Ch. 10: Chemical Quantities

10.1 The mole: a measurement of matterAvogadro’s number, mass of a mole|

10.2 Mole-mass and mole-volume relationshipsSTP

10.3 Percent composition(skip empirical formulas)

10.1 The Mole: A Measurement of Matter

You could measure the amount of sand in a sand sculpture by counting each grain of sand, but it would be much easier to weigh the sand. You’ll discover how chemists measure the amount of a substance using a unit called a mole, which relates the number of particles to the mass.

10.1

Measuring MatterWhat are three methods for measuring the amount

of something?• You often measure the amount of something by one

of three different methods—by count, by mass, and by volume.

10.1

Sample problem 10.1

Use dimensional analysis:

apples 0.15

1

0.2

12

1

1

90kg

dozen

kg

apples

dozenapples

for Sample Problem 10.1#1 on worksheet

kg5dozen 1

kg 0.2

bushel 2.0

dozen 1bushel 5.0

What is a Mole?– One mole (mol) of a substance is 6.02 1023

representative particles of that substance and is the SI unit for measuring the amount of a substance.

– A mole of any substance contains Avogadro’s number of representative particles, or 6.02 1023 representative particles.

– The term representative particle refers to the species present in a substance: usually atoms, molecules, or formula units.

10.1

What is a Mole?10.1

Sample problem 10.2

Sample Problem 10.2#4 on worksheet

moles 360.0particles10x02.6

mole

1

particles10x17.223

23

On your calculator be sure to put the denominator in parentheses or divide by both 6.02 and 1023

Sample problem 10.3

10.3

Sample Problem 10.3#5 on worksheet

atoms2410x75.2molecule

atoms4mol

molecules2310x02.61mol14.1

The Mass of a Mole of an Element

– The atomic mass of an element expressed in grams is the mass of a mole of the element.

– The mass of a mole of an element is its molar mass.

– Ex. On the periodic table, carbon has a mass of 12.011 amu. We say 12 grams per mole or just 12 grams.

10.1

The Mass of a Mole of an ElementOne molar mass of carbon, sulfur, mercury, and iron are

shown.

10.1

The Mass of a Mole of an Element10.1

The Mass of a Mole of a Compound– To calculate the molar mass of a compound, find

the number of grams of each element in one mole of the compound. Then add the masses of the elements in the compound.

10.1

Substitute the unit grams for atomic mass units. Thus 1 mol of SO3 has a mass of 80.1 g.

The Mass of a Mole of a CompoundMolar Masses of Glucose, Water, and Paradichlorobenzene

10.1

Sample problem 10.4

Sample Problem 10.4#7 on worksheet

phosphorus molar mass = 30.974 gchlorine molar mass = 35.453 g

1 mole of phosphorus = 30.974 g3 mole of chlorine = 3 x 35.453 = 106.359 g

molar mass of PCl3 = 30.974 + 106.359 = 137 g/mol

10.1 Section Quiz.

1. Three common ways of measuring the amount of something are by count, by mass, and

a. by temperature.b. by volume.c. by area.d. by density.

10.1 Section Quiz.

2. A mole of hydrogen gas, H2(g), contains 6.02 x 1023 a. molecules.b. atoms.c. amu.d. grams.

10.1 Section Quiz.3. The atomic mass of fluorine is 19.0 amu, so the

molar mass isa. 19.0 amu.b. 19.0 g.c. 6.02 x 1023 amu.d. 6.02 x 1023 g.

10.1 Section Quiz.

4. Calculate the molar mass of ammonium nitrate.a. 45.02 gb. 80.05 gc. 60.06 gd. 48.05 g

NH4NO3

14+4(1)+14+3(16) g

10.2 Mole–Mass and Mole–Volume Relationships

How can you guess the number of jelly beans in a jar? You estimate the size of a jelly bean and then estimate the dimensions of the container to obtain its volume. In a similar way, chemists use the relationships between the mole and quantities such as mass, volume, and number of particles to solve chemistry problems.

10.2

The Mole–Mass Relationship– How do you convert the mass of a substance to

the number of moles of the substance?• Use the molar mass of an element or compound to

convert between the mass of a substance and the moles of a substance.

10.2

Sample problem 10.5

Sample Problem 10.5#9 on worksheet

mass of carbon= 20 x 12.011 = 240.22 gmass of hydrogen = 42 x 1.008 = 42.336 gmass of C20H42 = 282.556 g/mol

g28.1mol

g556.2821

mol310x52.4

Sample problem 10.6

Sample Problem 10.6#11 on worksheet

mol210x42.30342.0g81.10

mol1

g110x70.3

The Mole–Volume Relationship– Avogadro’s hypothesis states that equal volumes

of gases at the same temperature and pressure contain equal numbers of particles.

10.2

The volume of a gas varies with temperature and pressure. Because of these variations, the volume of a gas is usually measured at a standard temperature and pressure.

Standard temperature and pressure (STP) means a temperature of 0°C or 273 K and a pressure of 101.3 kPa (kilopascals) or 1 atmosphere (atm).

The Mole–Volume Relationship

– At STP, 1 mol or, 6.02 1023 representative particles, of any gas occupies a volume of 22.4 L.

– The quantity 22.4 L is called the molar volume of a gas.

10.2

10.7

10.7

Sample Problem 10.7#13 on worksheet

L210x17.70717.0mol

L4.221

mol310x20.3

L9.82mol

L4.221mol70.3

The Mole–Volume Relationship

– Calculating Molar Mass from Density

10.2

Sample problem 10.8

Sample Problem 10.8#15 on worksheet

mol/g2.80mol

L4.22L

g58.3

The Mole Road Map10.2

The Mole Road Map10.2

The Mole Road Map10.2

The Mole Road Map10.2

p. 303 in textbook

10.2 Section Quiz.

1. Calculate the mass in grams of a sample containing 1.85 x 1034 molecules of water.

a. 3.07 x 1010 gb. 5.53 x 1011 gc. 188 gd. 8.46 x 103 g

10.2 Section Quiz.

2. Calculate the number of moles in a spoonful of table sugar (C12H22O11) having a mass of 10.5 g.

a. 32.6 molb. 3.59 103 molc. 3.07 10–3 mold. 1.85 1022 mol

10.2 Section Quiz.

3. What is the volume of 0.35 mol of oxygen gas at STP?

a. 32 Lb. 64 Lc. 7.8 Ld. 16 L

10.3 Percent Composition and Chemical Formulas

It helps to know the percents of the components in a shirt because they affect how warm it is, whether it will need to be ironed, and how it should be cleaned. You will learn how the percents of the elements in a compound are important in chemistry.

10.3

The Percent Composition of a Compound

– Percent Composition from Mass Data• The relative amounts of the elements in a compound

are expressed as the percent composition or the percent by mass of each element in the compound.

The Percent Composition of a Compound• How do you calculate the percent by mass of

an element in a compound?– The percent by mass of an element in a compound is the

number of grams of the element divided by the mass in grams of the compound, multiplied by 100%.

10.3

Sample problem 10.9

Sample Problem 10.9#18 on worksheet

Hg%0.93100xHgO g2.14

Hg g2.13

7.00%Ox100HgO 14.2g

O 1.0g

The Percent Composition of a Compound

Percent Composition from the Chemical Formula

10.3

Sample Problem 10.10#20 on worksheet

nitrogen mass is 14.007 g/molhydrogen mass is 1.008 g/molNH3 mass is 14.007+3(1.008)=17.031 g/mol

N%2.82100xNH g031.17

N g007.14

3

b. NH4NO3

nitrogen mass = 14.007 x 2 = 28.014 ghydrogen mass = 1.008 x 4 = 4.032 goxygen mass = 16.000 x 3 = 48.000 gmass of NH4NO3 = 80.046 g

N%0.35100xNONH g046.80

N g014.28

34

The Percent Composition of a Compound• You can use percent composition to calculate the number of

grams of any element in a specific mass of a compound.

– Propane (C3H8) is 81.8% carbon and 18% hydrogen. You can calculate the mass of carbon and the mass of hydrogen in an 82.0 g sample of C3H8.

10.3

Empirical Formulas

• The empirical formula gives the lowest whole-number ratio of the atoms of the elements in a compound.– The empirical formula of a compound shows the

smallest whole-number ratio of the atoms in the compound.

10.3

Empirical Formulas

• Ethyne (C2H2) is a gas used in welder’s torches. Styrene (C8H8) is used in making polystyrene.

• These two compounds of carbon have the same empirical formula (CH) but different molecular formulas.

10.3

Molecular Formulas10.3

Methanal, ethanoic acid, and glucose all have the same empirical formula—CH2O.

1. Calculate the percent by mass of carbon in cadaverine, C5H14N2, a compound present in rotting meat. a. 67.4% Cb. 58.8% Cc. 51.7% Cd. 68.2% C

10.3 Section Quiz.

10.3 Section Quiz.

3. Determine the molecular formula of a compound that contains 40.0 percent C, 6.71 percent H, and 53.29 percent O and has a molar mass of 60.05 g.

a. C2H4O2

b. CH2O

c. C2H3O

d. C2H4O

Ch. 10—What you need to know• Ch. 10 worksheet problems—Converting using Avogadro’s number, molar mass, and molar

volume• Who is Counting? Lab• % Composition of a Penny Lab• Measure by count, mass, volume• Avogadro’s number, mole, representative particles• Atomic mass, molar mass, molar volume• Mole-mass, mole-volume relationships• STP (standard temperature and pressure; 0º C or 273 K and 101.3 kPa or 1 atm)• Pa is a unit of pressure--pascals• Mole—SI unit of measure for amount of a substance• Percent composition

• The majority of the quiz is calculations. Be able to show work using dimensional analysis (“railroad tracks”) and include units.