Finding the Molar Mass and Dealing with Moles

Finding the molar mass: Examples: a) HCl 1.01g × 1 mol = 1.01g 1 mol 35.45 g × 1 mol = 35.45 g Cl = 1 mol 1.01 g + 35.45 g = 36.46 g H= So the molar mass of HCl (hydrogen chloride) is 36.46 grams per mole ( 36.46 b) g mol ). BeSO4 9.01g × 1 mol = 9.01g Be = 1 mol 32.07 g S= × 1 mol = 32.07 g 1 mol 16.00 g × 4 mol = 64.00 g O= 1 mol 9.01g + 32.06 + 64.00 g = 105.07 g So the molar mass of BeSO4 (beryllium sulfate) is 105.074 grams per mole ( 105.074 g mol ). This type of problem can be done using less space by combining the above steps into one. Instead of finding the mass of each individual element in the compound and then adding them together, do both as you go as follows: c) Ga2(CO3)3 69.72 g 12.01g 16.00 g + 3 mol C × + 9 mol O × = 319.74 g 1 mol Ga 1 mol C 1mol O So the molar mass of Ga2(CO3)3 (gallium carbonate) is 319.74 g mol . 2 mol Ga × Your turn. Using the same steps as above, find the molar mass of each of the following compounds. Don’t let the large molecules fool you; the same steps are used in each calculation. You might also want to try naming the compounds to help with nomenclature (except numbers 6, 9, 13, 14). 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) H2O HgO Hg2O I2 ICH3OH Ca(NO3)2 Al(OH)3 C12H22O11 Ba3(PO4)2 Sr(MnO4)2 (NH4)2Cr2O7 PtCl2(NH3)2 C23H40N7O17P3S Dealing with moles: Avogadro’s number is the key to this type of problem. Everyone knows what is meant when someone says they have a dozen somethings. It is automatic that a dozen means there are 12 of whatever somethings are being talked about. Avogadro’s number is the same thing except a little bigger and is used to describe the number of particles in one mole of substance. If I told you that I had a dozen pencils and asked you to tell me how many pencils I have, this is what you would do to find out: 3 dozen × 12 pencils = 36 pencils 1 dozen You can also find how many dozen pencils you have if you have 60 pencils: 1 dozen = 5 dozen 60 pencils × 12 pencils Just as 1 dozen pencils contains 12 pencils, 1 mole of particles contains 6.022x1023 particles. These particles can be anything, but in this class, they will always be atoms or molecules. A problem asking how many atoms there are in a certain number of moles will be set up EXACTLY the same way as the proceeding example of 3 dozen pencils. Examples: How many atoms are there in 5.62 moles of Potassium? a) 6.02 × 1023 atoms 5.62 mol × = 3.38 × 1024 atoms 1 mol How many moles are there in 1.16x1022 molecules of Br2? b) 1 mol 22 1.16 × 10 molecules × = 0.0193 mol 23 6.02 × 10 molecules Again it is your turn. As a hint for this review, as well as your tests and quizzes, EVERY time you see the phrase “how many atoms…” or “how many molecules…” in a question, you WILL use Avogadro’s number! 1) 2) 3) 4) 5) 6) How many moles are there in 1 mol of moles? How many atoms are there in 7.42 moles of tin? How many molecules are there in 3.14 moles of water? How many ATOMS are there in 8.22 moles of H2 molecules? How many moles are there in 5.87x1024 molecules of NaCl How many moles are there in 9.46x1018 molecules of AgNO3? Now for a little twist. These will be basically the same questions with one added step. In this case, you will be asked how many atoms or moles are represented by one PART of a molecule. Examples: How many sodium atoms are there in 3.75 moles of Na3PO4? a) The first step is to determine the number of sodium moles in one mole of Na3PO4. Look at the subscript to find out. There are 3 sodium moles in each mole of the compound. So: 3.75 mol Na 3 PO 4 × b) × 1 mol Na 3 PO 4 = 6.77 × 10 atoms Na 24 1 mole Na How many sulfur atoms are there in .512 moles of SO2? Once again, how many moles of sulfur are there in each mole of SO2? Looking at the subscript, we see that there is one mole of sulfur for each mole of SO2. So: .512 mol SO 2 × c) 6.02 × 10 atoms Na 23 3 mole Na 1 mol S 1 mol SO 2 6.02 × 10 atom S 23 × = 3.08 × 10 atom S 23 1 mol S If there are 7.84x1024 atoms of oxygen in a sample of hydrogen peroxide (H2O2), then how many moles of hydrogen peroxide are present? This is the last question, only in reverse. First find the number of moles of oxygen atoms in each mole of H2O2, which from the subscript, is 2. So: 1 mol O 1 mol H 2O 2 24 7.84 × 10 atoms O × × = 6.51 m ol H 2O 2 23 6.02 × 10 atoms O 2 mol O NOTE: The number of moles of one substance over the number of moles of another substance is called the mole to mole ratio. In the preceding example, the mole to mole ratio is 1:2, meaning there is one mole of H2O2 for every two moles of O. The mole to mole ratio is used in the majority (but not all) of the chemical calculations you will do in this class, so learn it well! d) How many moles of magnesium nitrate are present in a sample containing 1.14x1025 atoms of oxygen? First, find the mole to mole ration for oxygen to magnesium nitrate. There are 6 mole of O for each one mole of Mg(NO3)2 so the mole to mole ratio is 6 to 1. How did I know this? Look at the subscript OUTSIDE the parentheses, it is a 2. Now multiply that but the number of oxygen INSIDE the parentheses (which is 3) and you get a TOTAL of 6 oxygen for each Mg(NO3)2. So: 1.14 × 10 25 atomsO × 1molMg ( NO3 ) 2 1molO × = 3.16molMg ( NO3 ) 2 23 6molO 6.02 × 10 atomsO That’s right… your turn yet again. Think the problems through. They are all done the same way, but don’t just go through the motions, think about them and understand them! 1) 2) 3) 4) 5) 6) If a 1 liter flask contains 55.4 moles of H2O, how many atoms of hydrogen are in the flask? A sample has 1.93x1020 atoms of Iron. How many moles of Fe2O3 would this make? How many atoms of carbon are there in 6.15x10-8 moles of (CH3CH2CO2)2C6H4 How many moles of Ra(CN)2 are present if you have 8.34x1027 atoms of N How many atoms of hydrogen are there in 1.23x10-4 moles of Aspartame, C14H18N2O5 Calculate the mass (in grams) of 4.97x1024 molecules of sulfur dioxide. You have just gone over how to go back and forth between particles and moles. The next step is to start or end with a mass. The same methods will be used for this type of problem as were used in the last problems, but now a molecular or atomic mass will also be used. At this point, it may also help to start writing out a game plan for yourself before doing each problem. When you write a game plan, think about what is takes to get from one step to the next. If you are going from grams to moles, you will ALWAYS use the molar mass. Going from moles of one substance to moles of another will ALWAYS require a mole to mole ratio. Going from moles to grams will ALWAYS require a molar mass. If you write out a games plan for each problem, and now what each step requires, you are set to get the problem correct! Examples: a) How many atoms of oxygen are there in 52.6g of (NH4)3PO4? Game plan: grams (NH4)3PO4Æ mol (NH4)3PO4 Æ mol O Æ atoms O 52.6 g ( NH 4 ) 3 PO4 × b) 1mol ( NH 4 ) 3 PO4 4molO 6.02 × 10 23 atoms × × = 9.04 × 10 23 atomsO 140.04 g ( NH 4 ) 3 PO4 1mol ( NH 4 ) 3 PO4 1molO How many grams of mercury (II) bromide are present if you have 8.52x1019 atoms of mercury? Game plan: atoms Hg Æ mol Hg Æ mol HgBr2 Æ grams HgBr2 8.52 × 1019 atomsHg × c) 1molHgBr2 358.59 gHgBr2 1molHg × × = .0507 gHgBr2 23 1molHg 1molHgBr2 6.02 × 10 atomsHg What mass of fluorine is in 5.78x1024 molecules of NaBF4? Game plan: molecules NaBF4 Æ mol NaBF4 Æ mol F Æ grams NaBF4 5.78 × 1024 moleculesNaBF4 × 1molNaBF4 4molF 19.00 gF × × = 729.44 gF 23 6.02 × 10 moleculesNaBF4 1molNaBF4 1molF Your tu…. Never mind, you know what to do. What mass of rubidium is in 2.39x1020 molecules of Rb2SO4? 1) 2) How many sodium atoms are there in 6.53kg of NaHCO3? 3) What is the mass of iodine in 8.52x1020 molecules of CeI3? 4) How many oxygen atoms are in 1.2x10-3 grams of testosterone, C19H28O2? 5) What is the mass of a snowflake (think) containing 2.67x1019 atoms of hydrogen? 6) How many nitrogen atoms in 1.05x1021 molecules of caffeine, C8H10N4O2? 7) What is the mass of a Vitamin C tablet that has 5.13x1021 atoms of oxygen? The formula for Vitamin C is C6H8O6. 8) A sample of calcium acetate contains 5.98x1023 atoms of oxygen. What mass of hydrogen does it contain? 9) Home many iodine atoms are there in 28.3mg of carbon tetraiodide?