’s a two step process!!

32

33 Atoms/Molecules and Grams How many atoms of Cu are present in 35.4 g of Cu? 35.4 g Cu = 3.4 X atoms Cu 1 mol Cu 63.5 g Cu 6.02 x atoms Cu 1 mol Cu

34 Learning Check! How many atoms of K are present in 78.4 g of K?

35 Two Step Practice 1.How many atoms are there in g of gold? 2.How many molecules are there in 4.1 L of chlorine gas(Cl 2 )? 3.How many grams does 35.5 L of H 2 gas weigh?

36 Percent Composition This is percent by mass of each element in a compound %mass of element = mass of element x 100% mass of compound

37 Percent Composition What is the percent composition of propane (C 3 H 8 )? Mass of C in 1 mol propane = 36.0 g Mass of H in 1 mol propane = 8.0 g Molar mass of propane = 44.0 g/mol % C = __mass of C __ x 100% = mass of propane % H = ___mass of H__ x 100% = mass of propane

38 What is the percent nitrogen in the common fertilizer NH 3 ? Percent Composition

39 Percent Composition Practice Find the percent composition of: CaF 2 NaOH K 2 SO 4

40 Types of Formulas Molecular FormulaMolecular Formula The formula that states the actual number of each kind of atom found in one molecule of the compound. Empirical FormulaEmpirical Formula The formula of a compound that expresses the smallest whole number ratio of the atoms present. Note: Formula units (for ionic compounds) are always empirical formulas Note: Formula units (for ionic compounds) are always empirical formulas

41 Empirical vs Molecular Formulas The molecular formula of glucose is C 6 H 12 O 6 This indicates that one molecule of glucose contains 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen. The empirical formula of glucose would be CH 2 O. This is the lowest whole number ratio of atoms in the molecule.

42 Empirical vs Molecular Formulas The empirical formula and molecular formula can be the same, for example: H 2 O Two different molecules may have the same empirical formula, for example: C 2 H 4 and C 3 H 6 both have the empirical formula CH 2

43 Empirical vs Molecular Formulas Ethylene (used in welder’s torches) has a molecular formula of C 2 H 2. How many carbon atoms, how many hydrogen atoms? Styrene (foam peanuts) has a molecular formula of C 8 H 8. How many C, how many H? What is the empirical formula of these compounds?

44 Empirical vs Molecular Formulas What is the empirical formula of: C 6 H 10 O 4 C2H8N2C2H8N2 C3H8C3H8

45 Empirical vs Molecular Formulas Are these empirical or molecular formulas, or both? S 2 Cl 2 Na 2 SO 4 Al(OH) 3 H 2 O 2 C 3 H 8 C 2 H 6

46 How can we use percent composition to find the empirical formula? If we know that a compound consists of 59.9% Ti and 40.1 % O, what is its empirical formula? Take a 100 g sample of this compound. We know that there will be 59.9 g of Ti and 40.1 g of O in this sample.

47 How can we use percent composition to find the empirical formula? 59.9 g Ti x 1 mole = 1.25 mole Ti 47.9 g 40.1 g O x 1 mole = 2.5 mole O 16.0 g For every 1.25 moles of Ti, there are 2.5 moles of O

48 How can we use percent composition to find the empirical formula? For every 1.25 moles of Ti, there are 2.5 moles of O – but we need these ratios in whole numbers! Divide both numbers by the smaller number: 1.25 moles Ti ÷ 1.25 = 1 mole Ti 2.5 moles O ÷ 1.25 = 2 moles O The ratio is 1 mole Ti : 2 moles O The empirical formula is TiO 2

49 Practice – You Try! What is the empirical formula of a compound that is 69.6% S and 30.4 % N?

50 Practice What is the empirical formula of a compound that is 48.38% C, 8.12% H, and 43.5 % O?

51 How can we determine molecular formula from empirical formula and molar mass? 1.Given: empirical formula = CH 4 N molar mass is 60.0 g/mol Unknown: molecular formula 2.First, calculate the empirical formula mass. CH 4 N =30.0 g 3.Divide the molar mass by the empirical (efm) formula mass to obtain a whole number. 60.0/30.0 = 2 4.Multiply the subscripts by this value. 2(CH 4 N) = C 2 H 8 N 2

52 How can we determine molecular formula from empirical formula and molar mass? What is the molecular formula of a compound that has an empirical formula of CH 2 O and a molecular mass of g/mole?

53 Practice – You Try! Calculate the molecular formula of a compound whose molar mass is g and empirical formula is C 3 H 4 O 3.