2. The Mole Chemistry 6.0

3. The Mole I. Formulas & Chemical Measurements A. Atomic Mass 1. Definition: the mass of an atom, based on a C-12 atom, in atomic mass units, amu. 2. 1 amu = 1.66 x 10 -24 g = 1/12 the mass of a C-12 atom 3. Example: atomic mass of sodium = 23.0 amu B. Formula Mass 1. Definition: the sum of the atomic masses of all the atoms in a formula. 2. Example: formula mass of Fe 2 (SO 4 ) 3 = Fe: 2 x 55.8 = 111.6 S: 3 x 32.1= 96.3 O: 12 x 16.0 = 192.0 399.9 amu

4. C. MOLE 1. Atoms are too small to count or mass individually. It is easier to count many or mass many. amu gram ( atomic scale) (macroscopic scale) 18.0 g/mol mole 2. Mole = amount of substance that contains 6.02 x 10 23 particles mol abbreviated: mol 3. Avogadro’s Number = number of particles in a mole = 6.02 x 10 23 particles Particles can be atoms, ions, molecules, or formula units 4. Molar Mass = mass, in grams, per 1 mole of a substance units = grams/mole (g/mol) Example: the molar mass of H 2 O is

5. Getting to know the terms…MICROSCOPICMassMACROSCOPIC Molar Mass Atom Atomic mass amu Element g/mol Molecule Molecular mass amu Molecular Compound g/mol Formula Unit Formula mass amu Ionic Compound g/mol Diatomic Molecules HOFBrINCl H 2 O 2 F 2 Br 2 I 2 N 2 Cl 2

6. MOLE RELATIONSHIPS 1 Mole = 6.02x10 23 particles of substance (atoms, formula units, molecules) 1 Mole = mass (g) of substance from PT Also remember your formula information: 1 molecule = _________ atoms 1 formula unit = _________ ions or _________ atoms

7. II. Mole Conversions MUST use factor label! A. Moles & Mass 1. How many grams in 3.0 moles of water? know: 1 mole H 2 O = 2. How many moles in 60.0 g of copper? know: 1 mole Cu = B. Moles & Particles 1. How many atoms in 3.0 moles of copper? know: 1 mole Cu = 2. How many atoms in 3.00 moles of water? know: 1 mole H 2 O = know: 1 molecule H 2 O = 18.0 g H 2 O 63.5 g Cu 54 g H 2 O 0.945 g Cu 6.02 x 10 23 atoms of copper 6.02 x 10 23 molecules of H 2 O 1.8 x 10 24 atoms Cu 3 atoms 5.42 x 10 24 atoms

8. II. Mole Conversions MUST use factor label! C. Mass & Particles 1. How many atoms in 100.0 g of copper? know: 1 mole = _________ g copper 1 mole = 6.02 x 10 23 __________ of copper 2. How many oxygen atoms are in 75.0 g of sucrose, C 12 H 22 O 11 ? know: 1 mole = __________ g of C 12 H 22 O 11 1 mole = 6.02 x 10 23 _____________ of C 12 H 22 O 11 1 molecule of C 12 H 22 O 11 = 11 ________ of oxygen 63.5 atoms molecules 342.0 9.480 x 10 23 atoms Cu 1.45 x 10 24 atoms

9. Avogadro’s Law Amount - Volume Relationship. Equal volumes of gases at the same temperature and pressure contain an equal number of particles. molar mass volume 4 He222 Rn constant 1 mole gas = 22.4 L = 6.02 x 10 23 particles at STP (273 K & 1 atm)

10. Therefore because of Avogadro’s Law if these three gases have the same number of particles and are at the same temperature and pressure, they must take up the same volume. HeRnO2O2

11. Molar Mass does not affect volume of a gas

12. Avogadro’s Law At STP, the amount of gas is directly proportional to the volume. Problem #1: Which of the following samples of gases occupies the largest volume, assuming that each sample is the same temp and pressure? 50.0 g Ne 50.0 g Ar50.0 g Xe

13. Ideal Gas Law Although no “ideal gas” exists, this law can be used to explain the behavior of real gases under ordinary conditions. P = pressure (atm) V = volume (L or dm 3 ) n = number of moles R = 0.08206 Latm/molK universal gas constant T = Kelvin temperature Individual gas laws describe the relationships between these variables. Ideal gas law relates all 4 variables that describe a gas at one set of conditions. PV = nRT

14. Ideal Gas Law Problems 1.Calculate the volume of a gas balloon filled with 1.00 mole of helium when the pressure is 760. torr and the temperature is 0. o C. 22.4 L 2.Calculate the pressure, in atm, exerted by 54.0 g of xenon in a 1.00-L flask at 20. o C. 9.89 atm 3.Calculate the density of nitrogen dioxide, in g/L, at 1.24 atm and 50. o C. 2.15 g/L

15. B.Empirical Formulas 1.Definition: always the smallest whole-number ratio of the atoms, or ions, in a formula 2.Use experimental data to find the empirical formula 3.Examples a.Determine the empirical formula of a compound if a 2.500-g sample contains 0.900 g of calcium and 1.600 g of chlorine. b.Determine the empirical formula for an iron oxide that is 70.0% iron. Name the compound. CaCl 2 Fe 2 O 3 iron(III) oxide

16. C.Molecular Formula 1.Definition: the formula of a molecular compound. The molecular formula shows the actual number of atoms of each element present in 1 molecule of a compound. Molecular formula for benzene: C 6 H 6 Empirical formula for benzene: D.Molecular formula is always a whole- number multiple of the empirical formula. CH molecular formula = (empirical formula) n n = molar mass molecular formula molar mass empirical formula

17. Example Find the molecular formula of a compound that contains 42.5 g of palladium and 0.80 g of hydrogen. The molar mass of the compound is 216.8 g/mol. Empirical formula - PdH 2 Molecular formula – Pd 2 H 4

18. Concentration Definition: a measure of the amount of solute dissolved in a solution 1. Dilute solution: _________________________________ 2. Concentrated solution: _________________________________ Molarity (M) Moles of solute/Liters of solution = mol/L Molality (m) Moles of solute/mass of solvent = mol/kg ppm and ppb Used for very dilute solutions Drinking water additives or pollutants Atmospheric pollutants % Concentration by mass or volume a. Definition: 1% NaCl: 1 g NaCl per 100 g solution Small amount of solute in solution Large amount of solute in solution

19. Molarity or Concentration a. Definition: number of moles of solute per liter of solution 1 L = 1 dm 3 = 10 3 mL = 10 3 cm 3 = 10 3 cc b. Abbreviation: M Units: mol/L c. Preparation of solutions  Need to know the desired volume & calculate the mass of needed solute.  Prepare 500. mL of 1.0 M NaCl Transfer ________ grams of NaCl to a 500- mL volumetric flask, and add water to the line. *Note: Always add acid to water. 29

20. Problems – Molarity (mol/L) Molarity = mol solute/L solution 1.Calculate the molarity if 37 g of NaCl are dissolved in 150 mL of solution. 2.How many moles of HCl are present in 145 mL of a 2.25 M HCl solution? 3.How many grams of NaCl are contained in 2.5 L of a 1.5 M solution? 4.2 M NaCl 0.326 mol HCl 220 g NaCl

21. Problems – Molality (m) Molality (m) = mol solute/mass of solvent(kg) 1.Calculate the molality if 37 g of NaCl are dissolved in 500 g of water. 2.How many moles of HCl are present in a 2.25 m HCl solution that contains 750. g of water? 3.How many grams of water are needed to make a 1.50 m NaCl solution with 78.0 grams of NaCl? 1.26 mol NaCl/kg water 1.69 mol HCl 889 g NaCl