Relative Mass and the Mole

Relative Mass and the Mole How can atoms be counted using a balance? Why? Consider the following equation for a chemical reaction: 2H2 + O2  2H2O This can be interpreted as two molecules of hydrogen and one molecule of oxygen combining to form two water molecules. But how often do chemists limit their reactions to one or two molecules? Usually a reaction is done with an unimaginable number of molecules. How then do chemists know they have the right mix? The molecules need to be quickly counted! How do we count molecules? The answer is the unit called the mole. This activity will start by considering two egg farmers (a chicken farmer and a quail farmer). They produce such large numbers of eggs that they can’t count them all individually, so they count in dozens of eggs in some cases, while in other cases they use mass. Weighing is often easier than counting! Model 1 – Eggs Chicken Quail Ratio of numbers of eggs Ratio of masses of eggs Number of eggs in the sample Mass of the sample Number of eggs in the sample Mass of the sample 1 1 10 37.44 g 374.40 g 10 2.34 g 23.40g 1: 1 1: 1 16: 1 16: 1 438 16398.72g 438 1024.92g 1: 1 16: 1 1 dozen 449.28g 1 dozen 28.08g 1: 1 16: 1 1 million 37440000.00g 1 million 2340000.00g 1:1 16 : 1 1. Consider the data in Model 1. a. What is the mass of a standard chicken egg? 37.44g b. What is the mass of a standard quail egg? 2.34g c. Show mathematically how the 16:1 ratio of masses was calculated in the last column of Model 1. Ratio of masses of eggs = mass of 1 chicken egg / mass of 1 quail egg = 37.44g / 2.34g = 16 / 1 = 16 : 1 2. Use a calculator to complete the table in Model 1. Divide the work among group members. Reduce all ratios to the lowest whole numbers possible. Relative Mass and the 1 3. Imagine you have two baskets—one filled with quail eggs and one filled with the same number of chicken eggs. a. Which basket would be heavier? The basket filled with chicken eggs b. How many times heavier would that basket be? 16 times heavier c. Explain mathematically how it is possible for you to answer part b with confidence, even though you don’t know the actual number of eggs. 16 : 1 – 1 chicken egg is 16 quail eggs 16qe / 1qe = 1ce / 1qe 16qe = 1ce Therefore, for any number of eggs, the mass of chicken eggs is 16 times the mass of quail eggs 4. A farmer weighs out 32.0 kg of chicken eggs. a. What mass of quail eggs would he need to weigh out to have the same number of eggs in both samples? 16 / 1 = 32.0kg / x = 2.0kg of quail eggs b. If the farmer had weighed out 32.0 pounds of chicken eggs (rather than kilograms), what mass of quail eggs would he need to weigh out to have the same number of eggs in both samples? 16 /1 = 32.0 pounds / x = 2.0 pounds of quail eggs 5. A farmer makes up a new counting unit called a “cluckster.” a. If the farmer had 3 clucksters of chicken eggs and 3 clucksters of quail eggs, what could you say about the ratio of their masses? The ratio will still be 16 : 1 since it is the same egg just different counting unit b. Does it matter in this problem how many eggs are in a “cluckster”? Explain. It does not matter the number of eggs in a cluster, the ratio will still be the same as long as it is the same egg. Read This! Let’s take what we learned in the egg model and apply it to atoms. Like eggs, atoms of the same element may have slightly different masses (remember isotopes). The periodic table lists an average atomic mass for the atoms in a sample of each element. These masses are recorded in “atomic mass units” where 1 amu is approximately equal to the mass of a proton (or neutron). Model 2 – Atoms Oxygen Number of Mass of the atoms in sample the sample 1 16.00 amu 160.00amu 10 Sulfur Number of atoms in the sample 1 10 1 dozen 192.00amu 1 million 16000000.00amu 1 million 1 mole 16.00 grams 1 mole 1 dozen Ratio of numbers of atoms Ratio of masses of atoms 32.00 amu 320.00amu 1;1 1:2 1:1 1:2 384amu 1:1 1:2 1:1 1:2 1:1 1:2 Mass of the sample 32000000.00amu 32.00 grams Note: The masses shown for oxygen and sulfur have been rounded to make the arithmetic a bit easier. 6. What is the ratio of the mass of an oxygen atom to the mass of a sulfur atom? 1:2 7. Fill in the table in Model 2 in a similar fashion to the eggs table in Model 1. Divide the work evenly among group members. Reduce all ratios to the lowest whole numbers possible. 8. Circle the phrase below that completes the sentence. When two samples contain the same number of atoms the masses of the the ratio of the sample unrelated. samples will be equal. the ratio of the atom’s masses. . the masses are masses will be equal to 9. Explain why it is not necessary to know how many atoms are in “1 mole” to finish the last row of the table in Model 2. Since both elements have 1 mole then the ratio of number of atoms will be 1 : 1 10. How would the number of oxygen atoms in a 16.00 lbs sample compare to the number of sulfur atoms in a 32.00 lbs sample? 16.00lb / 32.00lb = 1/ 2 = 1: 2 Since the ratio of mass of oxygen to mass of Sulphur is 1: 2, the ratio of number of atoms will be 1 : 1 11. In the front of the room, there is a bottle that contains a 32.00 g sample of sulfur. This is 1 mole of sulfur. Estimate how many atoms are in the bottle. Your group must reach consensus. 1 mole = 6.022 * 1023 atoms 32.00 g of Sulphur = 1mole of Sulphur = 6.022 * 1023atoms Read This! A long time ago chemists discovered what you have just discovered: The relative masses of the elements can be used to “count” atoms. If you measure out a sample equal to an atom’s atomic mass in grams, you always end up with the same number of atoms. Chemists call that quantity the mole—a quantity of any sample whose mass is equal to its atomic mass in grams. Model 3 – Molar Mass Average Mass of One Mole of Particles (Molar Mass) Average Mass of a Single Particle 1 atom of hydrogen (H) 1 atom of copper (Cu) 1.01 amu 1 mole of hydrogen atoms (H) 1.01 g 63.55 amu 1 mole of copper atoms (Cu) 1 molecule of oxygen (O2) 32.01 amu 1 mole of oxygen molecules (O2) 32.01 g 1 molecule of water (H2O) 1 formula unit of sodium chloride (NaCl) 18.02 amu 1 mole of water molecules (H2O) 18.02 g 1 mole of sodium chloride 58.44 g formula units (NaCl) 58.44 amu 63.55 g 12. Look at a periodic table. What number in each element box would a chemist use to find the values in the “Average Mass of a Single Particle” column in Model 3? Atomic mass value (amu) 13. How is the mass of a single particle changed to get the mass of one mole of particles? Atomic mass value in grams 14. Which sample contains more atoms, 18.016 amu of water or 18.016 g of water? Explain. 1 atom = 18.016 amu, 6.022 * 1023 = 18.016g Therefore, 18.016g of water contains more atoms 15. If the formula mass of iron(II) sulfate (FeSO4) is 151.9 amu, what is the molar mass of iron(II) sulfate? Atomic mass (amu) = molar mass (g/mol) 151.9 amu of FeSO4 = 151.9g/mol of FeSO4 16. Use a periodic table to calculate the molar mass of ammonia (NH3). NH3 contain Nitrogen atom and 3 hydrogen atoms Atomic mass of NH3 = atomic mass of Nitrogen + atomic mass of 3 hydrogen = 14.01 amu + 3(1.01amu) = 17.04 amu Since atomic mass in amu is equal to molar mass in g/mol then the molar mass of NH3 is 17.04g/mol 17. How would the number of atoms in a 1.01 g sample of hydrogen compare to the number of atoms in a 63.55 g sample of copper? The number of atoms will be the same since it is 1 mole of both elements Read This! So how many “things” are in a mole? By estimating the size of atoms and taking volume measurements of 1 mole samples scientists can estimate that 1 mole = 6.022  1023 particles or 602 200 000 000 000 000 000 000 particles (More than you could count in a lifetime!) This number is called Avogadro’s number, named after Amedeo Avogadro. 18. Fill in the blanks below using a periodic table. Be sure to include units of g or amu on all masses. 1 atom of helium has a mass of 4.00 amu 1 mole of helium contains 6.022 * 1023 1 formula unit of calcium chloride (CaCl2) has a mass of 23 1 mole of CaCl2 contains 6.022 * 10 . atoms and has a mass of 110.98amu 4.00g . . formula units, and has a mass of 110.98g . Extension Questions 19. Use a periodic table to answer the following questions. a. Fluorine gas consists of diatomic molecules of fluorine (F2). How many molecules of fluorine are in one mole of fluorine? 6.022 * 1023 b. What is the mass of 1 mole of fluorine gas? F2 = 2 (atomic mass of fluorine) = 2 (19.00 amu) = 38 amu 1 mole of F2 = 38 g c. How many atoms of fluorine are in this sample? Show your work. F2 = 2 fluorine 1 mole of fluorine = 6.022 * 1023 atoms 2 moles of fluorine = 2 (6.022 * 1023 atoms) = 1.204 * 1024 atoms 20. The mass of one mole of lead (Pb) atoms is 207.2 g. Use a proportion to calculate the number of lead atoms in a 15.00 g sample of lead. 6.022 * 1023 / x = 207.2g / 15.00g x = 4.36 * 1022 atoms 21. What is the mathematical relationship between atomic mass units (amu) and grams (g)? 1 gram = 6.022 * 1023amu