3.1 The Concept of Moles and the Formula Mass

What is the Mole?

Owing to their tiny size, atoms and molecules cannot be counted by direct observation. But much as we do when “counting” beans in a jar, we can estimate the number of particles in a sample of an element or compound if we have some idea of the volume occupied by each particle and the volume of the container.

Figure 3.1 Counting Jelly Beans

Once this has been done, we know the number of formula units (to use the most general term for any combination of atoms we wish to define) in any arbitrary weight of the substance. The number will of course depend both on the formula of the substance and on the weight of the sample. But if we consider a weight of substance that is the same as its formula (molecular) weight expressed in grams, we have only one number to know: Avogadro’s number, 6.022141527 × 10²³, usually designated by N_A.

The mole is defined as the mass of compound or element that contains the same number of fundamental units as there are atoms in 12.000 grams of ¹²C (Carbon – 12 isotope).

This means that the atomic mass or atomic weight (12 grams) of carbon is equal to exactly 1 mole of carbon.

The mole as word was introduced by the German Chemist Wilhelm Ostwald in 1894 as a German unit in chemistry called Mol which was rooted from the German Molekül (molecule).

Furthermore, one mole equals 6.022 X 10²³ particles. These particles can be atoms, molecules or formula units.

You should know it to three significant figures:
N_A = 6.02 × 10²³

6.02 × 10²³ of what? Well, of anything you like: apples, stars in the sky, burritos. But the only practical use for N_A is to have a more convenient way of expressing the huge numbers of the tiny particles such as atoms or molecules that we deal with in chemistry. Avogadro’s number is a collective number, just like a dozen.

Think of 6.02 × 10²³ as the “chemist’s dozen”.

Example:

Each carbon atom weighs about 1.99625 X 10 ^{– 23} g, hence”

 [1.99625 X 10 ^{– 23} g / atoms] X [6.02214179 X 10²³ atoms] = 12.0217 g of Carbon – 12 isotope.

The value of 6.022 X 10²³ is called Avogadro’s number.

Now we can define 1 mole of a matter is given in the table below:

Things to understand about Avogadro’s number N_A

• It is a number, just as is “dozen”, and thus is dimensionless.

• It is a huge number, far greater in magnitude than we can visualize; see here for some interesting comparisons with other huge numbers.

• Its practical use is limited to counting tiny things like atoms, molecules, “formula units”, electrons, or photons.

• The value of N_A can be known only to the precision that the number of atoms in a measurable weight of a substance can be estimated. Because large numbers of atoms cannot be counted directly, a variety of ingenious indirect measurements have been made involving such things as Brownian motion and X-ray scattering.

• The current value was determined by measuring the distances between the atoms of silicon in an ultrapure crystal of this element that was shaped into a perfect sphere. (The measurement was made by X-ray scattering.) When combined with the measured mass of this sphere, it yields Avogadro’s number. But there are two problems with this: 1) The silicon sphere is an artifact, rather than being something that occurs in nature, and thus may not be perfectly reproducible. 2) The standard of mass, the kilogram, is not precisely known, and its value appears to be changing. For these reasons, there are proposals to revise the definitions of both N_A and the kilogram. See here for more, and stay tuned!

History of the determination of Avogadro’s number

Wikipedia has a good discussion of Avogadro’s number

What is the Formula Mass?

The formula mass of a substance is the sum of the average weighed atomic masses of each atom present in the chemical formula and is expressed in atomic mass units (amu). The formula mass of a covalent compound is also called the molecular mass. The mass in grams of 1 mole of substance is its molar mass and it has the unit of (g/mol)

Examples are posted in table below:

The two videos explain the concept of the mole:

Now let us look into the conversion of moles into grams for elements and compounds or molecules and vice versa.

Molar Mass

The molar mass is the mass of one mole of a substance, reported in grams. The molar mass is numerically equal to the formula weight but the units are different (g/mol or amu).

Calculation of molar mass: use the average atomic mass from periodic table. For example: molar mass of carbon 12.01 g/mol, Hydrogen 1.008 g/mol.

Below is a picture of 1 mol of different element in grams.

Molar mass of a compound is determined using the formula. Individual molar mass of the elements in a compound is taken and multiplied by its coefficients and added all together.

Example: Determine the molar mass of Glucose: C₆H₁₂O₆

Molar mass     C → 6*12.01 = (72.06 g/mol )+

H →(12*1.008= (12.096 g/mol ) +

O→( 6* 16.00)= (96 .00g/mol )

_____________________________________________________

                                                180.16 g/mol  

Watch the following video:

Questions:

1. Determine the molar mass of Eu.

Ans: 1. 151.965 g/mol

2.18.02 g/mol

• 96.07 amu

Conversion of moles into grams for elements:

Example:

How many grams can be calculated in 10.5 moles of Helium?

First of all, we should look at the average weighed atomic mass of Helium from the periodic table which turns to be 4.003 amu (atomic mass units). This value has the same unit of gram / mole.

Grams of Helium = 10.5 moles X 4.003 grams / moles = 42.0315 grams of Helium = 42.0 grams of Helium

Conversion of moles into grams for compounds or molecules:

Example:

How many grams can be calculated for 20.25 moles of sodium chloride NaCl?

When dealing with compounds or molecules, one should start calculating the molar mass of the compound or molecule first:

Molar mass of NaCl = the sum of average weighed atomic masses of each atom involved in the compound or molecule:

Molar mass of NaCl = Na  +  Cl  = 23.0 g/mole    +   35.5 g/mole = 58.5 g/mole

Grams of NaCl = 20.25 moles NaCl  X  58.5 g/mole NaCl = 1184.625 g = 1.18 X 10³ g NaCl

Conversion of grams into moles for elements:

Example:

How many moles can be calculated for 42.0 grams of Helium?

Moles of Helium = 42.0 g He X [mole / 4.003 g He] = 10.5 moles He

Conversion of grams into moles for compounds or molecules:

Example:

How may moles can be calculated for 1.18 X 10³ grams NaCl?

Molar mass of NaCl = Na  +  Cl  = 23.0 g/mole    +   35.5 g/mole = 58.5 g/mole

Moles of NaCl = [1.18 X 10³ grams NaCl]  X  [ moles / 58.5g NaCl] = 20.2 moles NaCl

Conversion of number of atoms, molecules or ions (formula units) of a matter into number of grams of the matter and vice versa:

The general scheme is shown below:

Figure 3.2 Concept Map of mass to mols

Ref: Commons.wikimedia.org/

Reference: https://chem.libretexts.org/Courses/Howard_University/General_Chemistry%3A_An_Atoms_First_Approach/Unit_1%3A__Atomic_Structure/Chapter_1%3A_Introduction/Chapter_1.7%3A__The_Mole_and_Molar_Mass

Videos covering the conversion of atoms, molecules, ions (formula units into grams of matter and vice versa are given below:

Examples:

The following activity has been taken from American Association of Chemical teachers (AACT)

Calculating Moles in Daily Life

Background

Now that we have discussed Avogadro’s number and molar mass, we are going to use these quantities to do some analysis of common items in your life. We’re going to look at a nickel, water, chalk and sugar and determine the number of particles within a given sample.

Prelab Questions

1. Define Avogadro’s number:

2. Define molar mass:

Objective

In this activity you will make a series of mass measurements. You will then convert these measurements to moles and molecules.

Safety

• Always wear safety goggles when handling chemicals in the lab.
• Wash your hands thoroughly before leaving the lab.
• Follow the teacher’s instructions for cleanup of materials and disposal of chemicals.
• Do not consume lab solutions, even if they’re otherwise edible products.

Procedure & Data Collection

1. Make the following measurements and calculations:

Calculations

Use information that you have collected above to help complete the following calculations.

Please show your work with proper dimensional analysis and significant figures.

1. A nickel is composed of 25.0% nickel and 75.0% copper.

1. Calculate the mass of nickel in the coin.                   

2. Calculate the number of moles of nickel in the coin.

3. Calculate the number of atoms of nickel in the coin.  

4. Calculate the mass of copper in the coin.                  

5. Calculate the number of moles of copper in the coin.

6. Calculate the number of atoms of copper in the coin.

8. Water
   1.  Calculate the molar mass of water               

2. Calculate the number of moles of water swallowed

3. Calculate the number of molecules of water swallowed

11. Table sugar (sucrose, C₁₂H₂₂O₁₁)

7. Calculate the molar mass of sucrose             

8. Calculate the number of moles of sugar in the packet

9. Calculate the number of molecules of sugar in the packet

10. Calculate the number of atoms on carbon in the packet

16. Assume the chalk was 100% calcium carbonate.

11. Using what we learned about naming chemicals, write the formula for calcium carbonate

12. Calculate the molar mass of calcium carbonate

13. Calculate the number of moles of calcium carbonate used in a single signature

14. Calculate the number of oxygen atoms in your signature

Analysis

1. What is the difference between calculations made for the nickel and the other materials? (hint: consider the composition of each material)

2. What other household items do you think we could perform similar calculations with? Make several suggestions and explain if necessary.

3. What household item wouldn’t work for such simple calculations and why not?

4. Why might a person be interested in this type of calculation?

5. Write a brief summary of what you learned in this lab that includes how the objective was met.

Figure 3.3 Conversion of Mass to mols to atoms or molecules

Ref: Commons.wikimedia.org/

Example#1: How many mols are present in 24.02 g of Carbon?

Since it is grams to mol conversion, molar mass is the conversion factor.

According to Periodic table molar mass of C= 12.01 g/mol

24.02 g C * 1 mol C               = 2.00mols of C

12.01 g C

Example#2: How many mols are present in 54.1 g of Carbon?

Since it is grams to mols, molar mass is the conversion factor.

Molar mass of H₂O= 1.008 + 2* 16.00= 18.02 g/mol

54.1 g H₂O * 1mol H₂O                     =3.00 mols of H₂O
18.02 g H2O

Example #3: How many grams are in 3.57 mols of CO₂?

Since it is mols to grams, molar mass is the conversion factor.

Molar mass of CO₂= 12.01 + (4*16.00)= 44.01 g/mol

3.57 mols of CO₂ * 44.01 1g CO₂        = 157 g of CO₂

1 mol CO₂

Example#4 : How many atoms are present in 35.0 g of Cu?

We will use both conversion factor, molar mass and avogadro’s number to solve this problem.

Pathway:

35.0 g Cu *  1mol Cu       *  6.022 *10²³ atoms Cu      = 3.32 *10²³ atoms of Cu
                      63.5 g Cu           1 mol Cu

Practice Questions

• How many mols of H₂O are in 75.0 g of H₂O?

2. How many grams are in 3.46 mols of NaCl?

Ans: 1. 4.16 mols H₂O

2. 202.2g NaCl

3. 6.02 * 10²³

4. 53.9 g Ag

5. 6.10 *10¹⁸ molecules

More Practice: Calculate the mass of  each of the following item in grams.

CHECK WITH YOUR INSTRUCTOR FOR CORRECT ANSWER: