Chapter 11: The Mole1

In what quantity do you purchase the following? Eggs? Shoes? Paper?

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.

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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.

Roses?

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Mass and the Mole

Abbreviated mol SI base unit to measure the amount of a substance Number of representative particles of carbon-12 in 12 g of C-12 6.02x1023 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.

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 CaCl2 = ____________________ 1 mole of N2O4 = ____________________ 1 mole of CH4 = _____________________

Converting Moles to Particles and Vice-versa

Converting Moles to Grams

# of moles x 6.02 x 1023 particles = particles 1 mole

Grams = moles x molecular mass (in g) 1 mole

# particles x

2 moles of CuSO4 = __________________g

1 mole________ = moles 6.02x1023 particles

3 moles of NaCl = ___________________g

Chapter 11: The Mole2

Converting Grams to Moles

Converting from mass to atoms

Moles = ____grams_____ molecular mass

You cannot make a direction conversion from the mass of a substance to the number of representative particles (atoms) in that substance.

779 g CuSO4 = _______________________mol 525 g ZnCl2 = _______________________mol

Atoms to mass conversion

# Atoms x

1 mole___ x molar mass = __g 6.02x1023 atoms 1 mole

1.2 x 1025 atoms of N = __________g

You have to convert to moles first, then moles to atoms. Step 1: Mass x _____mole_____ = # moles molecular mass

Step 2: #moles x 6.02x1023 atoms = #atoms mole 25.0 g Au = _?__ atoms

35.4 g Cu = _?__ atoms 5.5 x 1022 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.

Chapter 11: The Mole3 Chemical Compounds in Moles

Molar Mass of Compounds

You can also have a mole of different 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.

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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 (CCl2F2), 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 (Al2O3). How many moles of aluminum ions do you have?

Ex. Potassium chromate (K2CrO4) 2 mol K x 39.1 g = 1 mol K

78.2 g

1 mol Cr x 52 g = 1 mol Cr

52 g

4 mol O x 16 g = 1 mol O

64 g

Molar mass of K2CrO4 =

194.2 g

Determine the molar mass of methane (CH4)

Converting Moles to Mass

Converting Mass to Moles

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.

To convert mass of a compound to moles, determine the compound’s molar mass and set up your conversion factor.

What is the mass of 2.50 moles of allyl sulfide, (C3H5)2S?

How many moles are in 325 g of Ca(OH)2?

Chapter 11: The Mole4

Converting Mass of a Compound to Particles

Recap:

Remember, you can’t directly convert mass to particles; you must go through moles, first.

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.

How many particles of Al3+ and Cl1- are in 35.6 g of AlCl3? What is the first step: Find molar mass of AlCl3 Second step: Find # of moles of AlCl3 in 35.6 g Third step: Find the ratio of Al in AlCl3 Fourth step: Find the ratio of Cl in AlCl3 How would you find the mass in g of one formula unit of AlCl3? Start with the molar mass of AlCl3, and use the inverse of Avogadro’s number as a conversion factor.

Empirical and Molecular Formulas

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.

Percent Composition

Chemical Formulas of Compounds

Percent by mass of each element in a compound

Formulas give the relative numbers of atoms or moles of each element in a formula unit.

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Molar mass of element x 100 = % mass Molar mass of compound

Find the percent composition of Fe2O3 = 160 g Fe = 56 x 2 = 112 g 112 x 100 = 70% 160 CaCl2 H3PO4

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O = 16 x 3 = 48 g 48 x 100 = 30% 160

Always a whole number ratio (law of definite proportions) Ex. NO2: 2 atoms of O for every atom of N 1 mole of NO2 = 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.

Chapter 11: The Mole5

Empirical Formula

Writing an Empirical Formula

The empirical formula of a compound that expresses the smallest whole number mole ratio of the elements in the compound.

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!

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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.

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. 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 118.1 g/mol. Determine the empirical and molecular formulas for succinic acid.

Work space!

Chapter 11: The Mole6

Chapter 11: The Mole7

Hydrates

Determining the Formula of a Hydrate

Hydrates are solids in which water molecules are trapped

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 H2O/mol compound) 6. Rewrite the formula

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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

Example You have a 5.0-g sample of a hydrate of barium chloride. 1. Formula: BaCl2·xH2O [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: MgSO4 · 4H2O (magnesium sulfate tetrahydrate) 

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Prefixes are the same as used when naming covalent compounds 1 mono2 di3 tri4 tetra5 penta6 hexa7 hepta8 octa9 nona10 decaMass of water must be included in all calculations

After heating, the mass of the anhydrous BaCl2 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 H2O 3. Calculate the moles of water .74 g x 1 mol = 0.041 mol H2O 18 g 4. Calculate the moles of the compound 4.26 g x 1 mol = 0.02 mol BaCl2 208.3 g 5. Mol of H2O = .041 mol H2O = 2 Mol of BaCl2 .02 mol BaCl2

6. Rewrite the formula: BaCl2·2H2O Practice 2.50 g of hydrated copper sulfate (CuSO4·xH2O) reduces to 1.59 g after heating. What is the formula for the copper sulfate hydrate?