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The Mole Molar mass, percent composition, empirical and molecular formulas

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How many atoms are in here? What about weight?.

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Atomic Mass A single atom has a very small mass. on the order of 10 -23 grams per atom 1 atom has a mass of about 0.000 000 000 000 000 000 000 01g Because this mass is so small, we use a unit called amu to describe the mass of a single atom. 1 atom of carbon has a mass of 12.011 amu 1 atom of hydrogen has a mass of 1.00794 amu 1 atom of gold has a mass of 196.967 amu

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Formula Mass Formula Mass – the mass, in amu, of one formula unit of a compound. To calculate the formula mass of a compound; Count and record the number of each atom in the formula. Multiply the number of atoms by the mass of that atom from the periodic table. Add these products together.

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Definitions: Atom: The smallest particle of an element (ex: He). Molecule: The smallest particle of a compound (ex: H 2 O) Atomic Weight: The decimal number on the periodic chart (Units: amu) Formula Mass: add up the total atomic weights of the elements in a compound (Units: amu).

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Formula Mass Calculate the formula mass of Ca 1. Ca = 1(Ca) 2. Ca = 1(40.08) = 40.08 3. 40.08 amu 4. Units = amu Ca Cl

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Formula Mass Calculate the formula mass of CaCl 2 1. CaCl 2 = 1(Ca) + 2(Cl) 2. CaCl 2 = 1(40.08) + 2(35.45)= 110.98 1. 110.98 2. Units = amu Ca

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The Mole The mass of a single atom is too small a quantity for use in lab. We need to come up with a way to take atomic masses from the periodic table and turn them into a mass that is useable in lab. In 1811, Amedeo Avogadro determined the number of atoms in one mole of a substance.

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The Mole The mole establishes a relationship between the atomic mass unit (on periodic table) and the gram (used in lab). Mole (mol) - The amount of a pure substance that contains 6.02 x 10 23 particles of that substance. The mole is used to describe a huge amount of any extremely small particle. A mole of gold, a mole of salt and a mole of water each contain 6.02 x 10 23 individual units.

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The Mole One mole of oxygen, one mole of salt and one mole of water. Each sample contains one mole, 6.02 x 10 23, particles.

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Do you think that one mole of gold atoms is going to weigh the same as one mole of aluminum atoms? Why?

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It doesnt make much sense to weigh atoms in amu, because the units are so small…… If you express atomic mass (amu) in GRAMS instead of amu (like we did yesterday), than you have one MOLE of atoms.

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Molar Mass A molar mass is calculated the same way that you calculated formula mass (HUP, TWO, THREE, FOUR). The only difference is the unit that will be placed on the final answer because you are calculating the mass of one mole of a substance. If the formula mass of CaCl 2 is 110.98 amu, then the molar mass of CaCl 2 is 110.98 grams.

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Formula vs. Molecular Mass

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The Mole There are 6.02 x 10 23 carbon atoms in 12 grams, one mole, of carbon. There are 6.02 x 10 23 gold atoms in 197 grams, one mole, of gold. There are 6.02 x 10 23 formula units of calcium chloride in 110.98 grams, one mole, of CaCl 2.

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So, how do we use the mole in Chemistry? We use the mole to convert between the mass, volume and number of particles in a substance. We can make conversions from: Moles to particles and particles to moles. Moles to grams and grams to moles. Moles to volume of a gas and volume of a gas to moles. Any combination of the above categories!

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Molar Conversions

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Converting from Moles to Particles. How many particles of Sodium Chloride are there in 2.50 moles of Sodium Chloride (NaCl)? 2.50 mol NaCl x 6.02 x 10 23 part. = 1.51 x 10 24 1 mole part. NaCl

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Converting from Moles to Particles How many particles of gold are there in 4.25 moles of Au? 4.25 mol Au x 6.02 x 10 23 part.= 2.56x10 24 part 1 mole Au

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Converting from Particles to Moles. How many moles of gold are there in 1.5 x 10 24 atoms of gold? 1.5 x 10 24 atoms Au x 1 mole = 2.5 moles Au 6.02 x 10 23 atoms

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Converting from Particles to Moles How many moles of calcium chloride are there in 3.6 x 10 24 particles of CaCl 2 ? 3.6 x 10 24 units x 1 mole CaCl 2 = 6.0 mol CaCl 2 6.02 x 10 23 part.

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Converting from Mass to Moles How many moles of gold are there in 25.0 grams of gold? 25.0 g Au x 1 mole Au = 0.127 mol Au 196.97 g Au

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Converting from Mass to Moles How many moles of calcium chloride are there in 75.5 grams of CaCl 2 ? 75.5 g CaCl 2 x 1 mole CaCl 2 = 0.680mol CaCl 2 110.98 g CaCl 2

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Converting from Moles to Mass How many grams of Carbon are there in 4.2 moles of Carbon? 4.2 mole C x 12.01 g C = 50. g C 1 mole C

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Converting from Moles to Mass How many grams of water are there in 2.75 moles of water? The molar mass of water is: 16.00 + 1.01 + 1.01 = 18.02 g/mol 2.75 moles H 2 O x 18.02 g H 2 O = 49.6 g H 2 O 1 mole H 2 O

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Volume of Gases One mole of gas (6.02 x 10 23 particles of gas) occupies a volume of 22.4 liters at standard temperature and pressure. This is true if the gas is monatomic like Helium (He), diatomic like Oxygen (O 2 ) or a compound like Carbon dioxide (CO 2 ).

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Converting from Volume to Moles of a gas How many moles of oxygen are there in 10.0L of oxygen? 10.0L O 2 x 1 mole O 2 = 0.446 mole O 2 22.4 L O 2

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Converting from Volume to Moles of a gas How many moles of Carbon dioxide (CO 2 ) are there in 2.50 L of CO 2 gas? 2.50 L CO 2 x 1 mole CO 2 = 0.112 mole CO 2 22.4 L CO 2

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Converting from Moles to Volume of a gas How many liters of Helium are there in 3.6 moles of Helium? 3.6 moles He x 22.4 L He = 81 L He 1 mole He

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Converting from Moles to Volume of a gas What volume will 8.24 moles of CO 2 occupy? 8.24 mol CO 2 x 22.4 L CO 2 = 185 L CO 2 1 mole CO 2

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Multi-Step Conversions If you need to convert from: Mass to particles or particles to mass, Mass to volume or volume to mass, Volume to particles or particles to volume, then you need to perform a 2-step conversion. Notice the mole is not present in the starting or ending quantities. You will ALWAYS use the mole when converting between these units!

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Multi-Step Conversions How many formula units of calcium chloride are there in 10.0 grams of CaCl 2 ? 10.0 g CaCl 2 x 1 mole CaCl 2 x 6.02 x 10 23 units = 110.98 g CaCl 2 1 mole CaCl 2 5.42 x 10 22 formula units of CaCl 2

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Multi-Step Conversions What volume would 2.25 grams of hydrogen gas (H 2 ) occupy at standard temperature and pressure? 2.25 g H 2 x 1 mole H 2 x 22.4 L = 25.0 L H 2 2.02 g H 2 1 mole

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Multi-Step Conversions How many atoms of Argon gas are there in a typical light bulb (0.20 liters) at standard temperature and pressure? 0.20 L Ar x 1 mole x 6.02 x 10 23 atoms = 5.4 x 10 21 22.4 L 1 mole atoms Ar

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Percent Composition The Percent Composition – the percent by mass of each element in a compound. To calculate %Comp: mass of element x 100 = % by mass mass of compound

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Percent Composition Determine the percent by mass of each element in calcium chloride (CaCl 2 ). Ca1 x 40.08 = 40.0840.08 x 100 = 36.11% Ca 110.98 Cl2 x 35.45 = 70.9070.90 x 100 = 63.89% Cl 110.98 40.08 + 70.90 =110.98 (molar mass)

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Percent Composition Calculate the percent by mass of each element in Calcium sulfate, CaSO 4. Ca 1 x 40.08 = 40.0840.08 x 100 = 29.44% Ca 136.15 S 1 x 32.07 = 32.0732.07 x 100 = 23.55% S 136.15 O 4 x 16.00 = 64.00 64.00 x 100 = 47.01% O 136.15 40.08 + 32.07 + 64.00 = 136.15 molar mass

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Percent Composition You can determine the %Comp of a substance experimentally. Measure the mass of a sample Decompose the sample (usually by heating) to separate the component substances. Measure the mass of the substance that remains. Calculate %Comp as before

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Empirical Formula Empirical Formula – the smallest whole number mole ratio of elements in a compound. The empirical formula for a class of molecules is often the same for each sample. Examples: C 5 H 10 O 5 =CH 2 O C 6 H 12 O 6 =CH 2 O C 11 H 22 O 11 =CH 2 O

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Calculating Empirical Formula 1) Assume you are working with a 100.0g sample so the mass of each element will be the same as the percent of that element (for simplicity). 2) Convert each mass in grams to moles using the molar mass of the element. 3) Find the whole number ratio of these calculated amounts by dividing each mole value by the smallest number of moles calculated. 4) Round to whole numbers and use the ratio to determine the empirical formula.

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Calculating Empirical Formula A compound was found to contain 29.6% Calcium, 23.7% Sulfur and 46.8% Oxygen. What is the empirical formula for the compound? If you had a 100 gram sample, you would have 29.6g Ca, 23.7g S and 46.8g O.

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Calculating Empirical Formula Ca29.6g x 1 mole = 0.739 mol Ca 40.08g S 23.7g x 1 mole = 0.739 mole S 32.07g O 46.8 x 1 mole = 2.93 mole O 16.00g 0.739 = 1 0.739 = 1 2.93 = 3.96 0.739 0.739 0.739 Round to the nearest whole numbers, 1 : 1 : 4 Therefore the empirical formula is CaSO 4

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Molecular Formulas Molecular Formula – the actual number of atoms of each element in one molecule of a compound. The ratio of molecular mass to empirical mass is the same as the ratio of molecular formula to empirical formula.

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Calculating Molecular Formula Example: Molecular formulaMolecular Mass C 6 H 12 O 6 180.18 Empirical formulaEmpirical Mass CH 2 O30.03 Ratio C 6 H 12 O 6 = 6Ratio 180.18 = 6 CH 2 O 30.03

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Calculating Molecular Formula Ribose has a molar mass of 150g/mol and a chemical composition of 40.0%C, 6.67% hydrogen and 53.3% oxygen. What is the molecular formula for ribose? Begin by calculating the empirical formula for Ribose.

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Calculating the Molecular Formula for Ribose 40.0g x 1 mole = 3.33 mole C 12.01g 6.67g x 1 mole = 6.60 mole H 1.01g 53.3g x 1 mole = 3.33 mole O 16.00g 3.33 = 16.60 = 1.983.33 = 1 3.333.333.33 Empirical Formula for Ribose CH 2 O

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Calculating Molecular Formula Once you know the empirical formula, you can calculate the molecular formula. Covalent bonds can form in many different ratios. Use the empirical formula and the ratio of molar mass to empirical formula mass to determine the molecular formula.

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Calculating the Molecular Formula for Ribose The molecular mass of Ribose is 150 g/mol The empirical mass of Ribose is 30 g/mol (CH 2 O = 12.01 + (2 x 1.01) + 16.00 = 30.03 g/mol) 150 = 5Therefore, the Molecular 30formula is 5 times the Empirical Formula C 5 H 10 O 5

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The Formula of a Hydrate Hydrate – a compound that has a specific number of water molecules bound to its atoms. Examples: CaCl 2. 2H 2 O FePO 4. 4H 2 O MgSO 4. 7H 2 O

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Determining the Formula for a Hydrate To determine the formula of a hydrate, the sample must be heated to remove all of the water. The mass of the anhydrous sample is subtracted from the mass of the hydrated sample to determine the mass of water removed. The mass of the anhydrous sample and the mass of the water are used to determine the empirical formula and molecular formula as before.

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Determining the Molecular Formula of a Hydrate Cobalt (II) chloride is a hydrated salt. If 11.75g of this hydrate is heated, 9.25g of anhydrous cobalt chloride remains. What is the formula for this hydrate? 11.75g hydrated salt - 9.25g anhydrous salt 2.50g water

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Determining the Molecular Formula of a Hydrate 9.25g CoCl 2 x 1 mole = 0.0712 mol CoCl 2 129.83g 2.50g H 2 O x 1 mole = 0.139 mol H 2 O 18.02g 0.0712 = 10.139 = 1.95 0.07120.0712 1:2 ratio Therefore the formula for the hydrate is CoCl 2. 2H 2 O

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