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Chapter 10

Chemical Quantities

Get ready for some serious finger exercise!

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10.1 The Mole: Measurement of Matter

OBJECTIVES:– Describe methods of measuring the

amount of something– Define Avogadro’s number as it

relates to a mole of a substance– Distinguish between the atomic mass

of an element and its molar mass– Describe how the mass of a mole of a

compound is calculated

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How do we measure items? You can measure mass, or volume, or you can count pieces. We measure mass in grams. We measure volume in liters (or cm3). We count matter in MOLES.

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What is the mole?

We’re not talking about this kind of mole!

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Mole (abbreviated mol)

A mole is simply an amount (like a dozen) It is defined as the number of carbon

atoms in exactly 12 g of carbon-12 (12C). That amount (1 mole) = 6.022 x 1023 of

the representative particles 6.022 x 1023 = Avogadro’s number.

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Similar Words for Amounts

Pair: 1 pair of shoes

= 2 shoes Dozen: 1 dozen roses

= 12 roses Ream: 1 ream of paper

= 500 sheets of paper

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Representative Particles? Representative particles are the smallest

“units” of a substance that define it1) For a molecular compounds: it is the

molecule.2) For an ionic compounds: it is the

formula unit (lowest whole-number ratio of the ions).

3) For an element: it is the atom.» Remember the 7 diatomic elements?

(made of molecules)» Br2 I2 N2 Cl2 H2 O2 F2

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Types of questions How many oxygen atoms in the

following?

CaCO3

Al2(SO4)3

How many ions in the following?

CaCl2NaOH

Al2(SO4)3

3 atoms of oxygen

12 (3 x 4) atoms of oxygen

3 total ions (1 Ca2+ ion and 2 Cl1- ions)

2 total ions (1 Na1+ ion and 1 OH1- ion)

5 total ions (2 Al3+ + 3 SO42- ions)

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Parts of a Whole MoleParts of a Whole Mole Molecules are made of groups of atoms Molecules are made of groups of atoms Ionic compounds are made of ionsIonic compounds are made of ions The The subscriptssubscripts in the formulas of compounds give in the formulas of compounds give

the numbers of each type of elementthe numbers of each type of element

– COCO22 has has 22 O and 1 C atom per molecule O and 1 C atom per molecule» So one mole of COSo one mole of CO22 has one mole of C atoms and 2 moles of O atoms has one mole of C atoms and 2 moles of O atoms

– CaClCaCl22 has has 22 Cl Cl−− and 1 Ca and 1 Ca++ ion per formula unit ion per formula unit» So one mole of CaClSo one mole of CaCl22 has 2 moles of Cl has 2 moles of Cl−− and 1 mole Ca and 1 mole Ca++ ions ions

Tricycle analogyTricycle analogy– One tricycle has 1 One tricycle has 1 seatseat, 2 , 2 pedalspedals and 3 and 3 wheelswheels

– So the “formula” would be So the “formula” would be StStPePe22WhWh33

– How many of each “element” in a dozen tricycles? How How many of each “element” in a dozen tricycles? How many in one mole of tricycles?many in one mole of tricycles?

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Practice problems How many molecules in 4.56 moles of CO2? How

many atoms?

How many moles of water is 5.87 x 1022 molecules?

How many atoms are in 1.23 moles of C6H12O6? How many moles is 7.78 x 1024 formula units of

MgCl2?

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Measuring Moles Remember the mole is based on

the number of C atoms in 12 grams of carbon-12.1 AMU in atoms = 1 g in moles

This proportion is true for all elements in the periodic table.

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Gram Atomic Mass

Equals the mass of 1 mole of an element in grams (from periodic table)

12.01 grams of C has the same number of “pieces” as 1.008 grams of H and 55.85 grams of iron.

We can write this as: 12.01 g C = 1 mole C

(this is the molar mass) ( = ) We can count things by weighing them!

12.01 g C 1 mole C1 mole C 12.01 g C

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Practice Problems What is the mass in grams of 2.34 moles of carbon?

How many moles of magnesium is 24.31 g of Mg?

How many atoms of lithium is 1.00 g of Li?

How much would 3.45 x 1022 atoms of U weigh?

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What about compounds?

in 1 mole of H2O molecules there are two moles of H atoms and 1 mole of O atoms (think of a compound as a molar ratio)

To find the mass of one mole of a compound

– determine the number of moles of the elements present

– Multiply the number times their mass (from the periodic table)

– add them up for the total mass

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Calculating Formula Mass

Calculate the formula mass of magnesium carbonate, MgCO3.

24.3 g + 12.0 g + 3 x (16.0 g) = 84.3 g

the formula mass (or molar mass) for MgCO3 is 84.3 g/mol

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More PracticeMore Practice 1. What is the molar mass of sucrose (C1. What is the molar mass of sucrose (C1212HH2222OO1111)?)? 2. What is the molar mass of each of the following 2. What is the molar mass of each of the following

compounds?compounds?

a)a) phosphorus pentachloride (PClphosphorus pentachloride (PCl55))

b)b) uranium hexafluoride (UFuranium hexafluoride (UF66)) 3. Calculate the molar mass of each of the following 3. Calculate the molar mass of each of the following

ionic compounds:ionic compounds:

a)a) KMnOKMnO44

b)b) CaCa33(PO(PO44))22

4. How many moles is 3.52 x 104. How many moles is 3.52 x 102424 molecules of water? molecules of water? 5. How many atoms of zinc are in 0.60 mol of zinc?5. How many atoms of zinc are in 0.60 mol of zinc? 6. What is the mass of 1.00 mol of oxygen (O6. What is the mass of 1.00 mol of oxygen (O22)?)?

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10.2 Mole-Mass and Mole-Vol Relationships

OBJECTIVES:– Describe how to convert the mass of a

substance to the number of moles of a substance, and moles to mass

– Identify the volume of a molar quantity of gas at STP

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Molar Mass

Molar mass is the generic term for the mass of one mole of any substance (expressed in grams/mol)

The same as: 1) Gram Molecular Mass (for molecules)

2) Gram Formula Mass (ionic compounds) 3) Gram Atomic Mass (for elements)– molar mass is a broad term that encompasses

all these other specific masses

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Examples Calculate the molar mass of the following

and tell what the units are for each:

1. Na2S

2. N2O4

3. C

4. Ca(NO3)2

5. C6H12O6

6. (NH4)3PO4

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Molar Mass = Conversion Factor

Molar mass is the number of grams in 1.0 mole of atoms, ions, or molecules

We can make conversion factors from molar masses to change:

- from grams of a substance to moles

- OR, from moles to grams

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For Example How many moles is 5.69 g of Ca(OH)2?

– Want to convert grams to moles, so need a conversion factor with grams in denominator (to cancel grams) and moles in numerator to change the units to moles.

5.69 g 5.69 g Ca(OH)2 ? mole ? mole Ca(OH)2

? g ? g Ca(OH)2

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For Example Molar masses are equivalent values

of moles ↔ grams of a substance

1mole Ca = 40.1 g x 1 = 40.1 g 1 mol O = 16.0 g x 2 = 32.0 g 1 mole H = 1.0 g x 2 = 2.0 g

1 mole Ca(OH)2 = 74.1 g

1 mol Ca(OH)2 74.1 g Ca(OH)2

74.1 g Ca(OH)2 1 mol Ca(OH)2=

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For Example

How many moles is 5.69 g of Ca(OH)Ca(OH)22?

– Looking to convert grams to moles, so need a conversion factor with grams in denominator (to cancel grams) and moles in numerator to change the units to moles.

5.69 g Ca(OH)5.69 g Ca(OH)22 1 mol Ca(OH)1 mol Ca(OH)22

74.1 g Ca(OH)74.1 g Ca(OH)22

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For Example

How many moles is 5.69 g of Ca(OH)Ca(OH)22?

– Looking to convert grams to moles, so need a conversion factor with grams in denominator (to cancel grams) and moles in numerator to change the units to moles.

5.69 g Ca(OH)5.69 g Ca(OH)22 1 mol Ca(OH)1 mol Ca(OH)22

74.1 g Ca(OH)74.1 g Ca(OH)22

= 0.077 mol Ca(OH)2

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The Mole-Volume Relationship Many chemicals we’ll deal with are gases

- difficult to measure their masses But, we will still need to know how many moles of

gas we have we must know how many particles (atoms, ion,

molecules) are taking part in chemical reactions Easy to measure the volume of a gas, but 2 things

effect volumes of molar amounts of gases:

a) Temperature and b) Pressure If we compare all gases at the same T and P they all

occupy the approximately same volume

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Standard Temperature & Pressure(STP)

= = 0ºC (273 K) and 1 atm pressure At STP, 1 mole of any gas occupies a volume

of 22.4 L

- Called the molar volume This equality can also be a conversion factor

1 mole of any gas at STP = 22.4 L

1 mole gas 22.4 L 22.4 L 1 mole gas

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Practice Examples What is the volume of 4.59 mole of CO2

gas at STP?

How many moles is 5.67 L of O2 at STP?

What is the volume of 8.8 g of CH4 gas at STP?

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Density of a gas

Density = mass / volume for a gas the units are usually g / L

We can determine the density of any gas at STP if we know its formula. Use formula to calculate molar mass (= grams

in 1 mole of gas) Divide molar mass by molar volume (all gases

are 22.4 L / mole)

Mass of 1 mole in grams

Volume of 1 mole in L= grams in 1 L = density!

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Practice Examples (D=m/V)

Find the density of CO2 at STP

Find the density of CH4 at STP

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Another way: If given the density, we can find molar

mass of a gas. Again, “pretend” you have 1 mole at

STP, so V = 22.4 L.

D = m/V so… “m” = mass of 1 mole

m = D x V

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Using Density to Find Molar MassUsing Density to Find Molar Mass

What is the molar mass of a gas with a density of 1.964 g/L at STP?

How about a density of 2.86 g/L at STP?

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Summary

These four items are all equal

a) 1 mole

b) molar mass (in grams)

c) 6.02 x 1023 representative particles (atoms, molecules, or formula units)

d) 22.4 L of gas at STP

Thus, we can make conversion factors from these 4 values!

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Practice ProblemsPractice Problems

1. 1. What is the molar mass of each of the following compounds?What is the molar mass of each of the following compounds?

a. Ca. C66HH1212OO66 b. NaHCOb. NaHCO33 c. Cc. C77HH1212 d. KNHd. KNH44SOSO44

2. 2. Calculate the mass in grams of each of the following:Calculate the mass in grams of each of the following:

a. 8.0 mol lead oxide (PbO) a. 8.0 mol lead oxide (PbO)

b. 0.75 mol hydrogen sulfide (Hb. 0.75 mol hydrogen sulfide (H22S) S)

c. 1.50 x 10c. 1.50 x 10-2-2 mol oxygen (O mol oxygen (O22))

d. 2.30 mol ethylene glycol d. 2.30 mol ethylene glycol (C(C22HH66OO22))

3. 3. How many grams are in 1.73 mol of dinitrogen pentoxide (NHow many grams are in 1.73 mol of dinitrogen pentoxide (N22OO55)?)?

4. 4. How many grams are in 0.66 mol of calcium phosphate [CaHow many grams are in 0.66 mol of calcium phosphate [Ca33(PO(PO44))22]?]?

5. 5. Calculate the number of moles in each of the following:Calculate the number of moles in each of the following:

a. 0.50 g sodium bromide (NaBr) a. 0.50 g sodium bromide (NaBr)

b. 13.5 g magnesium nitrate [Mg(NOb. 13.5 g magnesium nitrate [Mg(NO33))22 ] ]

c. 0.0010 g chloromethane (CHc. 0.0010 g chloromethane (CH33Cl)Cl)

d. 1.02 g MgCld. 1.02 g MgCl22

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More Practice ProblemsMore Practice Problems

6. 6. A chemist plans to use 435.0 grams of ammonium nitrate A chemist plans to use 435.0 grams of ammonium nitrate (NH(NH44NONO33) in a reaction. How many moles of the compound is ) in a reaction. How many moles of the compound is

this?this?

7. 7. A solution is to be prepared in a laboratory. The solution A solution is to be prepared in a laboratory. The solution requires 0.0465 mol of quinine (Crequires 0.0465 mol of quinine (C2020HH2424NN22OO22). What mass, in ). What mass, in

grams, should the laboratory technician obtain in order to grams, should the laboratory technician obtain in order to make the solution?make the solution?

8. 8. What is the volume at STP of 2.66 mol of methane (CHWhat is the volume at STP of 2.66 mol of methane (CH44) gas?) gas?

9. 9. How many moles is 135 L of ammonia (NHHow many moles is 135 L of ammonia (NH33) gas at STP?) gas at STP?

10. 10. What is the density of carbon dioxide What is the density of carbon dioxide (CO(CO22) ) gas at STP?gas at STP?

11. 11. What is the molar mass of ethene What is the molar mass of ethene (C(C22HH44) if its density at STP ) if its density at STP

is 1.25 g/L?is 1.25 g/L?

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10.3: % Composition, Chemical Formulas

OBJECTIVES:

–Describe how to calculate the percent by mass of an element in a compound

–Interpret an empirical formula

–Distinguish between empirical and molecular formulas

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Calculating Percent Composition

Like all percent problems:

part

whole

1) Find the mass of each of the components (the elements),

2) Next, divide by the total mass of the compound; then x 100

x 100 % = percent

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Example Calculate the percent composition

of a compound that is made of 29.0 grams of Ag with 4.30 grams of S.

29.0 g Ag33.3 g total X 100 = 87.1 % Ag

4.30 g S33.3 g total

X 100 = 12.9 % S

Total = 100 %

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Using Formulae to Calculate % Mass

assume you have 1 mole of the compound…

If we know the formula we know the mass of the elements and the whole compound (from the periodic table!).

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Practice Problems Calculate the percent composition of

C2H4

Aluminum carbonate

Sample Problem 10.10, p.307 We can also use the percent composition

as a conversion factor (see p. 308)

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Read the Read the explanation at explanation at left.left.

Use that Use that information to information to help you help you complete the complete the practice problems practice problems below.below.

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Empirical and Molecular Formulas

• Example: molecular formula for benzene is Example: molecular formula for benzene is CC66HH66 (note that everything is divisible by 6) (note that everything is divisible by 6)

• Therefore, the empirical formula = Therefore, the empirical formula = CH (the (the lowest lowest wholewhole number ratio) number ratio)

Empirical formula: the lowest whole number ratio of atoms/ions in a compound

Molecular formula: the true number of atoms of each element in the molecules of a molecular compound.

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Formulas (continued)

Formulas for ionic compounds are ALWAYS empirical (the lowest whole number ratio = cannot be reduced).

Examples:

NaCl MgCl2 Al2(SO4)3 K2CO3

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Formulas (continued)

Formulas for molecular compounds MIGHT be empirical (lowest whole number ratio).

Molecular:

H2O

C6H12O6 C8H18

Empirical:

H2O

CH2O C4H9

Water

(Lowest whole number ratio)

Glucose Octane

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Determining Empirical Formulas Just find the lowest whole number ratio

C6H12O6

CH2Cl2 A formula is not just the ratio of atoms, it is

also the ratio of moles. In 1 mole of CO2 there is 1 mole of carbon

and 2 moles of oxygen. In one molecule of CO2 there is 1 atom of

C and 2 atoms of O.

= CH2O

= already the lowest ratio

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Calculating Empirical FormulasCan be calculated from the percent composition

because the sum of the parts always = 100%

1) Assume you have a 100 g sample

- the percentage become grams (75.1% = 75.1 grams)

2) Convert grams to moles.

3) Find lowest whole number ratio by dividing each number of moles by the smallest value.

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Example Calculate the empirical formula of a

compound composed of 38.67 % C, 16.22 % H, and 45.11 %N.

1) Assume 100 g sample, so 38.67 g C x 1mol C = 3.22 mole C

12.0 g C 16.22 g H x 1mol H = 16.22 mole H

1.0 g H 45.11 g N x 1mol N = 3.22 mole N

14.0 g N

2) Now divide each value by the smallest value

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Example

The ratio is 3.22 mol C = 1 mol C 3.22 mol N 1 mol N

The ratio is 16.22 mol H = 5 mol H 3.22 mol N 1 mol N

= C1H5N1 = CH5N

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Practice ProblemPractice Problem Caffeine is 49.48% C, 5.15% H, 28.87% N

and 16.49% O. What is its empirical formula?

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Empirical to Molecular Formula An empirical formula is the lowest ratio of atoms in

the compound, the actual molecule may have more atoms. By a whole number multiple.

For this type of problem, you are usually given the data to determine an empirical formula, then given a molar mass of the compound.

Divide the compound’s actual molar mass by the empirical formula mass yielding a whole number to increase each

coefficient in the empirical formula Caffeine has a molar mass of 194 g. what is its

molecular formula?

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Empirical to Molecular Formula Caffeine has a molar mass of 194 g. what is its molecular

formula? Recall the empirical formula for caffeine from the previous

example problem:

C4H5N2O

Find empirical formula mass

C = 4 x 12 g = 48 g/mol

H = 5 x 1 g/mol = 5 g/mol

N = 2 x 14 g/mol = 28 g/mol

O = 1 x 16 g/mol = 16 g/mol

Molar mass C4H5N2O = 97 g/mol

Molecular mass = 194 gEmpForm mass = 97 g

= 2

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Video Homework

Remember, every time you watch a video for chemistry, you are expected to take notes and complete all practice problems pointed out in the lecture.

You are also expected to THINK.

From now on, you are also expected to bring to class one intelligent question to ask me about the lecture.