The Mole Concept1. Relative Atomic Masses John Dalton was the first chemist to compile a list of relative atomic masses for atoms. At that time no one could weigh individual atoms so he did experiments which resulted in determining the “relative” masses of atoms. Since hydrogen is the lightest element, he arbitrarily assigned the mass of a hydrogen atom to be 1 amu (atomic mass unit). By reacting hydrogen with other elements he could determine their mass “relative” to hydrogen. From his experiments Dalton found that an oxygen atom has a relative mass of 16 amu. This means that an oxygen atom is 16 times as heavy as a hydrogen atom. Since Dalton, we have used elements other than hydrogen as the standard. Oxygen was once used and carbon is now the standard for comparison. But in any event a value of 1 amu for hydrogen is still the origin of our present day tables of relative atomic masses. 2. The Mole Amadeos Avogadro had an inspiration that greatly simplified calculations in chemistry. He reasoned that, if an atom of hydrogen weighed 1 amu and an atom of oxygen weighed 16 amu, by weighing out 1 gram of hydrogen and 16 grams of oxygen we would have an equal number of atoms. In fact if we weighed out the relative atomic mass of any element in grams we would always have the same number of atoms. He called that number of atoms a mole. 1gH All the Same Number of Atoms 12 g C 16 g O One Mole 24 g Mg 0 g/mole.1 grams Ca This same concept may be applied to molecules.0 x x 2 1 1 mole H2O = = = 2. 2 . When you buy donuts you often ask for a dozen donuts. Just add up the masses of the atoms to get the mass of one mole of a particular kind of molecule.02 x 1023 donuts 1 mole of pencils = 6. but that didn’t matter. Whether you buy a dozen chocolate donuts or a dozen glazed donuts or a dozen jelly donuts --. Sample Problem 1 Solution Calculate the molar mass of H2O.0 18. H2O is the formula for water. All that mattered was that a mole of any kind of atom was the same number of atoms. one mole of oxygen atoms or one mole of carbon atoms or one mole of hydrogen atoms is always the same number of atoms. 1 mole of oxygen atoms = 6. 1 mole Ca = 40. Today we are able to do experiments to allow us to count atoms.0 16.0 16.0 grams H2O The molar mass of H2O is 18.02 x 1023 3. Molar Mass We have already learned that the mass of one mole of any kind of atom can be determined by looking up that element on a list of relative atomic masses and expressing that mass in grams. It represents the fact that a water molecule contains 2 hydrogen atoms and 1 oxygen atom.The word mole is similar to other words in our language which stand for a particular count. Avogadro was not able to determine how many atoms were in a mole. Likewise. Look over the following examples to see how to determine the “molar mass” of any molecule.02 x 1023 oxygen atoms 1 mole of hydrogen atoms = 6.02 x 1023 hydrogen atoms 1 mole of donuts = 6.02 x 1023 pencils dozen gross pair mole 12 144 2 6.a dozen donuts is always the same number of donuts.02 x 1023 atoms. We now know that one mole of atoms equals 6. We make a chart to add up the mass of one mole of water by rewriting the formula vertically as follows: element relative atomic masses number of atoms total H O 1. 1 g/mole.45 gramsCa 1moleCa 6.18 x10 22 atomsCa 1 40.0 gramsH 2O x = 14. Each can be expressed in fraction form to solve chemistry problems via dimensional analysis.1 28. We are now ready to apply dimensional analysis/factor label to mole calculations.4 L of a gas at STP = molar mass of the element/compound Sample Problem 3 What is the mass of 0.0 gramsNaOH Sample Problem 5 How many atoms are contained in 1.45 grams of Ca? 1.1 14.9 gramsH 2O 1 1moleH 2O Sample Problem 4 How many moles of sodium hydroxide. 40.0 16.Sample Problem 2 Solution Ca N O Calculate the molar mass of Ca(NO3)2. Then use this as a conversion factor to get you from moles to grams. NaOH. Using Moles in Calculations You will remember from chapter 2 how we set up problems using dimensional analysis (factor label). 0.827 molesH 2O 18. are there in 450.1gramsCa 1moleCa 3 .gramsNaOH 1moleNaOH x = 11.0 x x x 1 2 6 1 mole Ca(NO3)2 = = = = 40.2 molesNaOH 1 40.0 96. g of the compound? Solution – First find the molar mass of NaOH.02 x10 23 atoms X X = 2. 1 mole = 6.0 164. 450.1 grams Ca(NO3)2 The molar mass of Ca(NO3)2 is 164. Then use this as a conversion factor to get you from grams to moles. In this chapter we have learned three new equivalencies.02 x 1023 particles = 22.827 moles of H2O? Solution – First find the molar mass of H2O. Calculate the number of atoms/molecules/formula units present in each of the following: 1.16x1023 molecules of carbon tetrachloride 5.0 gramsCO2 x x = 68. 29. Calculate the mass of each of the following: 1. 9. KOH 2. Calculate the molar mass of each of the following: 1. Copper (II) nitrate D.4 LCO2 x x = 122 LCO2 23 1 6.0 g potassium nitrate 2. 8. Sodium phosphate 7.8 gramsCO2 1 22.0 LCO2 1moleCO2 44.29 x10 24 moleculesCO2 1moleCO2 22. Then use this as a conversion factor to get you between grams and moles.0 L of carbon dioxide at STP? Solution – Find the molar mass of CO2.9 L of sulfur dioxide at STP . 3.7 L of N2 at STP 2. 35.02 x10 moleculesCO2 1moleCO2 Sample Problem 7 What is the mass of 45.23x1024 formula units of sodium chromate 3.70 moles of potassium chloride 2. 35.29x1024 molecules of carbon dioxide at STP? Solution – There is no need to calculate the molar mass of CO2 for this problem.8 L of dinitrogen monoxide at STP 3. 0. 16. Carbon tetrachloride 6.4 LCO2 1moleCO2 Problems A. Calculate the number of moles in each of the following: 1. Ca(NO3)2 4.83 moles iron 3. 26. CoCl3 3. 2. Iron (III) oxide B. 264 g of sodium hydroxide C. Molar masses are only necessary when starting with or ending with a mass.Sample Problem 6 How many liters are contained in 3. You have 263 liters of dinitrogen pentoxide gas at STP.88 L of O2 gas at STP? 8. How many formula units are contained in 0. Mixed Problems 1.0 grams of NH3 gas at STP? 4. What is the mass of 47.000 grams of Silver? 5.6 grams of sulfur hexafluoride at STP 2. What is the mass of this gas? 12. You have 8.847 grams of carbon dioxide at STP? 6. How many moles is this? 7.94 moles of carbon dioxide at STP F.000. What is the mass of 1. You have 6. What is the volume of 4. What is the volume of 3. What is the mass of 4.3 X 1028 formula units of copper (II) nitrate? 11.10x1018 atoms of argon at STP 3. What is the mass of 1 atom of iron? . How many molecules is this? 2. 1. What is the volume of 0.5 grams of silver nitrate. How many moles is this? 3.27 grams of nitrogen dioxide gas at STP? 18.82 L of N2 gas at STP.285 grams of potassium hydroxide? 16. What is the volume of 56.E.260 atoms of Neon gas at STP? 17. You have 618. What is the mass of 4. What is the volume of 52.9 moles of N2 gas at STP? 9.3 X 108 atoms of zinc. 5. 47. How many atoms would be found in 73.000 atoms of lithium? 13. What is the mass of 3. How many molecules are contained in 26 grams of water? 15. Calculate the number of liters present in each of the following.720 molecules of O2 gas? 14. 1.74 X 1016 formula units of sodium hydroxide? 10. 154. 3. 0.54x1023 molecules SO2 Part E 1.3x107 grams Cu(NO3)2 11.5 g/mole Part B 1.1 g/mole 4. 2480 g Na2CrO4 3. 4.89x10-4 L Ar 3. 56.5 L CO2 Part F 1.640 moles AgNO3 7. 201 g KCl 2. 5. 1.59x10-19 L Ne 17.16x10-6 grams NaOH 10. 1. 164. 6. 1. 4.06x1021 formula units KOH 16.30 L SF6 2. 165. 159.6 g/mole 5.Answers to Problems Part A 1.0 g/mole 6. 27.1 g/mole 2.431 L CO2 6.4 g/mole 3. 1. 1.98x10-19 grams O2 14.1x1026 atoms Ag 5. 1.60 moles NaOH 3. 1.83x1023 molecules N2 2.55x1023 formula units KNO3 2.5 g N2O Part D 1.5 L NH3 4.36 moles CCl4 Part C 1. 164. 68.0 g/mole 7.0x1023 atoms Fe 3. 1. 1.97 grams O2 8.4x10-15 moles Zn 3. 1. 1270 grams N2O5 12.4 L NO2 18. 6.4x10-16 grams Li 13. 7.59 moles N2 2. 187. 43. 5. 9x10-23 grams Fe 6 . 87 L N2 9.7x1023 molecules H2O 15. 58. 3. 8.