The mole is a SI unit that chemists use to measure the amount of a substance: an element, a covalent compound or an ionic compound. This tutorial will teach you what a mole is and how to use it to determine the mass or the number of particles in a sample of matter.

The Number of Particles in a Mole

You know that the number of objects in a pair there are two, in a dozen there are twelve, and in a ream there are five hundred. In a mole there are six hundred and two sextillion. Written out longhand that is 602,000,000,000,000,000,000,000 - in scientific notation it's 6.02 x 10ee23. This is a huge number because the particles you are counting (atoms, ions, unit cells or molecules) are extremely small. So it takes lots and lots of them to make an amount you can see.

To give you an example of how many 602 sextillion (one mole) is lets imagine you have a mole of pennies to count. You employ everyone in the world (six billion people) to help you count. Everyone will count 24 hours a day, seven days a week. (I know this is impossible since people have to eat and sleep but lets say they can.)

Each person counts 1 penny per second - a total of six billion pennies is counted each second. Each hour they can count a total 21.6 trillion pennies. Each day you count over 500 trillion pennies. How long would it take to count 1 mole (602 sextillion) pennies? Over 3 million years! If you laid out a mole of pennies end to end they would extend to the moon and back 7 times.

A mole of aluminum cans would cover the earth's surface (land and oceans) over 200 miles deep. A mole of chocolate chips would cover the earth over 500 feet deep. And yet in only 18 milliliters of water there is a mole of water molecules.

The Mass of a Mole (Molar Mass)

You obviously cannot measure a mole of an element by counting atoms. The atoms are too small to be seen and you don't have several billion years to spend counting. So how do you measure out a mole of an element? By massing it out on a balance - that's how. To find the mass of a mole of an element you simply take its atomic mass and change the unit from AMU to grams. This mass is called the molar mass.

It's that simple. So a mole of hydrogen atoms (602 sextillion atoms) has a molar mass of 1.008 grams. A mole of carbon atoms has a molar mass of 12.011 grams. And a mole of gold atoms has a molar mass of 196.97 grams.

So the molar mass (the mass of 602 sextillion atoms) of an element is the atomic mass expressed in grams.

Now that you can calculate the molar mass of an element you can take it to the next step - the molar mass of a compound.

Time to Review: You now know that a mole is a certain quantity of matter. You can measure quantity in different ways. For example you can count out a certain quantity or you could mass out a certain quantity. The number of objects and their mass are different measurements. It is important that you keep these measurements of quantity separate.

Molar Mass of a Compound

There are two types of compounds - those made of atoms that share valence electrons (covalent) and those composed of ions that make up a crystalline lattice (ionic). Although they are different you calculate the molar mass of covalent and ionic compounds exactly the same way.

To calculate the mass of a compound simply:

1. Determine the correct formula of the compound.
2. Add the atomic weights of all the atoms or ions present and express this mass it in grams.

To calculate the molar mass of sodium chloride you would add the molar mass of sodium (22.990 grams) to the molar mass of chlorine (35.453 grams). Adding these two masses together gives you 58.443 grams - the molar mass of sodium chloride. To calculate the molar mass of water you would double the molar mass of hydrogen ( 2 x 1.008 grams) and add the molar mass of oxygen (15.999 grams). This would give you 18.015 grams - the molar mass of water.

Because you must add up the masses of all atoms in a covalent compound or ions in a unit cell (aka: formula unit) in an ionic compound, it is of up most importance that you have the correct formula when calculating the molar mass of a compound. If you write the formula incorrectly you will fail to correctly find the molar mass of that compound.

Mole Conversions Using Dimensional Analysis

Suppose you were given 25.00 grams of copper(II) nitrate and asked to determine how many unit cells of copper(II) nitrate were in this sample. How would you do it?

First you would calculate the correct formula for copper(II) nitrate. Since it is ionic you would have to crisscross the valences and encase the nitrate polyatomic ion in parenthesis.

You must now calculate the molar mass of copper(II) nitrate by adding the atomic masses of one copper ion and two nitrate ions (1 Cu + 2N + 6O). The molar mass of copper(II) nitrate is 187.56 grams.

*Important: You can see that we now have two masses: the given mass and molar mass. It is crucial that you understand that these terms and not mix them up. The given mass of a compound is how much you are given in the problem. In this case you have a given mass of 25.00 grams. The molar mass of a compound is the mass of one mole (602 sextillion particles ) of that compound. This remains constant for a given compound.

Dimensional analysis will now allow us convert our given mass (25.00 grams) to the number of unit cells. Here is an important fact to remember: You cannot directly convert a given mass to number of particles - you must first convert it to moles. This means that we must first convert our given mass to moles, then convert our moles to number of unit cells.

Think of it like this: To get from mass to particles or vice versa, you must go over the mole bridge.

You would begin by placing your given mass over one and multiplying it times a conversion factor with 1 mole on top (numerator) and the molar mass (187.56 grams) on the bottom (denominator). If you multiplied through you would have how many moles in your given mass. But you cannot stop there. You must continue by multiplying by another conversion factor in which 602 sextillion unit cells is in the numerator and 1 mole is the denominator. When you multiply and divide through you would find that in 25.00 grams of copper(II) nitrate there are 80.2 sextillion unit cells.

Converting Given Mass to Particles

Here is another problem: You are given 53.73 grams of aluminum and asked to calculate the number of atoms in it. Your first conversion factor would consist of 1 mole over 26.99 g (the molar mass of Al). You could then calculate that you have 1.9907 moles of Al. But you want the number of atoms in your sample so you continue with a second conversion factor consisting of 602 sextillion atoms over 1 mole. Multiply the numerators then divide by 26.99 and you have your answer: 1.198 x 10ee24 atoms. Here is the work:

Converting Particles to Given Mass

Now lets reverse the process. You are asked to calculate the mass of 2.34 x 10ee22 silicon dioxide molecules.
Now you are going from number of particles to moles to mass. Here is how it would look:

Note: 60.09 grams is the molar mass of SiO2

Converting Moles to either Given Mass and/or Particles

You are told you have 5.63 moles of zinc(II) nitrate and asked to calculate it's mass and the number of particles. First you need to write the formula (Zn(NO3)2), and calculate the molar mass ( 1x Zn + 2 x N + 6 x O = 189.400 grams).

Going from moles to grams would be one step:

To get from moles to unit cells, start over with 5.63 moles and convert to particles:

Remember:

1) The atomic mass of an element expressed in grams is the mass of one mole of that element (molar mass).
2) The molecular mass (covalent) or formula mass (ionic) of a compound expressed in grams is the mass of one mole of that compound (molar mass).
3) Problems you will encounter will deal with 3 values: given mass (how much you are given), moles and the number of particles (atoms, molecules or unit cells).
4) Remember that given mass is the mass of the compound that you are given (it can be any amount) - not to be confused with molar mass, which is the mass of one mole of the compound (a constant).
5) In every conversion factor 1 mole will always show up. If you begin your DA with something other than moles (given mass or particles then 1 mole will show up in the numerator of our conversion factor). If you begin your DA with moles then 1 mole will show up in the denominator of your conversion factor.
6) Once you figure out the molar mass, you are either given moles, number of particles, or given mass. Whatever you start with is placed over one when you begin your DA. The unit of that given belongs in the denominator of your first conversion factor
7) Remember: you begin at Moleland or go to Moleland. If you start with moles, 1 mole is in the denominator of your first conversion factor. If you begin with given mass or particles, 1 mole shows up in the numerator. Hey! I already stated that but because it is extremely important I listed it twice.
8) The unit for particles - element: atoms, covalent compound: molecules, ionic compounds: unit cells (aka formula units). Wrong unit = no credit.
|9) Use sig figs in your answers and show your DA work. 6.02 x 10ee23 has 3 sig figs.

When doing mole conversions, remember that 1 mole shows up in every conversion factor. The only other values that you will ever encounter in a mole conversion factor is the molar mass of the substance or 602 sextillion particles (atoms, molecules or unit cells).

If you keep these in mind as you do mole conversions it becomes quite simple!

Need more help with moles? Visit Keynotes and check out Mr. G's Keynote presentation on Moles in Chapter 7.

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