The Mole

The following provides an overview of moles and the skills necessary for performing mole

conversions

Definition of a Mole

A dozen is a number that has been given a name. The same can be said for a mole. The only difference is that the number defined as a mole is very, very, very, very, very, very, very ,very, very, very, very, very, very, very, very, very, very, big!!!

1 mole = 6.02 x 1023

(602,000,000,000,000,000,000,000) Avogadro’s Number

Is A Mole Really That Big?

If an atom were the size of a marble and one mole of marbles were spread over the surface of the Earth, our planet would be covered by a 50 mi-thick layer.

Is A Mole Really That Big?A new supercomputer can count all of the people in the United States in one-quarter of a second, but it would take almost two million years for it to count one mole of people at the same rate.

Is A Mole Really That Big?

If you made $40,000 (4,000,000 pennies) every second at your job that you had been working at since the formation of earth 4.5 billion years ago, you would not yet have earned Avogadro’s number of pennies.

So How is a Mole Helpful?

Scientists obviously can’t mass quantities of chemicals in amu because an amu is far too small. When scientists work with a substance like H2O, they can’t deal with single molecules – we can’t see or mass 2 atoms of hydrogen and one atom of oxygen. Scientists obviously have to work with much larger quantities. To solve this problem, scientists use the mole. To be useful the mole has to be somehow related to amu. Officially, the mole (symbol mol) is the SI term for the amount of substance containing as many elementary particles as there are atoms in 0.012 kg of carbon-12 (which is about 6.02 x 1023atoms)

Where do you find how much a mole of something

weighs?The atomic mass given on the periodic table is not only the mass of one atom of that element, but it is also the mass (in grams) of 1 mole of the atoms of that element. Therefore, since the mass of one carbon atom is 12 amu, the mass of one mole of Carbon atoms would be 12 grams. When dealing with a molecule or compound you simply calculate the molecular/formula mass using the periodic table, and this (like with atoms) is not only the mass of one molecule/compound, but it is also the mass (in grams) of 1 mole of the molecule/compound. Therefore, since the mass of one molecule of ozone (O3) is 48 amu, the mass of one mole of ozone molecules would be 48 grams.

How much does it weigh?

1 mole of Oxygen

1 mole of Sodium

2 moles of Carbon

3 moles of Hydrogen

1 mole of H2O

16 grams

23 grams

24 grams

3 grams

18 grams

You may want to use your periodic table!

Mole Map

Atoms, Molecules,Particles,

Etc.

Moles

Mass (Grams)

If you use the map, you won’t get lost!!!

Excuse me, how do I get

to Atoms?

Just start at grams, go straight

through moles and you will

get to atoms.

This map is to help you navigate mole problems

Sample One Step Problem

Calculate the mass of 7.5 moles of Carbon.

Use the “map” to help figure it out

Mass (Grams)

Moles Atoms,

Molecules,Particles,

Etc.

What is the starting point in this problem?

What is the final destination in this problem?

How many steps/fractions will it take you to get there?

Calculate the mass of 7.5 moles of Carbon.7.5 moles of C grams of C

AtomsMolesMass (Grams) AtomsMolesMass (Grams) AtomsMolesMass (Grams)

One Step Problem

(7.5 moles of C)

(1)

(____________)

( )mole of C

grams of C

1

12 = 90 grams of C

Explanation#1 –Since you have already found the starting point, final destination, and thenumber of steps it will take, you shouldnow write down a little reminder ofall of this information.

#2 –Place your starting point overone. In this case you will be placing 7.5 moles of carbon over one.

#3 –Multiply between fractions and make sure the bottom unit of the new fraction is the same as the top unit of the previous fraction. In this case the unit is “mole of carbon.”

#4 –Since you are aware that it isnecessary to travel to grams you can simply place that unit on the top of the fraction. To determine the mass of a mole of carbon you use the periodic table.In this case, one mole of carbon has a mass of 12 grams. You plug these numbers into the fraction, letting the units guide you. You have now transitioned from moles to grams.

#5 –Now that you have arrived at your final destination (grams) you can simply cancel all other diagonal units.

#6 –Finally, multiply across the top, multiply across the bottom, and divide theproduct of the top by the product of the bottom. This will give you the final answer, which in this case is 90 grams of C.

Use Periodic table Use 1 Mole = 6.02x1023

Sample Two Step Problem

How many atoms are in 45.8 grams of Na?

Use the “map” to help figure it out

Mass (Grams)

MolesAtoms,

Molecules,Particles,

Etc.

What is the starting point in this problem?

What is the final destination in this problem?

How many steps/fractions will it take you to get there?

How many atoms are in 45.8 grams of Na?45.8 grams atoms of Na

AtomsMolesMass (Grams) AtomsMolesMass (Grams) AtomsMolesMass (Grams)

Two Step Problem

(45.8 grams of Na)

(1)

(_____________)

( )grams of Na

mole of Na

23

1

= 1.20 x 1024 atoms of Na

Explanation#1 –Since you have already found the starting point, final destination, and thenumber of steps it will take, you shouldnow write down a little reminder ofall of this information.

#2 –Place your starting point overone. In this case you will be placing 45.8 grams of sodium over one.

#3 –Multiply between fractions and make sure the bottom unit of the new fraction is the same as the top unit of the previous fraction. In this case the unit is “grams of sodium.”

#4 –Since you are aware that it isnecessary to travel to atoms, according to the “Mole Map,” you must stop at moles first. Therefore you should place that unit on the top of the fraction. To determine the mass of a mole of sodium you use the periodic table. In this case, one mole of sodium has a mass of 23 grams. You plug these numbers into the fraction, letting the units guide you. You have now transitioned from grams to moles.

#5 –Now that you have arrived at moles it will be necessary to continue your travels to atoms since moles is not your final destination. Once again, you need to multiply between fractions and make sure the bottom unit of the new fraction is the same as the top unit of the previous fraction. In this case the unit is “mole of sodium.”

#8 –Finally, multiply across the top, multiply across the bottom, and divide theproduct of the top by the product of the bottom. This will give you the final answer, which in this case is 1.20x1024 atoms of sodium.

Use Periodic table Use 1 Mole = 6.02x1023

(________________)

( )mole of Na1

atoms of Na6.02x102

3

#6 –Since you are at moles, it is now possible for you to travel to atoms; therefore you should place that unit on the top of the fraction. To determine the number of atoms in a mole of sodium you simply use 1 mole = 6.02x1023. You plug these numbers into the fraction, letting the units guide you. You have now transitioned from moles to atoms.

#7 –Now that you have arrived at your final destination (atoms) you can simply cancel all other diagonal units.

Sample Problem That Requires Some Prep Work Before Converting

Calculate the mass of two moles of the compound Ca(NO3)2.

What is different about this problem when compared to the others?

Ca(NO3)2 - it is not an atom

You should calculate the molar mass using your periodic table prior to using your map and subsequently converting

Ca = 40g x 1 = 40 g/molN = 14g x 2 = 28 g/molO = 16g x 6 = 96 g/mol

1 mole of Ca(NO3)2 = 164 g

Now that you know the molar mass of Ca(NO3)2 you can use your map and convert

Sample Problem That Requires Some Prep Work Before Converting

Calculate the mass of two moles of the compound Ca(NO3)2.

Use the “map” to help figure it out

Mass (Grams)

Moles Atoms,

Molecules,Particles,

Etc.

What is the starting point in this problem?

What is the final destination in this problem?

How many steps/fractions will it take you to get there?

Calculate the mass of two moles of the compound Ca(NO3)2.

2 moles of Ca(NO3)2 grams of Ca(NO3)2

1 mole of Ca(NO3)2 = 164 g

Continuation of Problem After Prep Work is Complete

(2 moles of Ca(NO3)2)

(1)

(__________________)

( )mole of Ca(NO3)2

grams of Ca(NO3)2

1

164

= 328 grams of Ca(NO3)2

Explanation#1 –Since you have already done somepreliminary work and determined themass of a mole of Ca(NO3)2, found the starting point, final destination, and thenumber of steps it will take, you shouldnow write down a little reminder ofall of this information.

#2 –Place your starting point overone. In this case you will be placing 2 moles of Ca(NO3)2 over one.

#3 –Multiply between fractions and make sure the bottom unit of the new fraction is the same as the top unit of the previous fraction. In this case the unit is “mole of Ca(NO3)2.”

#4 –Since you are aware that it isnecessary to travel to grams you can simply place that unit on the top of the fraction. To determine the mass of a mole of Ca(NO3)2 you have already used your periodic table and you calculated a mass of 164 grams. You plug these numbers into the fraction, letting the units guide you. You have now transitioned from moles to grams.

#5 –Now that you have arrived at your final destination (grams) you can simply cancel all other diagonal units.

#6 –Finally, multiply across the top, multiply across the bottom, and divide theproduct of the top by the product of the bottom. This will give you the final answer, which in this case is 328 grams of Ca(NO3)2..

Use Periodic table Use 1 Mole = 6.02x1023

CompoundsMolesMass (Grams) CompoundsMolesMass (Grams) CompoundsMolesMass (Grams)