Chapter 10

Chapter 10

Chemical Quantities

1

Measuring Matter

measure the amt of something by

• by count, • by mass, and • by volume.

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Measuring Matter (1)

• Atoms, molecules and formula units are extremely small.

• so many of them in even the smallest sample that it’s impossible to actually count.

• Counting unit: mole.

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mole (mol)

• SI base unit used to measure the amt (# of representative particles) of a sub.

Measuring Matter (2)

• 1 mole of C =

# C atoms in exactly 12 g pure C-12 =

6.02 x 1023 atoms of C

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Representative particles

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Representative particles Substance

atoms Elements, cpds

Molecules Covalent (molecular cpds)

Formula units Ionic cpds

Ions, e- Ionic cpds

1 mole of anything contains 6.02 x 1023 rep particles.

Measuring Matter (3)

atoms, molecules, formula units, e-, ions.

Avogadro’s #

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What is a Mole? (1)substance Representative

particlesChemical formula

# of representative particles in 1 mole

Atomic nitrogen

atoms N 6.02 x 1023 atoms

Nitrogen gas molecules N2 6.02 x 1023 molecules

Water molecules H2O 6.02 x 1023 molecules

Calcium ions ions Ca2+ 6.02 x 1023 ions

Calcium Fluoride

formula units CaF2 6.02 x 1023 formula units

Sucrose molecules C12H22O12 6.02 x 1023 molecules

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6.02 x 1023 -----Avogadro’s number (A)

Measuring Matter (4)

602,000,000,000,000,000,000,000

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Question 1

Calculate the # of molecules in 15.7 mol CO2.

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Answer

9.45 x 1024 molecular CO2

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Convert moles to # of atoms

Propane is a gas used for cooking and heating. How many atoms are in 2.12 mole of propane (C3H8).

Measuring Matter (6)

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The rep particle in H2O is water molecule.

The rep particle in Cu is Cu atom.

Measuring Matter

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Measuring Matter

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The rep particle in NaCl is NaCl formula unit.

• 1 mole contains 6.02 x 1023 rep particles.

Converting Moles to Particles

• write a conversion factor that relates rep particles to moles of a sub.

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Find how many particles of sucrose are in 3.50 moles of sucrose.

• There are 2.11 x 1024 molecules of sucrose in 3.50 moles.

Converting Moles to Particles

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Question 2

Calculate the # of moles in 9.22 x 1023 atom Fe.

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Answer

1.53 mol Fe

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Zn is used as a corrosion-resistant coating on iron and steel. It is also an essential trace element in your diet. Calculate the # mol that contain 4.50 x 1024 atoms Zn.

Converting Particles to Moles

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• Multiply the # Zn atoms by the conversion factor that is the inverse of Avogadro’s #.

Converting Particles to Moles

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The Mass of a Mole

molar mass

• mass in g of 1 mole of any pure sub (an element or a cpd)

• molar mass of any element = its atomic mass

• has the units g/mol.

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• molar mass of a cpd = sum of the # of g of each element in one mole of the cpd

• has the units g/mol

Converting Mass to Moles

• A roll of Cu wire has a mass of 848 g.

• How many moles Cu are in the roll?

• Use the atomic mass Cu given on the PT to apply a conversion factor to the mass given.

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Converting Moles to Mass

Calculate the mass of 0.625 moles of Ca.

• Use the molar mass Ca to apply a conversion factor to the # moles given.

• According to the PT, the atomic mass Ca is 40.078 amu.

• So the molar mass Ca is 40.078 g.

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Converting Moles to Mass

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Question 3

Calculate the mass of 6.89 mol Sb.

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Answer

839g Sb

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Question 4

A chemist needs 0.0700 mol Se for a rxn. What mass Se should the chemist use?

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Answer

5.53g Se

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Converting Mass to # of Particles

Calculate the # atoms in 4.77 g Pb.

• To find the # of atoms in the sample, you must first determine how many moles are in 4.77 g Pb.

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Converting Mass to # of Particles

According to data from the PT, the molar mass of Pb is 207.2 g/mol. Apply a conversion factor to convert mass to moles.

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Converting Mass to # of Particles

Now use a 2nd conversion factor to convert moles to # particles.

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Converting Mass to # of Particles

Convert from # particles to mass

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# moles = # particles divided by Avogadro’s #

Mass = # moles multiplied by molar mass

Moles of Cpds

• 1 mole is Avogadro’s # (6.02 x 1023) of particles of a sub.

• If the sub is a molecular cpd (e.g. ammonia (NH3), a mole is 6.02 x 1023 molecules of NH3.

• If the sub is an ionic cpd (e.g. baking soda-- NaHCO3), a mole is 6.02 x 1023 formula units of NaHCO3

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Moles of Cpds

1 mole of a cpd contains as many moles of each element as are indicated by the subscripts in the formula for the cpd.

• e.g. 1 mole NH3 consists of 1 mole N atoms and 3 moles H atoms.

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Molar Mass of a Cpd

• The molar mass of a cpd is the mass of 1 mole of the rep particles of the cpd.

• Because each rep particle is composed of 2 or more atoms, the molar mass of the cpd is found by adding the molar masses of all of the atoms in the rep particle.

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Molar Mass of a Cpd

molar mass NH3 = mass 1 mole N atoms + the mass 3 moles H atoms.

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Molar Mass of a Cpd

You can use the molar mass of a cpd to convert between mass and moles

Molar mass NH3 = molar mass N + 3 (molar mass H)

Molar mass NH3 = 14 g + 3(1g) = 17 g/mol

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Converting Mass of a Cpd to Moles

• The molar mass H2O as a conversion factor to determine moles H2O.

• Notice that 1.000 kg is converted to

1.000 x 103 g for the calculn.

molar mass H2O = 2(molar mass H) + molar mass O

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Converting Mass of a Cpd to Moles

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Molar Volume (1)

STP std temp (0°C or 273 K) and pressure

(1 atm pressure or 101.3kPa)

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Molar volume Volume of a mole of gas

Molar Volume (2)

At STP, volume of any gas is 22.4L

At STP, density of a gas

= molar mass divided by molar volume

= molar mass (g) divided by 22.4 L

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At STP, 1 mol of any gas occupies a vol of 22.4 L

Molar Volume (2)

What is the vol of 3.20 x 10-3 mol CO2 at STP?

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Molar Volume (3)

What is the vol of 3.70 mol N2 at STP?

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Molar Volume (4)

At STP, what volume do 1.25 mol He occupy?

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Molar Volume (5)

At STP, what vol. do 0.335 mol C2H6 occupy?

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Question 5

Calculate the # of moles in 17.2 g of benzene (C6H6).

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Answer

0.220 mol C6H6

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CST example 1

A 3.00 moles

B 6.00 moles

C 12.0 moles

D 16.0 moles

48

How many moles of CH4 are contained in 96.0 g of CH4?

CST example 2

A 0.5 moles

B 2.0 moles

C 3.01 x 1023 moles

D 6.02 x 1023 moles

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How many moles of C-12 are contained in exactly 6 g of C-12?

CST example 3

A 5.16 x 1030

B 3.01 x 1023

C 1.20 x 1024

D 1.10 x 1028

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How many atoms are contained in 97.6 g of platinum (Pt)?

CST example 4

A 1.5 x 1023

B 3.3 x 1023

C 1.9 x 1026

D 2.4 x 1024

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How many atoms are in a chromium sample with a mass of 13 g?

CST example 5

When methane (CH4) gas is burned in the presence of oxygen, the following chemical rxn occurs.

CH4 + 2O2 → CO2 + 2H2OIf 1 mole of methane reacts with 2 moles of oxygen, then

A 6.02x1023 molecules of CO2 and 6.02x1023 molecules

of H2O are produced.

B 1.2x1024 molecules of CO2 and 1.2x 1024 molecules

of H2O are produced.

C 6.02x1023 molecules of CO2 and 1.2x1024 molecules of

H2O are produced.

D 1.2x1024 molecules of CO2 and 6.02x1023 molecules of

H2O are produced.

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CST problem 6

How many moles of chlorine gas are contained in 9.02 x 1023 molecules?

A 1.5 moles

B 2.0 moles

C 6.02 moles

D 9.03 moles

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The Mass of a Mole of an Element

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The atomic mass of an element• expressed in g is the mass of a mole of the

element.

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

The Mass of a Mole of an Element

One molar mass of C, S, Hg, and Fe are shown.

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The Mass of a Mole of an Element

The Mass of a Mole of a Cpd

The Mass of a Mole of a Cpd

How is the mass of a mole of a cpd calculated?

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The Mass of a Mole of a Cpd

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To calculate the molar mass of a cpd, find the # of g of each element in 1 mole of the cpd. Then add the masses of the elements in the cpd.

The Mass of a Mole of a Cpd

Substitute the unit g for a.m.u. Thus 1 mol of SO3 has a mass of 80.1 g.

59

Quiz

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

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Quiz

3. The atomic mass of fluorine is 19.0 amu, so the molar mass is• 19.0 amu.• 19.0 g.• 6.02 x 1023 amu.• 6.02 x 1023 g.

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Quiz

4. Calculate the molar mass of ammonium nitrate.• 45.02 g• 80.05 g• 60.06 g• 48.05 g

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Converting Moles to Particles

• the rep particle is a molecule, • so the # of molecules of sucrose is obtained

by multiplying 3.50 moles of sucrose by the conv. factor, Avogadro’s #.

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Find the # of rep particles in a # of moles just as you found the # of roses in 3.5 dz.

Converting Particles to Moles

• Use the inverse of Avogadro’s # as a conversion. factor.

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Find out how many moles are represented by a certain # of rep particles

Mass of a Mole

• e.g. 12.011 amu for C, 1.008 amu for H, and 4.003 amu for He.

• These differences occur because the recorded values are weighted averages of the masses of all the naturally occurring isotopes of each element.

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atomic masses can be found on the PT, but the values shown are not integers.