Chapter 3/9Chapter 3/9Chemical Reactions and Chemical Reactions and

QuantitiesQuantities

The MoleThe Mole

Calculations Using Molar MassCalculations Using Molar Mass

MOLE CONCEPTSo far we were in the microscopic world of atoms and molecules. But it is very important that chemists be able to measure and observe, in order to gather data.

To do this we must take sufficient quantities of atoms and molecules.

How many atoms or molecules must the chemists take?

Let us not bother about the numbers but instead call this amount a mole.

Oxygen was the best candidate to define a mole.

•The most universal atom at the time was oxygen.

•About 50% of the earth crust is oxygen.

•Oxygen can react with all the other atoms.

Let us weigh 32 grams of oxygen gas (O2) and define this amount of molecules as one mole of oxygen gas molecules.

If we react this amount with the following atoms and the weight of the products obtained were as given, how much will one mole of the atoms of Fe, H, and S weigh?

2 Fe + O2     2 FeO ; 144 grams FeO2 H2 + O2     2 H2O ; 36 grams H2OS + O2     SO2 ; 64 grams SO2

2Fe + O2     2 FeO ; (144 grams - 32grams) /2 = 56g (Fe)

2 H2 + O2     2 H2O ; (36 grams - 32 grams)/4 = 1g (H)

S + O2     SO2 ; (64 grams - 32 grams) = 32g (S)

So chemists agreed that the number of molecules in 32 grams of gaseous oxygen should be known as a mole of molecules.

By reacting other atoms with oxygen chemists were able to determine how much a mole of all other atoms weigh.

The purpose of the mole concept was to scale up the quantity of atoms and molecules so that we can conduct experiments.

It was only later that Amedeo Avogadro found that one mole of oxygen gas is compromised of 6.022x10²³ molecules, give and take a few molecules.

In his honor this number is known as Avogadro's Number.

So we often say that a mole of an element or compound contains Avogadro's number of particulars.

Q: How would you describe a stinky chemist?

A: Mole-odorous

Collection Terms

1 trio

1 six-pack Cola

1 dozen donuts

1 gross of pencils

= 3 singers

= 6 cans Cola drink

= 12 donuts

= 144 pencils

A Mole of Particles

Contains 6.02 x 1023 particles

1 mole C

1 mole H2O

1 mole NaCl

= 6.02 x 1023 C atoms

= 6.02 x 1023 H2O molecules

= 6.02 x 1023 Na+ ions and

6.02 x 1023 Cl– ions

Q: How does Avogadro write to his friends?

A: By e-mole!

More Examples of Moles

Moles of elements

1 mole Mg = 6.02 x 1023 Mg atoms

1 mole Au = 6.02 x 1023 Au atoms

Moles of compounds

1 mole NH3 = 6.02 x 1023 NH3 molecules

1 mole C9H8O4 = 6.02 x 1023 aspirin molecules

• If 6.02 x 1023 hydrogen atoms were laid side by side, the total length would encircle the earth about a million times.• The mass of 6.02 x 1023 Olympic shotput balls is about equal to the mass of the Earth.• The volume of 6.02 x 1023 softballs is about equal to the volume of the Earth.

Avogadro’s Number (N) = 6.02 x 1023

How big is this?

Learning Check M1

Suppose we invented a new collection unit called a mep. One mep contains 8 objects.

A. How many paper clips in 1 mep?

1) 1 2) 4 3) 8

B. How many oranges in 2.0 meps?

1) 4 2) 8 3) 16

C. How many meps contain 40 gummy bears?

1) 5 2) 10 3) 20

Solution M1

Suppose we invented a new collection unit called a mep. One mep contains 8 objects.

A. How many paper clips in 1 mep?

3) 8

B. How many oranges in 2.0 meps?

3) 16

C. How many meps contain 40 gummy bears?

1) 5

Q: How would you describe Avogadro's room while he was a teenager?

A: A Molar mess

How many particles are in 3.0 How many particles are in 3.0 moles of Al?moles of Al?

Using Avogadro’s Number in Calculations

Review Conversion FactorsReview Conversion Factors• Make a T-chart•Put whatever information the problem gave you in the top left•Put the units of whatever you were given in the bottom right of the T•Put the units of what you want to find in the top right.

3 moles=

particles

mole

Avogadro's Number

6.02 x 1023 particles

1 mole

or

1 mole

6.02 x 1023 particles

Each of these can be used as a conversion factor

=3 moles 6.02 x 1023 particles 1 mole

Ans: 1.81 x 1024 particles

Learning Check M2

1. Number of atoms in 0.500 mole of Al1) 500 Al atoms

2) 6.02 x 1023 Al atoms3) 3.01 x 1023 Al atoms

2.Number of moles of S in 1.8 x 1024 S atoms1) 1.0 mole S atoms2) 3.0 mole S atoms3) 1.1 x 1048 mole S atoms

Solution M2

1. Number of atoms in 0.500 mol of Al3) 3.01 x 1023 Al atoms

2. Number of moles of S if a sample of S contains 1.8 x 1024 S atoms2) 3.0 mole S atoms

23

Q: Why did Avogadro stop going to a chiropractor on October 24th?

A: He was only tense to the 23rd.

Rufus’ favorite food is rice. But he rarely eats it even though it is economical and easily prepared. He knows it is healthy for him and he was told once that one serving is 12,000 grains. So every time Rufus wants to eat rice he has to prepare 2 hr. ahead of time and count out 12,000 grains.

How can we help my friend Rufus?

A Rice Analogy

Weighing can be used as a way to count!

Rufus’ favorite food is rice. But he rarely eats it even though it is economical and easily prepared. He knows it is healthy for him and he was told once that one serving is 12,000 grains. So every time Rufus wants to eat rice he has to prepare 2 hr. ahead of time and count out 12,000 grains.

How can we help my friend Rufus?

A rice analogy

1 grain of rice weighs an average of 19 mg.

12000 grains 19 mg 1 g

1 grain 1000mg = 228 grams

How do we measure the mass of an object that is too small to be seen?

Atomic Mass Unit

The atomic mass unit (amu) has been used as a standard for a mass of an atom.

1 amu = 1.66 x 10-24 g = 1/12 mass of a 12C atom

1 proton = approx. 1 amu

• one atom of potassium 39K weighs 39 amu.• one atom of zinc 65Zn weighs 65 amu.

Atomic mass gives us the mass of one atom.

Molecular mass gives us the mass of one molecule (mC)

•one water (H2O) molecule = 18 amu (2-H, 1-O = 2amu + 16amu)

•one glucose (C6H12O6) molecule = 144 amu (6C, 12H, 6O = [6 C x12amu] + [12 H x 1 amu] + [6 O x 16amu]

Answer:

Atomic mass, as shown in the periodic table, is the weighted average mass of all isotopes found in nature.

Question:

Why is the mass of carbon 12.011 amu according the periodic table instead of just 12?

Why is the mass of chlorine 35.453 amu ?

Molar Mass

Number of grams in 1 mole of particles

Equal to the numerical value of the atomic mass

(from Periodic Table)

Review: Atomic MassThe mass of the atom in atomic mass units (amu)

What value for the atomic mass is given for carbon on the periodic table?

12.0 amu

What value for the atomic mass is given for magnesium on the periodic table?

24.3 amu

How much do 6.02 x 1023 carbon atoms weigh if one atom weighs 12.0 amu and 1 amu equals 1.66 x 10-24 g

= 12.0 grams6.02 x 1023 molecules 12.0 amu

1 molecule

1.66 x 10-24g

1 amu

1 mole of C atoms = 12.0 g1 mole of Mg atoms = 24.3 g1 mole of Cu atoms = 63.5 g

The MOLAR MASS is equal to the numerical

value of the atomic mass (from Periodic

Table)

1 mole of C atoms = 6.02 x 1023 atoms1 mole of Mg atoms = 6.02 x 1023 atoms1 mole of Cu atoms = 6.02 x 1023 atoms

Q: How did Avogadro get through the desert?

A: He rode on a camole

Learning Check M3

Give the molar mass to 0.1 g

A. 1 mole of Br atoms = ________

B. 1 mole of Sn atoms = ________

Solution M3

Give the molar mass to 0.1 g

A. 1 mole of Br atoms = 79.9 g

B. 1 mole of Sn atoms = 118.7 g

Molar Mass of Compounds

Mass in grams of 1 mole of a compound is equal numerically to the sum of the atomic masses of the atoms in the compound.

1 mole of CaCl2 = ? grams

1 mole Ca x 40.1 g/mole = 40.1 g

+ 2 moles Cl x 35.5 g/mole = 71.0 g

111.1 g = 1 mole CaCl2

1 mole of N2O4 = ? grams

2 moles N x 14.0 g/mole = 28.0 g + 4 moles O x 16.0 g/mole = 64.0 g

94.0 g = 1 moleN2O4

Learning Check M4

A. 1 mole of K2O = ______g

B. 1 mole of antacid Al(OH)3 = ______g

Solution M4

A. 1 mole of K2O

2 K x 39.1 g/mole = 78.2 g

+ 1 O x 16.0 g/mole = 16.0 g

94.2 g = 1 mole K2O

B. 1 mole of antacid Al(OH)3

1 Al x 27.0 g/mole = 27.0 g

+ 3 O x 16.0 g/mole = 48.0 g

+ 3 H x 1.0 g/mole = 3.0 g

78.0g = 1 mole Al(OH)3

Learning Check M5

Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake of

serotonin by the brain. It has a molar mass

of

1) 40.0 g/mole

2) 262 g/mole

3) 309 g/mole

Solution M5

Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake of

serotonin by the brain. It has a molar mass

of

3) 309 g/mole

17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0)

+ 1 O (16.0)

Molar Mass Factors for CH4

Molar mass of CH4 = 16.0 g

16.0 g CH4 and 1 mole CH4

1 mole CH4 16.0 g CH4

Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors.

Learning Check M7

Acetic acid CH3COOH is the acid in vinegar . It

has a molar mass of 60.0 g/mole.

1 mole of acetic acid = ____________

1 mole acetic acid or g acetic acid g acetic acid 1 mole acetic acid

Solution M7

Acetic acid CH3COOH is the acid in vinegar . It

has a molar mass of 60.0 g/mole.

1 mole of acetic acid = 60.0 g

1 mole acetic acid or 60.0 g acetic acid 60.0 g acetic acid 1 mole acetic acid

Calculations with Molar Mass

Moles

Number of grams

molar mass

Both Avogadro’s number and the molar mass can be used as conversion factors.

These two give us the ability to….

Let us look at both of these unit factors:

12.00 g Carbon-12 1 mole of Carbon-12 atoms

= 1

= 1 1 mole carbon-12 6.022 x 1023 atoms of carbon-12

Q: What does Avogadro put in his hot chocolate?

A: Marsh-mole-ows!

All About Mole Calculations

How many moles are in 22 grams of copper metal?

Step 1:Looking at the diagram above (your roadmap), we can see that we are going between grams and moles, which is a one-step conversion. Furthermore, we can see that we need to use the atomic mass of copper as our conversion factor.

The Four Steps to Solving Mole Problems:

Step 2: •Make a T-chart, and put whatever information the problem gave you in the top left. •Put the units of whatever you were given in the bottom right of the T•Put the units of what you want to find in the top right.

Step 3: Put the conversion factors into the T-chart in front of the units on the right. As we saw from the "map", the conversion factor between grams and moles is the atomic mass of copper. Because we measure atomic mass in grams, you need to put the atomic mass in front of the unit "grams of copper". What do you put in front of moles? Whenever you do a calculation of this kind, you need to put "1" in front of moles, like you see here:

Step 4: Cancel out the units from the top left and bottom right, then find the answer by multiplying all the stuff on the top together and dividing it by the stuff on the bottom. In this case, you'd multiply 22 by one and divide the result by 63.5. Your answer, 0.35 moles of copper:

            

                                                                                                         

And that's how you do a one-step problem of this And that's how you do a one-step problem of this kind!kind!

Moles and Grams

Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al?

3.00 moles Al ? g Al

Molar mass of Al

1 mole Al = 27.0 g Al

Setup

3.00 moles Al 27.0 g Al

1 mole Al

=

Answer = 81.0 g Al

Learning Check M9

The artificial sweetener aspartame

(Nutri-Sweet) formula C14H18N2O5 is

used to sweeten diet foods, coffee and

soft drinks. How many moles of

aspartame are present in 225 g of

aspartame?

Solution M9

2. Setup

225 g aspartame 1 mole aspartame

294 g aspartame

= 0.765 mole aspartame

1. Molar mass of Aspartame C14H18N2O5

(14 x 12.0) + (18 x 1.01) + (2 x 14.0) + (5 x 16.0) = 294 g/mole

Q: On which American mountain was Avogadro's face carved in stone?

A: Mount Rushmole