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 23or 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 Unitsper 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
Predicting Mass of a Reactant and Product Steps • You can not move directly from the mass of one substance to the mass of the second • You MUST convert the given mass to moles first! • The coefficients of balanced reactions tell you the NUMBER OF MOLESof 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
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
Convert the given mass to moles Find the # of moles of N2using molar mass (3.75g N2)(1 mol N2) (28.0 g N2) • The coefficients of balanced reactions tell you the NUMBER OF MOLESof 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