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## Stoichiometry of Chemical Reactions ( Q3 U2)

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**Stoichiometry**• 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**The Mole**• 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**How many particles are in a mole?**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 !**Counting Particles in a Mole**There are 6.02 x 10 23 Carbon atoms in a mole of carbon There are 6.02 x 10 23CO2 molecules in a mole of CO2 There are 6.02 x 10 23sodium ions in a mole of sodium There are 6.02 x 10 23marbles 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!**Molar Mass**• 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!**What do we need to know to answer this?**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.**Relating Mass to Moles**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 and Formula Mass**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**Relating the Mass of an Atom to the Mass of a Mole of**substance. Steps • Find the average Atomic Mass of the element on the PT. (state it in grams instead of atomic units) • 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. • 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.**Let’s Practice**Calculate the molar mass of each of the following: • N2 • Cl2 • Br2 • I2 • H2 • F2**Molar Mass Answers**Calculate the molar mass of each of the following: • N2 = 14.007g X 2 =28.014 g/mol • Cl2 = 35.453g X 2 =70.906 g/mol • Br2 = 79.904g X 2 =159.808 g/mol • I2 = 126.904g X 2 =253.808 g/mol • H2 = 1.008g X 2 =2.016 g/mol • F2 = 18.998g X 2 =37.996 g/mol**Now, let’s do the same for an example reaction!**Steps • Count the number and type of atoms • Find the Atomic Mass of each atom type, on the periodic table. Write it in grams. • Multiply the mass times the # of Atoms. Then add the totals**How do we calculate Molar Mass?**• Count the number and type of atoms Ethanol (C2H5OH) • Find the Atomic Mass of each atom type, on the periodic table. Write it in grams. • Multiply The mass X the # of Atoms. Then add the totals.**How do We Calculate Molar Mass?**Example: Calcium Chloride (CaCl2 )**Now You Do Some**What is the molar mass of each of the following? • Fe2 O3 • H2O • CO2 • NaCl • NH3 • BaI2**Molar Mass Answers**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**Now that we know how to find Molar Mass What is the next**step? 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?**Finding the number of atoms in a given mass**Steps to finding the number of atoms in a given mass of a sample • Use PT to find the molar mass of the substance • Convert the mass of the substance to number of moles in the sample (convert using mass of one mole as conversion factor) • Use the number of atoms in a mole to find the number of atoms in the sample • Solve and check answer by canceling out units**Finding the number of atoms in a sample of an element**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)=1.81 X 1023 Fe atoms (55.8g Fe) (1 mol Fe) Step 3: Use the number of atoms in a mole to find the number of atoms in the sample = 1.18 X 1023**Calculate the number of atoms in the given samples**• 25.0 g silicon, Si • 1.29 g chromium, Cr**Answers**(25.0 g Si )(1 mol Si )(6.02 X 1023 Si atoms ) 1 28.1g Si 1 mol Si = 5.36 X1023 atoms Si (1.29 g Cr )(1 mol Cr )(6.02 X 1023 Cr atoms ) 1 52.0g Cr 1 mol Cr = 1.49 X1022 atoms Cr**Practice: Determine the number of Atoms in a given**sampleRemember: (given mass X 1 mole per molar mass X atoms per 1 mole) • 98.3g mercury, Hg • 45.6g gold, Au • 10.7g lithium, Li • 144.6g tungsten, W**Answers**1. (98.3 g Hg )(1 mol Hg )(6.02 X 1023 Hg atoms) 1 200.6g Hg 1 mol Hg = 2.95 X1023 atoms Hg 2. (45.6 g Au )(1 mol Au )(6.02 X 1023 Au atoms) 1 197.0g Au 1 mol Au = 1.39 X1023 atoms Au 3. (10.7 g Li )(1 mol Li )(6.02 X 1023 Li atoms) 1 6.94g Li 1 mol Li = 9.28 X1023 atoms Li 4. (144.6 g W )(1 mol W )(6.02 X 1023 W atoms) 1 183.8g W 1 mol W = 4.738 X1023 atoms W**Determining the Number of formula units in a sample**Steps • Use the PT to calculate the molar mass of one formula unit • Convert the given mass of the compound to the number of molecules in the sample (use the molar mass as the conversion factor) • Multiply the moles of the compound by the number of the formula units in a mole (Avagadro’s number) and solve • Check by evaluating the units**The mass of a quantity of Iron(III) oxide is 16.8g. How many**formula units in the sample? • 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) (16.8 g Fe2O3)(1 mol Fe2O3)(6.02 X 1023Fe2O3 Formula units) 1 159.6g Fe2O3 1 mol Fe2O3 = 6.34 X1022 Fe2O3 Formula units**How many Formula Units in each sample?**• 89.0g sodium oxide (Na2O) • 10.8g boron triflouride ( BF3)**Answers**• 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 (given mass X 1 mole per molar mass X molecules per 1 mole) (89.0 g Na2O)(1 molNa2O)(6.02 X 1023Na2OForm Units) 1 62.0g Na2O 1 mol Na2O = 8.64 X1023 Na2OFormula units**Answers Continued**• 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 ( given mass X 1 mole per molar mass X molecules per 1 mole) (10.8 g BF3)(1 molBF3)(6.02 X 1023BF3Form units) 1 67.8g BF3 1 mol BF3 = 9.59 X1022 BF3 Formula units**How do we find the number of moles if given the mass?**Steps • Determine the molar mass • Change given mass to moles by using molar mass as the conversion factor. (1/molar mass)**Example of Grams to Moles**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 molsucrose) 1 342.0g sucrose = 2.0 X10-02moles of sucrose**Determine the number of moles in each sample**• 16.0g sulfur dioxide, SO2 • 68.0g ammonia, NH3 • 17.5g copper(II) oxide, CuO**Answers**• 16.0g sulfur dioxide, SO2 (16.0g/1) (1mole/64.1g ) = 0.250 mol SO2 • 68.0g ammonia, NH3 ( 68.0g/1) (1 mole/ 17.0g) = 4.00 mol NH3 • 17.5g copper(II) oxide, CuO ( 17.5g/1) (1 mole/ 79.1g) = 0.22 mol CuO**How do we find the mass if given the moles?**Steps: • Find the molar mass of the compound • Use the molar mass to convert the given number of moles to a mass (moles) X (g/mol) • Solve • Check using dimensional analysis (make sure units cancel and leaves only grams)**Ex: What mass of water must be weighed to obtain 7.50 mol of**H2O? • 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!**Practice Determining the Mass from the Molar Quantities:**• 3.52 mol Si • 1.25 mol aspirin, C9H8O4 • 0.550 mol F2 • 2.35 mol Barium Iodide, BaI2**Answers: Molar Quantity Problems**(moles) X (g/mol) • What mass of Si = 3.52 mol Si (3.52 mol Si)(28.1g Si) = 98.9g Si 1 (1 mole Si) • 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)**Answers: Molar Quantity Problems, part 2**• 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) • 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)**What We Should Know & Be Able To Do At This Point!**Know: • What stoichiometry is • What a mole is • How to calculate molar mass of an element and of a compound • How to determine the number of atoms or formula units in a given mass of sample • How to determine the number of moles in a given mass of a sample • How to determine the mass of a given molar quantity**Using Moles**• 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 • When one of the reactants in a reaction are used up, the reaction stops. • The reactant that is used up is called a limiting reagent**Predicting Mass of a Reactant and Product**• You can not move directly from the mass of one substance to the mass of the second Steps • Write a balanced equation • Convert the given mass to moles first! • The coefficients of balanced reactions tell you the NUMBER OF MOLESof each chemical in the reactant. (these are used as the conversion factor) • 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 to mass**Example: Predicting Mass of a Reactant and Product**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 andthe 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**How many grams of Hydrogen are required for 3.75g of**nitrogen to react completely? What mass of Ammonia is formed? N2 + 3H2 2NH3 • Convert the given mass to moles Find the # of moles of N2using molar mass (3.75g N2)(1 mol N2) (28.0 g N2) To find the mass of H2 needed: The coefficients of the balanced equation shows 3 mol of H2react with 1 mole ofN2 . Multiply moles of N2 by this ratio. • (3.75g N2)(1 mol N2) ( 3 mol H2) (28.0 g N2) (1 molN2) Once you know the number of moles of any reactant H2use the coefficients in the equation to convert the moles of the other reactants and products To find the mass of hydrogen, multiply the moles of H2 by the mass of 1 mole of H2. (3.75g N2)(1 mol N2) ( 3 mol H2)( 2.0g H2) =3.75 X1 X3 X2.0=0.084 g H2 (28.0 g N2) (1 molN2) (1 mol H2)28.0**What mass of Ammonia is formed?N2 + 3H2 2NH3**To find the mass of ammonia produced: • Use the mole ratio of ammonia molecules to nitrogen molecules to find the moles of ammonia formed. (3.75g N2)(1 mol N2) ( 2 mol NH3) (28.0 g N2) (1 mol N2) • Use the molar mass of ammonia, 17.0g to find the mass of ammonia formed. (3.75g N2)(1 mol N2) ( 2 mol NH3) (17.0g NH3) = 3.75 X1 X2 X17.0=4.55gNH3 (28.0 g N2) (1 mol N2) (1 mol NH3) 28.0**Let’s try another one together!**When potassium chlorate (KClO3) is heated, it decomposes to form potassium chloride and oxygen gas 2KClO3 2KCl + 3O2 • How many grams of KCl are formed when 28.0g of KClO3 decompose? (28.0g KClO3)(1 mol KClO3) ( 1mol KCl) (74.6g KCl) = 17.0gKCl (122.6 g KClO3) (1 mol KClO3) (1 mol KCl) • Use the mass of KCl you determined in part a to calculate the mass of oxygen gas produced. (17.0g KCl) (1 mol KCl) ( 3 mol O2) (32g O2) = 10.9g O2 (74.6 g KCl) (2 mol KCl) (1 mol O2)**Try These Problems**• The combustion of propane (C3H8), a fuel used in backyard grills, produces carbon dioxide and water vapor. C3H8 + 5O2 3CO2 + 4H2O What mass of carbon dioxide forms when 95.6g of propane burns? • Solid xenon hexafluoride is prepared by allowing xenon gas and fluorine gas to react. Xe + 3F2 XeF6 How many grams of fluorine are required to produce 10.0 g of XeF6? • Using the previous reaction, how many grams of xenon are required to produce 10.0g of XeF6 ?**Answers**• 287 g CO2 • 4.65 g F2 • 5.35 g Xe**Using molar volumes in Stoichiometric Problems**• Avogadro’s principle states that equal volumes of gasses at the same temperature and pressure contain equal numbers of moles of gasses. • The molar volume of a gas is the volume that a gas occupies at 1 atmosphere( 101 kPa, or 760 mm Hg) of pressure and a temp of 0.0° C or 273°K (STP). • At STP, the volume of 1 mole of any gas is 22.4L, (there masses may be different ). • Molar volume is often used in calculations, BUT BE SURE YOU ARE AT STP!