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The study of the quantitative relationships between reactants and products in a reaction It is used to answer questions like; If I have this much reactant, how much product can I make? If I want this much product, how much reactant do I need? These questions have real life application, particularly in manufacturing. It allows us to convert the mass of a substance to the number of particles (atoms, ions or molecules) it contains. These numbers can be really large, so they are counted in groups Much like when we count a lot of pennies we stack them in 10’s and count by 10 Atoms are very tiny, so small that the grouping we use to count them must be very large MOLE; the group (unit of measure) used to count atoms, molecules, formula units or ions of a substance 1 mole of a substance has a particular number of particles in it! Much like 1 dozen always means 12; whether it is 12 eggs 12 oranges or 12 gold bars The number of particles in a mole = 6.02 x 10 23 or 602,000,000,000,000,000,000,000 ! This is known as Avogadro’s Number Using this, We can easily count the number of particles in all kinds of things ! There are 6.02 x 10 23 Carbon atoms in a mole of carbon There are 6.02 x 10 23 CO2 molecules in a mole of CO2 There are 6.02 x 10 23 sodium ions in a mole of sodium There are 6.02 x 10 23 marbles in a mole of marbles That’s a lot of marbles! The Size of a mole of a substance changes, the bigger the substance the more space a mole of the substance takes up, but the number of particles in a mole is always the same! Chemicals do not come bundled in moles, like a dozen eggs comes in a 1 dozen or 1 ½ dozen package so we use the mole as a grouping unit. The mass of 1 mole of a pure substance called it’s molar mass If I want to produce 500g of methanol using the following equation, CO2 +3H2 CH3OH + H20 how many grams of CO2 and H2 do I need? These are the questions stoichiometry answers! If I want to produce 500g of methanol using the following equation; CO2 +3H2 CH3OH + H20 How many grams of CO2 and H2 do I need? This equation relates the molecules of reactants and products, NOT THEIR MASSES! 1 molecule of CO2 and 3 molecules of H2 will make 1 molecule of CH3OH We need to relate the masses to the number of molecules. Remember; The average atomic masses of the elements are found on the Periodic Table! We can use the atomic masses on the PT to relate the mass of the compound to the mass of a mole! Molar mass: The mass (in grams)of one mole of a molecule or a formula unit Molecular mass: mass in atomic mass units of just one molecule Formula Mass: mass in atomic mass units of one formula unit of an ionic compound Steps 1. Find the average Atomic Mass of the element on the PT. (state it in grams instead of atomic units) a) b) 2. Example: molar mass of Fe = 55.847 g Example: molar mass of Pt = 195.08 g If the element is a molecule, count the number of atoms in the molecule then multiply the atomic mass by the number of atoms. a) Example: O2, the mass of O =16.0g There are 2 atoms of O in the O2 molecule , 2 atoms X 16.0g = 32.00g is the molar mass of the molecule. Calculate the molar mass of each of the following: 1. N2 2. Cl2 3. Br2 4. I2 5. H2 6. F2 Calculate the molar mass of each of the following: 1. N2 = 14.007g X 2 =28.014 g/mol 2. Cl2 = 35.453g X 2 =70.906 g/mol 3. Br2 = 79.904g X 2 =159.808 g/mol 4. I2 = 126.904g X 2 =253.808 g/mol 5. H2 = 1.008g X 2 =2.016 g/mol 6. F2 = 18.998g X 2 =37.996 g/mol Steps 1. Count the number and type of atoms 2. Find the Atomic Mass of each atom type, on the periodic table. Write it in grams. 3. Multiply the mass times the # of Atoms. Then add the totals 1. Count the number and type of atoms Ethanol (C2H5OH) 2. 3. Atom type Amount of each atom C 2 H 6 O 1 Find the Atomic Mass of each atom type, on the periodic table. Write it in grams. Atom type Amount of atom Ave. Atomic Mass in g C 2 12.0 H 6 1.00 O 1 16.0 Multiply The mass X the # of Atoms. Then add the totals. Atom type Amount of atom Ave. Atomic Mass in g Total C 2 12.0 =24.0 H 6 1.00 =6.0 O 1 16.0 =16.0 Molar Mass Of Ethanol (C2H5OH) = 46.0g/mole Example: Calcium Chloride (CaCl2 ) Atom Types Amount of Atoms Ave. Atomic Mass in g Total Ca 1 40.1 40.1 Cl 2 35.5 71.0 Mass of 1 mol of CaCl2 (molar mass) 111.1 g/mole What is the molar mass of each of the following? 1. Fe2 O3 2. H2O 3. CO2 4. NaCl 5. NH3 6. BaI2 Fe2 O3 = 55.85g X 2= 111.7 g 16.0g X 3 = 48.0g = 159.7 g/mol _______________________________________________ H2O = 1.01g X 2 = 2.02 16.0g X 1 = 16.0 = 18.02 g/mol _______________________________________________ CO2 = 12.01g X 1 = 12.01 16.0g X 2 = 32.0 = 44.01 g/mol ________________________________________________ NaCl = 22.99 gX1 = 22.99 35.45g X1 = 35.45 = 58.44 g/mol ________________________________________________ NH3 =14.01g X 1 = 14.01 1.01g X 3 = 3.03 = 17.04 g/mol ________________________________________________ BaI2 = 137.33g X 1 = 137.33 126.90g X 2 = 253.80 = 391.13 g/mol If I want to produce 500g of ethanol using the following equation; 6CO2 +17H2 3C2H5OH + 9H20 How many grams of CO2 and H2 do I need? The Molar Mass Of Ethanol (C2H5OH) = 46.0g/mole Now we need to find the number of atoms in the sample. How many molecules of ethanol are in 500g? Steps to finding the number of atoms in a given mass of a sample 1. Use PT to find the molar mass of the substance 2. Convert the mass of the substance to number of moles in the sample (convert using mass of one mole as conversion factor) 3. Use the number of atoms in a mole to find the number of atoms in the sample 4. Solve and check answer by canceling out units The mass of an iron bar is 16.8g. How many iron(Fe) atoms are in the sample? Step 1: Use PT to find the molar mass of the substance : The molar mass of Fe =55.8g/mole Step 2: Convert the given mass of the substance to number of moles in the sample: Fe =55.8g/mole (16.8g Fe) (1 mol Fe) (6.022 X 1023 Fe atoms) (55.8g Fe) (1 mol Fe) = 1.81 X 10 23 Fe atoms Step 3: Use the number of atoms in a mole to find the number of atoms in the sample = 1.18 X 1023 1. 25.0 g silicon, Si 2. 1.29 g chromium, Cr ( 25.0 g Si ( 1.29 g Cr 1 mol Si ) ( 28.1g Si ) ( 6.02 X 1023 Si atoms 1 = 5.36 X1023 atoms Si 1 mol Cr ) ( 52.0g Cr ) ( 1 = 1.49 X1022 atoms Cr 1 mol Si ) 6.02 X 1023 Cr atoms 1 mol Cr ) 1. 2. 3. 4. 98.3g mercury, Hg 45.6g gold, Au 10.7g lithium, Li 144.6g tungsten, W 1 mol Hg 1. 98.3 g Hg 1 200.6g Hg = 2.95 X1023 atoms Hg ( )( )( 6.02 X 1023 Hg atoms 1 mol Hg 23 Au atoms 45.6 g Au 1 mol Au 6.02 X 10 2. 1 197.0g Au 1 mol Au = 1.39 X1023 atoms Au ( )( )( 1 mol Li 3. 10.7 g Li 1 6.94g Li = 9.28 X1023 atoms Li ( )( )( 1 mol W 4. 144.6 g W 1 183.8g W = 4.738 X1023 atoms W ( )( 6.02 X 1023 Li atoms 1 mol Li )( ) 6.02 X 1023 W atoms 1 mol W ) ) ) Steps 1. Use the PT to calculate the molar mass of one formula unit 2. Convert the given mass of the compound to the number of molecules in the sample (use the molar mass as the conversion factor) 3. Multiply the moles of the compound by the number of the formula units in a mole (Avagadro’s number) and solve 4. Check by evaluating the units Calculate the molar mass (Fe2O3) 2 Fe atoms 2X 55.8 = 111.6 3 O atoms 3 X 16.0 = +48.0 molar mass 159.6 g/mol (given mass X 1 mole per molar mass X Form Units per 1 mole) 1. ( 16.8 g Fe2O3 1 )( 1 mol Fe2O3 6.02 X 1023 Fe2O3 Formula units 159.6g Fe2O3 1 mol Fe2O3 )( = 6.34 X1022 Fe2O3 Formula units ) 1. 89.0g sodium oxide (Na2O) 2. 10.8g boron triflouride ( BF3) 89.0g sodium oxide (Na2O) Calculate the molar mass (Na2O) 2 Na atoms 2X 23.0 = 46.0 1 O atoms 1 X 16.0 = +16.0 molar mass 62.0 g/mol 1. (given mass X 1 mole per molar mass X molecules per 1 mole) ( 89.0 g Na2O 1 )( 1 mol Na2O )( 62.0g Na O 6.02 X 1023 Na2O 2 = 8.64 X1023 Na2O Formula units Form Units 1 mol Na2O ) 10.8g boron trifloride ( BF3) Calculate the molar mass (Na2O) 1 B atom 1X 10.8 = 10.8 3 F atoms 3 X 19.0 = +57.0 molar mass 67.8 g/mol 2. ( given mass X 1 mole per molar mass X molecules per 1 mole) ( 10.8 g BF3 1 )( 1 mol BF3 6.02 X 1023 BF3 Form units 67.8g BF3 1 mol BF3 )( = 9.59 X1022 BF3 Formula units ) Steps 1. Determine the molar mass 2. Change given mass to moles by using molar mass as the conversion factor. (1/molar mass) Calculate the number of moles in 6.84g sucrose (C12H22O11) 12 C atoms 12 X 12.0 = 144.0 22 H atoms 22 X 1.0 = 22.0 11 O atoms 11 X 16.0 = +176.0 molar mass 342.0 g/mol (given mass/1) X (1 mole/ molar mass) ( 6.84 g sucrose 1 1 mol sucrose ) ( 342.0g sucrose) = 2.0 X10-02 moles of sucrose 1. 2. 3. 16.0g sulfur dioxide, SO2 68.0g ammonia, NH3 17.5g copper(II) oxide, CuO 1. 16.0g sulfur dioxide, SO2 (16.0g/1) (1mole/64.1g ) = 0.250 mol SO2 2. 68.0g ammonia, NH3 ( 68.0g/1) (1 mole/ 17.0g) = 4.00 mol NH3 3. 17.5g copper(II) oxide, CuO ( 17.5g/1) (1 mole/ 79.1g) = 0.22 mol CuO Steps: 1. Find the molar mass of the compound 2. Use the molar mass to convert the given number of moles to a mass (moles) X (g/mol) 3. Solve 4. Check using dimensional analysis (make sure units cancel and leaves only grams) 1. 2. 2. 3. Find the molar mass of the compound (H2O) H - 2 atoms – 1.0 = 2.0 O - 1 atom - 16.0 = 16.0 18.0 g/mol Use the molar mass to convert the given number of moles to a mass (moles) X (g/mol) (7.5 mol H2O) ( 18.0 g H2O) ( 1 mol H2O) Solve : 7.5 X 18.0g H2O = 135 g H2O Check using dimensional analysis (make sure units cancel and leaves only grams) “mol H2O” cancel each other out, units are correct! 1. 2. 3. 4. 3.52 mol Si 1.25 mol aspirin, C9H8O4 0.550 mol F2 2.35 mol Barium Iodide, BaI2 (moles) X (g/mol) 1. What mass of Si = 3.52 mol Si (3.52 mol Si) (28.1g Si) = 98.9g Si 1 (1 mole Si) 2. What mass of C9H8O4 = 1.25 mol aspirin, C9H8O4 C -9 atoms – 12.0 – 108.0 H- 8 atoms – 1.0 8.0 O – 4 atoms – 16.0 - 64.0 180.0g/mol (1.25 mol C9H8O4) (180.0g C9H8O4) = 225.0g C9H8O4 1 (1 mole C9H8O4) 3. What mass of F2 = 0.550 mol F2 F- 2 atoms – 19.0 = 38.0 g/mol (0.550 mol F2 ) (38.0 g F2) = 20.9g F2 1 (1 mole F2) 4. What mass of BaI2 = 2.35 mol Barium Iodide, BaI2 Ba-1 atom – 137.3 - 137.3 I – 2 atoms – 126.9 - 253.8 391.1g/mol (2.35 mol BaI2) (391.1g BaI2) = 919.1g BaI2 1 (1 mole BaI2) Know: 1. What stoichiometry is 2. What a mole is 3. How to calculate molar mass of an element and of a compound 1. How to determine the number of atoms or formula units in a given mass of sample 2. How to determine the number of moles in a given mass of a sample 3. How to determine the mass of a given molar quantity Review of Calculation Rules To Find molar (atomic mass of each atom) X (amount of each mass (g/mol) atom) Then add together mass of all atoms (g/mol) To Find the # atoms in a given mass (given mass) X (1mole) /(molar mass(g)) X (# atoms) /(1 mole) To Find the # moles in a given mass (given mass) X (1mole)/(molar mass(g)) X (#atom)/(1mole) To Find the mass(g) of a given molar quantity (#moles) X (grams/1 mole)(from molar mass) Balanced chemical equations relate moles of reactants to moles of products Just like when baking, reactants have to be mixed in the proper proportions to make a certain amount of the desired product Specific amounts of reactants produce specific amounts of product We can use balanced chemical equations and moles to PREDICT the masses of reactants or products Steps You can not move directly from the mass of one substance to the mass of the second 1. You MUST convert the given mass to moles first! 2. The coefficients of balanced reactions tell you the NUMBER OF MOLES of each chemical in the reactant 3. Once you know the number of moles of any reactant or product use the coefficients in the equation to convert the moles of the other reactants and products Ammonia gas is synthesized from nitrogen gas and hydrogen gas according to the balanced equation : N2 + 3H2 2NH3 How many grams of hydrogen gas are required for 3.75g of nitrogen gas to react completely? What mass of ammonia is formed? Reactants and products are related in terms of moles The amount of H2 needed depends on the moles of N2 present in 3.75g and the ratio of moles of H2 to moles of N2 in the equation. The amount of ammonia formed depends on the ratio of moles N2 to moles of ammonia Convert the given mass to moles Find the # of moles of N2 using molar mass 1. (3.75g N2) (1 mol N2) (28.0 g N2) 2. 3. The coefficients of balanced reactions tell you the NUMBER OF MOLES of each chemical in the reactant Once you know the number of moles of any reactant or product use the coefficients in the equation to convert the moles of the other reactants and products