1. Christopher G. Hamaker, Illinois State University, Normal IL © 2005, Prentice Hall The Mole Concept

2. Avogadro’s Number Avogadro’s Number is the number of atoms in 12.01 grams of carbon. Its numerical value is 6.02 × 10 23. Therefore, a 12.01 g sample of carbon contains 6.02 × 10 23 carbon atoms.

3. The Mole The mole (mol) is a unit of measure for an amount of a chemical substance 1 mol = Avogadro’s Number = 6.02 × 10 23 units We can use the mole relationship to convert between the number of particles and the mass of a substance.

4. Molar Mass The atomic mass of any substance expressed in grams is the molar mass (MM) of that substance. The atomic mass of iron is 55.85 amu. Therefore, the molar mass of iron is 55.85 g/mol. Since oxygen occurs naturally as a diatomic, O 2, the molar mass of oxygen gas is 2 times 16.00 g or 32.00 g/mol.

5. Calculating Molar Mass The molar mass of a substance is the sum of the molar masses of each element. What is the molar mass of magnesium nitrate, Mg(NO 3 ) 2 ? The sum of the atomic masses is: 24.31 + 2(14.01 + 16.00 + 16.00 + 16.00) = 24.31 + 2(62.01) = 148.33 amu The molar mass for Mg(NO 3 ) 2 is 148.33 g/mol.

6. Mole Calculations I – Molar Mass Calculate the Molar Mass of KCl A. 39 grams/mol B. 35.5 grams/mol C. 74.5 grams/mol D. 71 grams/mol Calculate the Molar Mass of Na 2 SO 4 A.23 grams/mol B.142 grams/mol C.110 grams/mol D.174 grams/mol

7. Mole Calculations We will be using the Dimensional Analysis Method again. Recall: –First we write down the units given –Second we write down the units we want to get to. –Third we write down the conversion factors needed. –Fourth, we apply the conversion factor(s) to convert the given units to the desired units

8. What is the mass in grams of 1.33 moles of titanium, Ti? 1. What are we given? 1.33 moles of titanium 2. What do we want? Mass in grams of titanium 3. Conversion Factor: Use the molar mass of Ti: 1 mol Ti = 47.88 g Ti = 63.7 g Ti 1.33 mole Ti × 47.88 g Ti 1 mole Ti Mole Calculations II Mole-to-Gram/Gram-to Mole Conversions

9. How many grams are in 4.5 moles of Li 2 O? A.135 grams B.103.5 grams C.175.5 grams D.0.15 grams How many moles are in 25 grams of water (H 2 O)? A.0.72 moles B.1.39 moles C.1.56 moles D.12.5 moles Mole Calculations II Mole-to-Gram/Gram-to Mole Conversions

10. Mole Calculations III Conversions using Avogadro’s Number How many sodium atoms are in 0.120 mol Na? –Step 1: we have 0.120 mol Na –Step 2: we want atoms of Na –Step 3: 1 mole Na = 6.02 × 10 23 atoms Na = 7.22 × 10 22 atoms Na 0.120 mol Na × 1 mol Na 6.02 × 10 23 atoms Na

11. Mole Calculations I How many moles of potassium are in 1.25 × 10 21 atoms K? –Step 1: we have 1.25 × 10 21 atoms K –Step 2: we want moles K –Step 3: 1 mole K = 6.02 × 10 23 atoms K = 2.08 × 10 -3 mol K1.25 × 10 21 atoms K × 1 mol K 6.02 × 10 23 atoms K

12. Mole Calculations III Conversions using Avogadro’s Number How many moles are in 3.4 x 10 24 molecules of HCl? A.35.4 moles B.5.6 moles C.17.71 moles D.1.12 moles

13. Mole Calculations III Two Step Problems Now we will use the molar mass of a compound to convert between grams of a substance and moles or particles of a substance. 6.02 × 10 23 particles = 1 mol = molar mass If we want to convert particles to mass, we must first convert particles to moles and than we can convert moles to mass.

14. What is the mass of 2.55 × 10 23 atoms of lead? We want grams, we have atoms of lead. Use Avogadro’s number and the molar mass of Pb = 87.8 g Pb 2.55 × 10 23 atoms Pb × 1 mol Pb 6.02×10 23 atoms Pb 207.2 g Pb 1 mole Pb × Mole Calculations III Two Step Problems

15. How many grams are in 8.22x10 24 molecules of CH 4 ? A. 0.68 grams B. 218 grams C.1.47 grams D. 273 grams Mole Calculations III Two Step Problems