Chapter 11: The Mole 1

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1 Chapter 11: The Mole 1 In what quantity do you purchase the following? Eggs? Shoes? Paper? Roses? Chemists have created their own counting unit to measure atoms, molecules, or formula units in a sample. The mole is the unit used to measure the amount of a substance. Abbreviated mol SI base unit to measure the amount of a substance Number of representative particles of carbon-12 in 12 g of C x10 23 particles; 602 billion trillion known as Avogadro s number, in honor of the scientist who determined the volume of one mole of gas (1811). The number he determined is the same for all gases. How big is a mole? 1. Enough 12-oz. aluminum cans to cover the surface of the earth to a depth of over 200 miles. 2. Enough of unpopped popcorn kernels to spread over the U.S. to a depth of more than 9 miles. 3. Enough marbles to cover the surface of the earth to a depth of more than 6 Km. Converting Moles to Particles and Vice-versa # of moles x 6.02 x particles = particles 1 mole # particles x 1 mole = moles 6.02x10 23 particles Mass and the Mole The mass of a mole of one element will be different from the mass of a mole of another element because each element has a different composition. Remember the atomic mass unit? An atom of carbon-12 has a mass of 12 amu. Mass related to the mass of a mole The mass in grams of one mole of any pure substance is called its molar mass. Units for molar mass is g/mol. Equal to the numerical value of the average atomic mass (from PT) o 1 mole of C atoms = 12.0 g o 1 mole of Mg atoms = 24.3 g o Called a gram formula mass when used with ionic compounds Find the molar mass (round to the tenths place) for: 1 mole of Br atoms = 1 mole of Sn atoms = Molar mass of molecules and compounds Mass in grams of 1 mole of a compound equals the sum of the atomic masses of the elements involved. 1 mole of CaCl 2 = 1 mole of N 2 O 4 = 1 mole of CH 4 = Converting Moles to Grams Grams = moles x molecular mass (in g) 1 mole 2 moles of CuSO 4 = g 3 moles of NaCl = g

2 Chapter 11: The Mole 2 Converting Grams to Moles Moles = grams molecular mass 779 g CuSO 4 = mol 525 g ZnCl 2 = mol Atoms to mass conversion # Atoms x 1 mole x molar mass = g 6.02x10 23 atoms 1 mole 1.2 x atoms of N = g Converting from mass to atoms You cannot make a direction conversion from the mass of a substance to the number of representative particles (atoms) in that substance. You have to convert to moles first, then moles to atoms. Step 1: Mass x mole = # moles molecular mass Step 2: #moles x 6.02x10 23 atoms = #atoms mole 25.0 g Au = _? atoms 35.4 g Cu = _? atoms 5.5 x atoms He = g Wrap up! Mass must always be converted to moles before being converted to atoms. Atoms must always be converted to moles before calculating their mass.

3 Chapter 11: The Mole 3 Chemical Compounds in Moles You can also have a mole of different compounds. Each compound will have the sum of the molar masses of the component elements. In one mole of a compound, the ratio of moles of each element is the same as for one molecule. o Ex. In a molecule of freon (CCl 2 F 2 ), you have 1 atom of C, 2 atoms of Cl, and 2 atoms of F. In a mole of Freon, you would have 1 mole of C, 2 moles of Cl, and 2 moles of F. You have 1.25 moles of aluminum oxide (Al 2 O 3 ). How many moles of aluminum ions do you have? Molar Mass of Compounds To determine the molar mass of a compound, use the periodic table to determine the mass of one mole of each element in the compound. Ex. Potassium chromate (K 2 CrO 4 ) 2 mol K x 39.1 g = 78.2 g 1 mol K 1 mol Cr x 52 g = 52 g 1 mol Cr 4 mol O x 16 g = 64 g 1 mol O Molar mass of K 2 CrO 4 = g Determine the molar mass of methane (CH 4 ) Converting Moles to Mass To convert moles to mass in grams, you first determine the molar mass of the compound. Then, you multiply by the number of moles given. What is the mass of 2.50 moles of allyl sulfide, (C 3 H 5 ) 2 S? Converting Mass to Moles To convert mass of a compound to moles, determine the compound s molar mass and set up your conversion factor. How many moles are in 325 g of Ca(OH) 2?

4 Chapter 11: The Mole 4 Converting Mass of a Compound to Particles Remember, you can t directly convert mass to particles; you must go through moles, first. How many particles of Al 3+ and Cl 1- are in 35.6 g of AlCl 3? What is the first step: Find molar mass of AlCl 3 Second step: Find # of moles of AlCl 3 in 35.6 g Third step: Find the ratio of Al in AlCl 3 Fourth step: Find the ratio of Cl in AlCl 3 How would you find the mass in g of one formula unit of AlCl 3? Start with the molar mass of AlCl 3, and use the inverse of Avogadro s number as a conversion factor. Empirical and Molecular Formulas Percent Composition Percent by mass of each element in a compound Molar mass of element x 100 = % mass Molar mass of compound Find the percent composition of Fe 2 O 3 = 160 g Fe = 56 x 2 = 112 g O = 16 x 3 = 48 g 112 x 100 = 70% 48 x 100 = 30% CaCl 2 H 3 PO 4 Recap: 1. Molar mass (# of grams/1 mol) and the inverse (1 mol/# of grams) are the conversion factors between the mass of a substance and the number of moles of the substance. 2. Avogadro s number and its inverse are the conversion factors between the moles of a substance and the number of representative particles. 3. To convert between the number of moles of a compound and the number of moles of atoms or ions contained in the compound, you need the ratio of moles of atoms (or ions) to 1 mole of compound (or its inverse). a. The ratios are shown in the subscripts in the chemical formula. Percent means parts per 100, so the percents by mass of all the elements of a compound must always add up to 100. Chemical Formulas of Compounds Formulas give the relative numbers of atoms or moles of each element in a formula unit. Always a whole number ratio (law of definite proportions) Ex. NO 2 : 2 atoms of O for every atom of N 1 mole of NO 2 = 2 moles of O atoms to every 1 mole of N atoms If we know, or can determine, the relative number of moles of each element in a compound, we can determine a formula for the compound.

5 Chapter 11: The Mole 5 Empirical Formula The empirical formula of a compound that expresses the smallest whole number mole ratio of the elements in the compound. Ratio provides the subscripts in the empirical formula Ionic formulas are always empirical formulas The empirical formula may (or may not) be the same as the molecular formula) o If different, the molecular formula will always be a simple multiple of the empirical formula Molecular Formula The molecular formula states the actual number of each kind of atom found in the compound. More than one compound can have the same empirical formula Molecular formula = empirical formula multiplied by a factor by which everything is multiplied. Writing an Empirical Formula 1. Determine the mass in grams of each element present, if necessary. a. If the problem gives you a percent composition, assume a 100 g sample. 2. Calculate the number of moles of each element from the masses. 3. Divide each of the elements by the smallest number of moles to obtain the simplest whole number ratio. 4. If whole numbers are not obtained in step 3, multiply through by the smallest number that will give all whole numbers. a. Note: do not round off numbers prematurely! Practice time! Determine the empirical formula for a compound that has 40.05% S and 59.95% O. To determine the molecular formula: 1. Calculate the empirical formula 2. Calculate the empirical formula mass by multiplying number of moles by the molar mass 3. Divide the given molar mass by the mass of the empirical formula 4. Multiply subscripts in the empirical formula by the answer in #3. Work space! Molecular formula = (empirical formula)n Practice time! Succinic acid is composed of 40.68% carbon, 5.08% hydrogen, and 54.24% oxygen and has a molar mass of g/mol. Determine the empirical and molecular formulas for succinic acid.

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7 Chapter 11: The Mole 7 Hydrates Hydrates are solids in which water molecules are trapped A compound that has a specific number of water molecules bound to its atoms Ex. Opal colors is the result of the presence of water in the mineral Anhydrous means water has been removed from a hydrate Determining the Formula of a Hydrate 1. Write the formula for the solid 2. Determine the mass of the water (original mass anhydrous mass) 3. Calculate the moles of water (Mass/18g) 4. Calculate the moles of compound 5. Determine the amount of water (mol H 2 O/mol compound) 6. Rewrite the formula Example You have a 5.0-g sample of a hydrate of barium chloride. 1. Formula: BaCl 2 xh 2 O [you don t know x] Uses for Hydrates Used to store solar energy Anhydrous materials are used as desiccants (drying agents) Naming Hydrates When hydrates are named, the number of water molecules associated with each formula unit of the compound is written following a dot: MgSO 4 4H 2 O (magnesium sulfate tetrahydrate) Prefixes are the same as used when naming covalent compounds 1 mono- 2 di- 3 tri- 4 tetra- 5 penta- 6 hexa- 7 hepta- 8 octa- 9 nona- 10 deca- Mass of water must be included in all calculations After heating, the mass of the anhydrous BaCl 2 has a mass of 4.26 g. 2. To find x, subtract the anhydrous mass from the original mass. 5.0g 4.26g = 0.74 g H 2 O 3. Calculate the moles of water.74 g x 1 mol = mol H 2 O 18 g 4. Calculate the moles of the compound 4.26 g x 1 mol = 0.02 mol BaCl g 5. Mol of H 2 O =.041 mol H 2 O = 2 Mol of BaCl 2.02 mol BaCl 2 6. Rewrite the formula: BaCl 2 2H 2 O Practice 2.50 g of hydrated copper sulfate (CuSO 4 xh 2 O) reduces to 1.59 g after heating. What is the formula for the copper sulfate hydrate?